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Kinematics and dynamics of barred spiral galaxies

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Title:
Kinematics and dynamics of barred spiral galaxies
Creator:
England, Martin Nicholas, 1954-
Copyright Date:
1986
Language:
English

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Subjects / Keywords:
Ellipses ( jstor )
Galaxies ( jstor )
Galaxy rotation curves ( jstor )
Gas density ( jstor )
H I regions ( jstor )
Hydrogen ( jstor )
Milky Way Galaxy ( jstor )
Spiral arms ( jstor )
Velocity ( jstor )
Velocity distribution ( jstor )

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University of Florida
Holding Location:
University of Florida
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All applicable rights reserved by the source institution and holding location.
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AEQ2504 ( ltuf )
16656178 ( oclc )
0030321794 ( ALEPH )

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KINEMATICS AND DYNAMICS OF BARRED SPIRAL GALAXIES


BY


MARTIN NICHOLAS ENGLAND

























A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1986








"To the Reader Concerning the Hypothesis of this Work"


Andrew Osiander cl543 in

"De Revolutionibus Orbium Caelestium"

N. Copernicus





It is the job of the astronomer to use painstaking and

skilled observation in gathering together the history of the

celestial movements, and then, since he cannot by any line

of reasoning reach the true cause of these movements to

think up or construct whatever causes or hypotheses he

pleases such that, by the assumption of these causes, those

same movements can be calculated from the principles of

geometry for the past and for the future, too. And if

[mathematical astronomy] constructs and thinks up causes--

and it has certainly thought up a good many--nevertheless it

does not think them up in order to persuade anyone of their

truth but only in order that they may provide a correct

basis for calculation. And as far as hypotheses go, let no

one expect anything in the way of certainty from astronomy,

since astronomy can offer us nothing certain.












Plato: Timaeus





As being is to becoming, so is truth to belief. If

then, Socrates, amid the many opinions about the gods and

the generation of the universe, we are not able to give

notions which are altogether and in every respect exact and

consistent with one another, do not be surprised.














ACKNOWLEDGEMENTS


It is rather difficult to acknowledge all the people

who in one way or another have contributed to this document

without using the standard oft-repeated phrases so common in

these sections of dissertations.

Dr. Stephen Gottesman led me through the intricacies

of the VLA and extraglactic radio astronomy. This was no

trivial achievement as he was dealing with someone who was

initially a confirmed optical stellar spectroscopist. His

success in this can be measured by the results contained in

the next few hundred pages. Not only was he my dissertation

chairman but a person who was always willing to help in

other matters of general well-being, and above all, a

friend.

Dr. James Hunter, who continually challenged me with

his seemingly "straightforward" problems, acted as

cochairman for the dissertation. He is also responsible for

showing an observational astronomer that theoretical

astronomy is not the great insurmountable barrier that it

was first considered to be. He, probably more than anyone

else, taught me the virtue of sitting down with something,

as with his course work problems (generally unpleasant) and

pe rseve ring until it was done The s ati sfac ti on of

completing the problem was worth the effort.

iv








The rest of my committee, Drs. Thomas Carr, Haywood

Smith and Gary Ihas, performed their duties competently and

allowed me the fre edom, within guidelines, to do as I

pleased.

The 21cm observations utilized in this dissertation

were obtained at the Very Large Array of the National Radio

Astronomy Observatory. The National Radio Astronomy

Observatory is operated by Associated Universities, Inc.,

under contract with the National Science Foundation. My

thanks to all the staff, especially Drs. Jacqueline van

Gorkom and Patrick Palmer. They not only helped make a

competent spectral line observer out of me but introduced me

to the mountains of southwest New Mexico.

My thanks go also to Drs. Bruce and Debra Elmegreen who

made their surface photometry available and to Drs. C.

Telesco and I. Gatley who allowed me to use their 2.2um

data.

The diagrams and photographs were produced by Paul

Gombola and Hans Schrader.

Computing was done using the facilities of the

Astronomy Department and the Northeast Regional Data Center

(NERDC). I thank the numerous people who provided free

consultation in the hallways and helped with problems as

diverse as image processing and dissertation printing.

Thanks especially to Virginia Hetrick and Jim Parkes. This

dissertation was produced using UFTHESIS on NERDC.








Irma Smith typed the equations and the "fiddley bits",

and provided typing services throughout my stay in Florida.

Finally, my heartfelt thanks must go to my parents,

Michael and Maureen England, who supported and actively

e nc our aged their "professional student ." Wi thout their

support none of the next few hundred pages would have been

written. I hope that I can repay them someday for their

sacrifices and dedication.

My wife, Shei la, has been a veritable "Rock of

Gibraltar" and has put up with more and had less than any

wife and woman should reasonably be expected to endure. It

is all over now and it is to her and my parents that this

volume is dedicated.

















TABLE OF CONTENTS


PAGE


ACKNOWLEDGEMENTS ..

LIST OF TABLES ....

LIST OF FIGURES ....

ABSTRACT .......


.ix


. . . xiv


CHAPTER

I. INTRODUCTION.......


Selection Criteria... ....
Survey Galaxies.........
NGC 1073 . . .
NGC 1300 . . .
NGC 3359 . . .
NGC 3992 . . .

II. RADIO OBSERVATIONS ...........

HI As A Kinematic Tracer .....
Aperture Synthesis Theory .....
Observing Strategy and Calibration
Map-Making and Image Processing ..


. . 18


. .


III. DETERMINATION OF THE NEUTRAL HYDROGEN PROPERTIES

Spectrum Integration Techniques ......
Neutral Hydrogen Distribution .......
Continuum . . . . .
Kinematics of the Neutral Hydrogen ....
Mass Models . . . .

IV. SURFACE PHOTOMETRY ...............

Calculation of the Volume Mass Distribution
Surface Photometry of NGC 1300 ......
Modeling the I Passband Features ....
Comparisons Between Different Passbands
Triaxial Ellipsoid ...........


. 79

. 79
..86
.113
.115
.132

.140

.142
.146
.146
.165
.175


vii









































































viii


V. MODELING .


. . . 185


The Beam Scheme ..........
Hydrodynamical Modeling of NGC 1300


.185
.200
.200
.207
.210
.234


. .


. .


Triaxial Bar Models ....
Oval Distortion Models ...
Composite Models ......
Bulge Models ........


VI. RESULTS FROM OTHER GALAXIES ...


247


NGC 3359 . . .
Observational Results ..
Hydrodynamical Models ..
NGC 3992 . . .


.247
.247
.252
.255
.256
.261
.263
.264
.269


. .


. .
. .


Observational Results ...
Hydrodynamical Models ...
NGC 1073 . . .
Observational Results ...
Hydrodynamical Models ...


VII. PROPERTIES OF BARRED SPIRAL GALAXIES

Observational Comparisons ...
Dynamical Properties .....

VIII. SUMMARY .. . . .


272

272
275

282


Neutral Hydrogen Results for NGC 1300 .
Hydrodynamical Results ........
Dynamical Properties .........


. .283


APPENDIX


A. DERIVATION OF VOLUME BRIGHTNESS DISTRIBUTIONS

B. OVAL DISTORTIONS FOR N=1 TYPE TOOMRE DISKS .

BIBLIOGRAPHY . . . . .


287

291


.299


BIOGRAPHICAL SKETCH .


305















LIST OF TABLES


TABLE PAGE

1.1. Global Properties of Survey Galaxies .. .. .. 14

2.1. Properties of Survey Calibrators .. ..... 38

2.2. Image Signal and Noise Characteristics ...... 53

3.1. Signal Characteristics for Spectrum Integration 85

3.2. Summary of Neutral Hydrogen Observations for
NGC 1300 .. .. ..... .. 139

4.1. Bar Projection Parameters for NGC 1300 ... 183

6.1. Summary of Integrated Properties of NGC 3359 ..254

6.2. Summary of Integrated Properties of NGC 3992 262

6.3. Summary of Integrated Properties of NGC 1073 ..270

8.1. Summary of Results for NGC 1300 .. .. .. 284
















LIST OF FIGURES


FIGURE PAGE

1.1. Survey Galaxies .. .. .. .. ... .. .. 9

2.1. Spheroidal Convolving Function .,, 43

2.2. (u,v) Coverage .. .. .. ... .. .. .. 45

2.3. Spectral Line Channel Maps ., 55

2.4. Wide Field Map .,,, 76

2.5. Channel Zero ., ., 77

3.1. Neutral Hydrogen Distribution Contour Plot 88

3.2. Neutral Hydrogen Distribution with the Optical
Image .. .. .. .. ... .. ... 89

3.3. Neutral Hydrogen Distribution Gray Scale Image 91

3.4. Neutral Hydrogen Distribution False Color
Image .. ... .. .... .. .. 92

3.5. Logarithmic Fit to Spiral Arms ., ., 96

3.6. Deprojected Azimuthal Profiles ., ., 97

3.7. HII Regions in NGC 1300 ,, ., 98

3.8. Deprojected HI Surface Density 104

3.9. Profiles Through HI Surface Density
Distribution ... .. ... 107

3.10. Continuum Emission .. .. .. 114

3.11. Velocity Contours ... ... .. ... 116

3.12. False Color Representation of Velocities .. 117

3.13. Velocity Field Superimposed on Optical Object .119









3.14.

3.15.

3.16.

3.17.

3.18.

3.19.

4.1.

4.2.

4.3.

4.4.

4.5.

4.6.

4.7.

4.8.

4.9.

4.10.

4.11.

4.12.

4.13.

4.14.

4.15.

4.16.

4.17.

4.18.

4.19.

5.1.


Angle-Averaged Rotation Curve 125

Wedge Rotation Curve .. ......... 126

Optical and HI Rotation Curves .. .. 129

Rotation Curve to 6.4 arcmin ... 131

Mass Models for NGC 1300 .... 134

HI Observed Global Profile .. .. .. 138

NGC 1300 Gray Scale I Passband ... 147

Contour Plot of I Plate ... ... 148

Convolved I Passband Image NGC 1300 ......151

Bar Brightness Profiles ... ... 153

Disk Surface Brightness .. ..... 155

Bulge Component Model ... ......... 158

Bulge Subtracted Disk Profile .... 159

Bulge Subtracted Contour Plot . .. 160

I Band Model Isophotes .. .. .. 163

I Band Model Profiles .. .. .. .. 164


Gray Scale of Blue Passband .. 166

Contour Plot Blue Passband .... 167

Minor-axis Profiles Blue and I Passbands 169

Profile Comparison 171

Comparison of Blue and I Profiles .. 172

Contour Plot 2.2um ..... 176

False Color Plot 2.2um ... .... 177

Flux Profile 2.2um .. .. .. .. 179


Comparison Between Different Wavelengths 180

Dependence of Rotation Curve on Projection
Parameters .... ........ 198










5.2.


5.3.


5.4.


5.5.


5.6.


5.7.

5.8.


5.9.

5.10.

5.11.

5.12.

5.13.

5.14.

5.15.

5.16.

5.17.

5.18.

5.19.

5.20.

5.21.

5.22.


5.23.

6.1.

6.2.

6.3.


6.4.


Gas Response for Disk and Triaxial .


Velocity Field for Bar and Triaxial

Model Rotation Curve ........


Supermassive Bar Rotation Curve ..

Oval Distortion Model Gas Response .

Oval Distortion Model Velocity Field


Composite Model Gray Scale .....

Composite Model Contour Plot ....


Composite Model Velocity Field ...

Composite Model Rotation Curve ...

Slow Pattern Speed Model Gray Scale

Velocity Field Vectors .......

Velocity Field in Perturbation Frame

Noncircular Velocities .......


Gas Response for Bulge Model ....

Density Compared with Observations .


Bulge Model Velocity Field .....

Velocity Compared with Observations


Comparison of Rotation Curves ...

Velocity Vectors for Bulge Model ..

Velocity Field in Perturbation Frame

Noncircular Velocities .......

HI Distribution NGC 3359 ......


Velocity Field NGC 3359 ......

Rotation Curve NGC 3359 ......


HI Distribution NGC 3992 ......


. . 202


. .. .204


. . 205


. . 206

. . 211


. . 212


. . 215

. . 216

. . 217

. . 218

. . 225

. . 229

. . 230


. . 231

. . 236

. . 237

. . 238

. . 239

. . 241


. .. .242

. . 243

. . 244


. . 249

. . 250

. . 253


. . 257


6.5. Velocity Field NGC 3992


258


xii









6.6. Rotation Curve NGC 3992 .. .. ... .. 260

6.7. HI Distribution NGC 1073 .........265

6.8. Velocity Field NGC 1073 .. ... .. .. 266

6.9. Rotation Curve NGC 1073 ......... 268


xiii














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



KINEMATICS AND DYNAMICS OF BARRED SPIRAL GALAXIES


By


Martin Nicholas England


December 1986


Chairman: S. T. Gottesman
Cochairman: J. H. Hunter, Jr.
Major Department: Astronomy



The kinematics and dynamics of a group of barred spiral

galaxies are analysed. Hydrodynamical models using the

"beam scheme" are calculated and provide a set of dynamical

properties for barred spiral galaxies.

Neutral hydrogen radio observations of NGC 1300 show

the galaxy to be an excellent example of a grand design

spiral system. The HI gas is confined almost entirely to the

spiral arms with very little interarm gas. These HI arms

correlate very well with the position of the optical arms.

The HI arms can be traced through about 310 degrees in

azimuth. The central region, the region occupied by the bar,

is deficient in gas.


X1V








The velocity field shows that circular motion is the

dominant component but that large non-circular motions,

mainly in the arms, are present. The rotation curve rises

to a maximum of 185km/sec at r=2.5' and then remains

essentially flat out to about r=3.2'.

Near infrared surface photometry is used to calculate a

triaxial ellipsoidal figure for the bar. Blue and 2.2um

photometry is analysed and compared with the I band and 21cm

observations.

Hydrodynamical models for NGC 1300 are partially

successful in reproducing the obse rved mo rpho logy and

kinematics of NGC 1300. Various combinations of parameters

are investigated and a composite "best model" presented.

This model consists of an n=1 Toomre disk, a triaxial bar,

an l=2 oval distortion and a halo. The pattern speed of

19.3km/sec/kpc places corotation just outside the end of the

bar.

Hydrodynamical models for NGC 1073, NGC 3359 and NGC

3992 are examined and compared with that for NGC 1300. This

results in a set of dynamical properties for barred spiral

galaxies.














CHAPTER I
INTRODUCTION


Barred spiral galaxies present a very interesting but

very difficult problem for astronomers. De Vaucouleurs

(1963) in his sample of 994 spiral galaxies found that about

37% are pure barred galaxies, while another 28% are mixed

spirals. The remaining galaxies are pure spirals, and are

thus in the minority. Therefore, barred systems are common,

and a good understanding of the physical processes occurring

in them would give insight into the formation and

maintenance of the observed spiral structure.

Until recently the comparison of theoretical models and

observations of barred spiral galaxies has not been very

fruitful for a number of reasons. Hydrodynamical

calculations have indicated that the gas distribution and

kinematics in barred spiral galaxies are very sensitive

tracers of the underlying gravitational potential (Roberts,

Huntley and van Albada, 1979). This is due to the fact that

the gas may respond in a highly non-linear way to even small

deviations from axial symmetry (Sanders and Huntley, 1976).

Theory is capable of producing high resolution models of gas

kinematics and structure. However, the observations have

either not had sufficient spatial resolution for a good








comparison to be made, or their spatial coverage has been

poor. Traditionally, optical measurements of the kinematics

of spiral galaxies have provided high spatial resolution but

very poor spatial coverage as they have relied upon HII

regions. The distribution of these regions is patchy; Hodge

(1969) has distributions of HII regions in spiral galaxies.

These regions are not a good tracer of the kinematics of the

gas in barred spiral galaxies. These HII regions are mainly

in the inner regions and spiral arms. However, they would

provide an excellent complement for some other, more global,

gas tracer.

Neutral hydrogen is known to be distributed over large

regions in spiral galaxies and could provide the global

kinematic tracer needed to test the theoretical models

re sul t s. However, until recently, obse rvati ons of the

neutral hydrogen in barred spiral galaxies have been made

using single dish radio telescopes. These observations do

not have the required spatial resolution needed to compare

with the theories, and even have difficulty in isolating the

bar from the underlying disk. The National Radio Astronomy

Observatory Very Large Array (NRAO VLA) is a sensitive

instrument of high resolution, on the order of 20" for the

HI emission from barred spiral systems. The VLA is sensitive

enough that a complete two-dimensional map of the velocity

field can be completed in a reasonable amount of observing

time, even though there are no bright, nearby, easily-








observed large barred spirals. Thus, observations of the

gas kinematics and structure can now be made that can

confront theoretical models in a quantitative fashion.

High resolution mapping of the gas kinematics in barred

systems, combined with two-dimensional hydrodynamical

modeling, could address the following questions (Teuben et

al., 1986):

1. What is the radial mass di stribution in barred

systems?

2. Are principal resonances present in barred spiral

galaxies? Sanders and Huntley (1976) have shown that

the gas flow changes character at the resonances,

consistent with the dominant periodic orbits. Within

the inner Lindblad resonance, gas flow is on

elliptical streamlines oriented perpendicular to the

bar maj or- axi s. Determining the location of the

resonances, combined with the radial mass

di stribution, would allow an estimation of the

pattern speed of the bar.

3. What is the character of the gas motions? Elliptical

streaming is recogni zab le as a skewing of the

velocity contours along the major-axis (Bosma, 1981).

The degree of skewing is related to the bar strength

(Sanders and Tubbs, 1980).

4. What is the nature of the parallel, straight dust

l ane s in barred spiral galaxies of type SBb? In








hydrodynamical calculations, such structures arise

naturally as shocks. These dust lanes often lie along

the leading edge of the rotating bar, for example NGC

1300 and NGC 1365, and as yet there have been no

unambiguous, kinematic verifications that they are

actually associated with shocks. Ondrechen and van

der Hulst (1983) have shown that for NGC 1097 the

radio continuum emission is enhanced along the dust

lanes, which is to be expected from compression in

shock regions.

Asymmetries in the mass distribution, such as barlike

configurations or oval distortions, play an important role

in the dynamics of galaxies. Various numerical simulations

have indicated that barlike configurations are robust and

long- lived and may be a preferred configuration for

gravitationally interacting particles (Miller, 1971, 1976,

1978; Ostriker and Peebles, 1973; Hohl, 1978; Miller and

Smi th, 1979 ). Evidence, both theoretical (Sanders and

Huntley, 1976) and experimental (Sanders and Huntley, 1976;

Huntley, Sanders and Roberts, 1978; Sanders and Tubbs, 1980)

has been presented that supports the origin of spiral arms

as being the dynamical response of a gaseous disk to a

rotating stellar bar. On the other hand, it may be the case

that spiral arms could result from either the dynamical

response of the gas to a rotating barred-spiral potential

(Liebovitch, 1978; Roberts, Huntley and van Albada, 1979) or








from the effects of self-gravity in a bar-driven disk of gas

(Huntley, 1980). Evidence that the gas in barred galaxies

does "sense" the presence of a stellar bar is concluded from

a morphological study of barred systems (Kormendy, 1979).

Other observational features which may have significant

implications for the modeling process are

1. The sharp bending of the bar into spiral arms.

2. The presence of luminous, giant HII regions which

often distinguish the spiral arms from the bar in the

region where the arms break from the bar.

The basic aim of this study is to observe a variety of

barred spiral galaxies and to calculate theoretical models

for each galaxy, using some of the observational parameters

as input quantities for the modeling procedure. The VLA was

used to provide detailed, high resolution observations of

the properties of the atomic hydrogen in each of the

galaxies at the highest possible si gnal- to-no ise ratio.

These observations provide an estimate of the rotation curve

for each galaxy and allow the mapping of the galaxian

velocity field and neutral hydrogen gas distribution.

Observations in the near infrared region (1 =82501) are

reduced to provide data for an "observed" bar, after some

M/L assumptions. This bar is used as an input parameter for

the modeling procedure. Optical observations of the gas

kinematics, where available, are used to complement the

neutral hydrogen kinematical information.







The modeling procedure consists of a hydrodynamical

computer code, the "beam scheme" of Sanders and Prendergast

(1974), kindly provided by Dr. J. M. Hunt ley. This code

calculates the response of a gaseous disk to an imposed

perturbati on, for ex amp le a bar figure or an oval

distortion. The results from these models are compared with

the observations of the kinematics and distribution of the

neutral hydrogen gas.



Selection Criteria

The sample of barred spiral galaxies used for this

study was selected using several criteria;

1. The galaxy should be large, with an optical diameter

of at least 5'.

2. The bar should be prominent and large in comparison

with the 15"-30" beam synthesized at the VLA.

3. The HI surface brightness should be reasonably high

to allow observations with good signal-to-noise

ratio.

4. The object should not be too far south.

5. The system should be symmetrical.

6.The inclination of the disk of the galaxy, with

respect to the sky plane, should not be too high.

7. Surface photometry, especially in the near infrared,

I passband (A =82501) should be available.








8. A variety of types of barred spiral galaxy should be

obtained.

The first four criteria are used to ensure that the

observations are feasible in a reasonable amount of

observing time, and that the signal-to-noise ratio is

optimal. The size of the object and the bar allow good, high

resolution observations to be made and the declination

requirement is imposed to obtain as circular a synthesized

beam as possible. Criterion 5 is used to facilitate the

modeling procedure. If the galaxies are not symmetric-al, the

complexity of the modeling procedure is increased greatly.

Criterion 6 avoids the problems associated with observing a

galaxy with a line-of- sight through a di sk of finite

thickness. The availability of surface photometry,

especially near infrared (Criterion 7) allows an approximate

determination of the underlying distribution of non-gaseous

lumi nou s matter (stars) in the gal axy Near infrared

photometry gives valuable information on the distribution of

the bar mass as it can penetrate, to some extent, the dust

lanes. This in turn provides constraints on the non-

axisymmetric bar component of the gravitational potential

which is required as input data for the modeling procedure.

Lastly, a variety of galaxies is needed, spanning a range of

galaxy types. This will allow some general conclusions to be

drawn about barred spiral galaxies as a class of object.








The galaxies NCC 1073, NGC 1300, NGC 3359, NGC 3992

satisfy most of the selection criteria.



Survey Galaxies

The four galaxies used in this study are shown in

Figure 1-1 (a-d). These photographs are taken from various

sources. Other photographs of these galaxies which may be of

interest are near infrared exposures in Elmegreen (1981),

yellow and hydrogen alpha images in Hodge (1969), and for

NGC 1073, NGC 1300 and NGC 3359 blue exposures from the

Palomar 200" in Sandage (1961). Table 1-1 lists some global

properties of these galaxies compiled from a variety of

sources. No independent effort has been made to verify

these parameters. As can be seen from Figure 1-1 these

galaxies all have rather different morphologies and each

should present different problems for the modeling

procedure. Thu s, a wide range of morphological types is

represented by this sample and should allow some general

conclusions to be drawn.



NGC 1073

This galaxy, shown in Figure 1-1 (a), is classified as

an SBT5 by de Vaucouleurs, de Vaucouleurs and Corwin (1976)

and as an SBc(sr) by Sandage (1961). The two prominent

spiral arms do not begin at the ends of the bar, but at 300

from the ends. The bar has a bright, central, elliptical




















Figure 1-1. Survey Galaxies. Optical photographs
of the four galaxies used in this survey.

A. NGC 1073 (Arp and Sulentic, 1979).
B. NGC 1300 (National Geographic--Palomar Sky Survey).
C. NGC 3359 (N~ational Geographic--Palomar Sky Survey).
D. NGC 3992 (National Geographic--Palomar Sky Survey).

In all photographs north is to the top and east is
to the left except for NGC 3359 where north is to the top
and west is to the left.














N










6

4;







: .- ..



E .

":C2






'*
rti


ir
re Irs
I~." '?''.*r~5~3




"rIt I


Figure 1-1 cont.


(Part A).





Figure 1-1 cont.


(Part B3).





















'


~ W
ei









a le





























Figure 1-1 cont. (Part C).








*
*











.~ *










,* *


Figure 1-1 cont.


(Part D).













Parameter NGC 1300 NGC 1073


Right Ascensiorit 3 17 25.2 2 41 09.0

Dec linatiord -19 35 29.0 1 09 54.0

Morphological TypdP SBT4 SBT5

Distance (Mpc)c 17.1 1.

Photometric Diameter D25 (arcmin) 6.5 4.9
Photometric Diameter (kpc) 32.3 19.4

Dimensions of Optical Bar (arcmin) 2.3x0.5 1.2x0.2

Corrected Blue Luminosityd~(1101 Lo) 2.39 0.93

Corrected Blue Magnitude 10.7 11.2


Parameter NGC 3359 NGC 3992


Right Ascensiod*~ 10 43 20.7 11 55 01.0

DeclinatiorP 63 29 12.0 53 39 13.0

Morphological Typeb SBT5 SBT4

Distance (Mpc)c 11.0 14.2

Photometric Diamete D25(aramin) 6.3 7.6
Photometric Diameter (kpc) 20.2 31.4

Dimensions of Optical Bar (arcmin) 1.7xO.6 1.7x0.5

Corrected Blue Luminosityd(1010 Lo) 1.08 2.40

Corrected Blue Magnitude 10.6 10.22

a Gallouet, Heidmann and Dampierre (1973).
b De Vaucouleurs, de Vaucouleurs and Corwin (1976).
c De Vaucouleurs and Peters (1981).
d Calculated using above values of distance and magnitude,
and using I(o)=+5.48 (Allen, 1973).


TABLE 1.1

Global Properties of Survey Galaxies





15

region, decreasing in brightness noticeably before meeting

the arms. The ring is not complete and there are no straight

absorption lanes. Both the arms and the bar can be resolved

into many knots. The west arm appears to bifurcate at about

the end of the bar. Arp and Sulentic (1979) identified three

quasars in the field of NGC 1073, namely objects 1,2 and 3

in Figure 1-1 (a).



NGC 1300

NGC 1300, Figure 1-1 (b), is described by Sandage

(1961) as the prototype of the pure SBb(s) system. It is

classified as an SBT4 by de Vaucouleurs, de Vaucouleurs and

Corwin (19'76). The bar is very prominent, di stinct and

smooth in texture, with two straight dust lanes emerging at

an angle from the nucleus and following the bar to its ends

and turning sharply and following the inside of the spiral

arms. The two arms start abruptly at the ends of the bar

each forming almost complete ellipses with the nucleus and

the other end of the bar being the approximate faci. They

can be traced through almost 3400



NGC 3359

Thi s galaxy, Figure 1-1 (c), described by Sandage

(1961) as being a broken ring galaxy, is classified an

SBc(rs), and as an SBT5 by de Vaucouleurs, de Vaucouleurs

and Corwin (1976). A fairly prominent two-armed pattern








emerges from a strong central bar. The arms are asymmetric,

with the arm beginning at the southern end of the bar being

far less structured than the other. This arm appears to

break up into two or more segments whereas the other arm

more closely follows a "grand design" spiral pattern. There

is a high degree of resolution of both bar and arms into

knots.



NGC 3992

Significant spiral structure (two bifurcated arms or

possibly even a three-arm patte rn ) eme rge s from an

incomplete ring surrounding the bar in NGC 3992 (Figure 1-1

(d)). De Vaucouleurs, de Vaucouleurs and Corwin (1976)

classify this galaxy as an SBT4. Two absorption lanes are

visible emerging from a bright, central nuclear region. The

bar is smooth in texture but the arms can be resolved easily

into knots.

This dissertation will describe in detail, the

obse rvati ons reduction and analysis, and hydrodynamical

modeling of NGC 1300. Data for NGC 1073, NGC 3359 (Ball,

1984, 1986) and NGC 3992 (Hunter et al., 1986) are published

elsewhere and only the conclusions are utilized here. The

neutral hydrogen data collection, reduction and analysis are

described in Chapters 2 and 3. Surface photometry in the

blue, near infrared and 2.2um passbands is discussed in

Chapter 4, with the results from Chapters 3 and 4 being used






17

in the hydrodynamical mode ling in Chapter 5. The

observational and modeling results for NGC 1073, NGC 3359

and NGC 3992 are summarized in Chapter 6 and comparisons

between these galaxies are made in Chapter 7. A summary of

all the results is presented in Chapter 8.















CHAPTER II
RADIO OBSERVATIONS



HI As A Kinematic Tracer

To successfully model and understand the dynamics of a

barred spiral galaxy, some sort of tracer of the dynamics of

the system is needed. Any tracer which is closely associated

with the gas may be used. Several components are available

for use as this tracer. Observations of the optical Hydrogen

alpha line provide velocities for HII regions, which are

associated with hot young stars which have recently formed

from the gas. Observations of the other Population I

component, molecular gas clouds, also could provide the

kinematical information needed. However, both these

measurements have serious drawbacks. The HII observations

have high spatial resolution but generally very incomplete

coverage. This is due to the clumpiness of these regions

which means that only velocities near the hottest stars can

be measured. Molecular hydrogen, which presumably makes up a

significant portion of the molecular clouds, is difficult to

detect. Carbon monoxide, CO, the second most abundant

interstellar molecule, coexists with molecular hydrogen and

can be used to map the molecular regions in galaxies and

elucidate the varying rates of star formation (Black, 1985;






19

Dalgano, 1985). CO is usually far more concentrated in the

inner disk (Morris and Rickard, 1982), although it does

appear to follow the intensity distribution of the blue

light (Young et al., 1984; Young, 1985). The CO transitions

are fairly easy to excite and lie in the milIlimeter

wavelength region.

A dominant component of the gas of the interstellar

medium consists of neutral hydrogen, HI, in its ground

state. It is well-distributed spatially and is relatively

easy to detect. This gas has a spin temperature, T'S, of

approximately 100K (Mihalas and Binney, 1981 p485). The

ground state is split into two hyperfine levels separated by

6x176 eV. This energy difference is extremely small; it

corresponds to a temperature T=0.07K (through E=ktT), well

below the ambient temperature of the surrounding medium,

and, consequently, much of the gas is in the upper level.

The upper level, or ortho-state, has the dipole moments of

the electron and nucleus parallel and the lower level, the

para- state has the dipole moments anti-parallel. The

probability of the forbidden ortho-para radiative

transition, the F=1 to F=0 spin-flip transition, is so low

that the mean lifetime of the excited level is 1.1x107yrs.

In contrast, the collisional de-excitation timescale is much

shorter, 400yrs at N =20atoms/cm3, than the radiative de-

excitation timescale, even in the low densities typical of

the interstellar medium. This implies that collisions can






20

establish equilibrium populations in the two levels, which

means that there will be nearly three atoms in the upper

level (which is threefold degenerate) to every one in the

lower level.

Because the collisional excitation and de-excitation

rates are so much faster than the rate of radiative decay,

the atomic populations n1 and n2 in the two levels will be
essentially the same as those expected in thermodynamic

equilibrium. Thus,

n2/n1 (2 91) exp (-hv/kTS) (2-1)

where g2 l1=3 is the ratio of the degeneracies of the two

levels. In a typical cloud TS=100K, so (h v/kTS =6. 8x10- and
exp (-h v/kTSWO.9993, giving,


n2/n1 ~ 2 1 = 3* (2-2)

In terms of probability coefficients,

nlC12 = n2(C21+A21) = n2C21(1+A21/C21) (2-3)

where Cl2 and C21 are collisional probabilities and A21 is
the Einstein probability coefficient for spontaneous

radiative decay from level 2 to level 1. As A21 is small,

nlC12 = n2C21 (2-4)

and approximate equilibrium is established. Although A21 is
small ~2.868x10-15 sec-1, radiative decay is the observable

transition mechanism. The large column densities along a

typical line-o f- sight in a galaxy make thi s radi ative





21

transition detectable. This transition is observable at a

frequency of 1420.40575MHz (ho=21.105cm). Its observation

was predicted by van de Hulst (1945) and first measured by

Ewen and Purcell (1951). Muller and Oort (1951) and

Christiansen and Hindman (1952) confirmed the measurement.

Neutral hydrogen generally covers a region larger than

the observed optical object and thus provides good coverage

of the whole disk of the galaxy and not just selected

regions, as do Hydrogen alpha observations. If the outermost

regions are excluded, then HI is among the flattest and

thinnest of the disk components of ours and other galaxies

(Jackson and Kellerman, 1974). This allows the

determination, with a reasonable degree of confidence, of the

two-dimensional location of any observed emission. This gas

is pervasive enough that the emission recorded by radio

telescopes appears to be continuously distributed.

If the neutral hydrogen gas is assumed to be optically

thin, a simple integration of the brightness temperature,

TB' over velocity, V, determines the column density, Nh, of
the gas at that point (Mihalas and Binney, 1981 p489):


Nhx~) 1826 118 B(xy) dV, (2-5)



where V is in km/s, T is in Kelvin~and, Nh in atoms/cm2

The mean temperature-weighted velocity at a point is

given by the first moment with respect to velocity,










= B(x'y) V(x,y)dv
-m (2-6)

TB(x,y) dV






If the neutral hydrogen gas is not optically thin this

will lead to an underestimate of the surface density. In

this case the observed brightness temperature, Tf'B would

approach the physical, spin temperature of the gas, TS.
In general,

TB (-e) (2-7)


and, for an optically thin gas, t<<1, TB:6b, while for an

optically thick gas, TB=S(iaa n iny 1981 p487).

The highest observed brightness temperature for NGC

1300, averaged over the beam, was 16.95K. Assuming a mean

temperature for the gas of 100K (McKee and Ostriker, 1977;

Spitzer, 1978) gives an approximate optical depth of t=0.19,

thereby justifying the optically thin assumption. Although

this leads to an underestimate of the column density the

effect is <15% at the peak emission and will be less at

other points. As the "optical depth structure" of the medium

is not known, the assumption of an optically thin medium

will be retained.








Thus, in summary, neutral hydrogen provides a good

tracer for the kinematics of the gas in a galaxy;

1. It is well distributed spatially.

2. It is relatively easy to observe.

3. As sumi ng it is optically thin, the above simple

expressions hold for the column density of the gas

and the mean velocity of the gas at an observed

location, equations 2-5 and 2-6.



Aperture Synthesis Theory

The neutral hydrogen content of NGC 1300 was observed

using the Very Large Array (VLA) of the National Radio

Astronomy Observatory (NRAO). The VLA is the largest and

most sensitive radio telescope which exploits the principle

of earth- rotati on ape rture synthe si s. The array is a

multiple-interferometer instrument using a' maximum of 27

antennae. As the basic theory of interferometry and earth-

rotation aperture synthesis is well covered in Fomalont and

Wright (1974), Hjellming and Basart (1982), Thompson (1985),

D' Addario (1985), Clark (1985) and, from an electrical

engineer's perspective in Swenson and Mathur (1968), only a

brief discussion will be given here and some fundamental

results quoted.

The basic process of interferometry is the cross-

correlation of signals from two antennae observing the same

source. The resulting signal is analogous to the





24

interference pattern in the classical optical double slit

experiment. The cross-correlation of these two signals

produces information on both the intensities of sources in

the beam of the antennae and on their positions relative to

the pointing position of the antennae. Any distribution of

radio emission in the beam of an antenna can be considered

as a superposition of a large number of components of

different sizes, loc nations and orientations. As the

relationship between intensity distributions and the

components can be described in terms of a Fourier integral,

it follows that an interferometer pair, at any instant,

measures a single Fourier component of the angular

distribution of sources in the beam pattern. The essential

goal in radio aperture synthesis observations is to measure

a large number of these Fourier components. This procedure

allows the reconstruction of an image of the spatial

intensity distribution of sources in the beam. The VLA

achi eve s the measurement of a large number of Fourier

c omponent s by using multiple interferometer pairs and

allowing their geometric relationships with the sources in

the sky to change by utilizing the rotation of the earth,

hence the term earth- rotati on aperture synthes i s. For

multiple interferometer pairs, N antennae, there are

N (N- 1 )/2 different baselines, or s amp le s of the Fourier

components, at any one instant. The VLA has a maximum of 27

antennae or 351 samples of the Fourier components. These








samples are not all unique as there is redundancy in the

baselines.

The output from a two element interferometer can be

shown to be


V'(u,v) = I(x,y) exp[-i2n(ux+vy)]dx dy (2-8)


where I' (x,y) is the observed brightness distribution,

V' (u,v) is the observed complex visibility, and u,v are

projected spacings in east and north directions

re spec ti vel1y sometimes called spatial f requ enc ie s

(Hjellming and Basart, 1982).

Thi s shows that a single measurement of the complex

vi sibili ty, y*I, corre spending to a particular projected

baseline, or particular (u,v) point, gives a single Fourier

component of I', the observed brightness distribution. The

similarity theorem of Fourier transforms (Bracewell, 1965)

shows that large extent in the (x,y) plane means small

extent in the (u,v) plane and vice versa. Thus, achievement

of high spatial resolution requires large spacings between

the antennae in an interferometer pair, and conversely,

large scale structure requires low spatial fr equenci es,

short spacings.

Equation 2-8 can be inverted to give the observed

brightness distribution I' as a function of the measured

complex visibilities, V' ,









I'(x,y) =lv V'(uv expl i~nuxivy)]du dv (2-9)



where I' is the product of the true brightness distribution

Io and the single antenna power pattern A,


I'(x,y) = A(x,y) I (x,y) (2-10)

These results have been calculated in the absence of

noise. Since all observations measure only a finite number

of (u,v) points and all contain noi se I' c anno t be

determined uniquely or without error. A later section deals

with the problem of missing complex visibilities and the

non-uniqueness of the solution of equation 2-9.

The extension of these results to spectral line

observations introduces several complications. The signal

has to be divided into a number of independent, narrow-band

spectral channels At the VLA thi s is achi eved by

introducing an additional delay, t., into the signal path.
This delay destroys the coherence of the received signals

except for those in a narrow frequency range centered on

some frequency v .. Changing this delay changes the frequency

v and allows the signal to be divided into a number of

independent, narrow-band channels. The integration of

equation 2-8 over bandwidth gives

V'(u,v,t) = ~lI'(x,y)Fiv)exp[-i~vt.+2n(ux~vy)] dxdy at
(2-11)








where F(v)is the frequency bandpass function.

Due to the symmetry of the delays introduced, only the

real part needs to be Fourier transformed, giving (Hjellming

and Basart, 1982)


Re[V'(u,v,t)]exp(i2nyt)dt=


I'~I(xy,y F(viexpli2ny(ux~vy)]dx dy. (2-12)






This is the Fourier transform at one of the frequencies

and contains all the visibility information necessary to map

the source at that frequency. Equivalently, as the number of

delays t. is finite, this procedure allows the mapping of
the narrow-band channels. The right hand side of equation

2-11 contains the bandpass function,F(v) which must be

calibrated. This is done by observing a strong continuum

source, which is assumed to exhibit no spectral variation

over the quite narrow total bandpass normally used for

spectral line work.



Observing Strategy and Calibration

In an interferometer, such as the VLA, high resolution

is achieved by using large separations of the antennae.

Conversely, broad structure requires relatively small

spacings; thus, both long and short spacings are required to






28

measure both the small scale and the extended structure in a

galaxy. However, the higher the resolution, the poorer the

brightness sensi tivi ty Thi s conflict demand s that a

compromise be made between sensitivity and resolution.

The minimum detectable flux density, AS .,depends
min'
only upon system temperature, bandwidth, integration time

and effective collecting area, viz.,


miS a aT /Ae FEG (2-13)


where T is the system temperature in Kelvin, A is the
SYS e
effective collecting area, av is the bandwidth in Hz, and, t

is the integration time in hours.

The effective collecting area A =lAT where A is the
e T
total area and r, is the aperture efficiency.

However, for resolved sources the detectable brightness

temperature is the important quantity, and


TB =Amin BEAM (-4


where BBEAMV is the synthesized beam solid angle.

The synthesized beam is the power pattern of the array

as a whole, rather than the power pattern of an individual

antenna. Thus, for a point source, the synthesized beam is

the observed normal ised bri ghtne ss di stributi on .

Consequently, as resolution is improved the brightness

sensitivity is degraded, and vice versa.






29

If observing time were unlimited, the choice of arrays

would be an easy undertaking. The resolution required would

dictate the largest separation of the antennae, and the

required signal-to-noise ratio would dictate the amount of

integration time needed. However, as observing time is

limited, in order to determine which array configurations

were practical to use for this project required

consideration of both the resolution needed to observe the

structure and the sensitivity needed to ensure that the

majority of the gas was observed. Another factor which had

to be considered was that, as the VLA was used as a

spectrometer, the sensitivity in each narrow line channel is

relatively poor. With these considerations in mind, it soon

became evident that the two lowest resolution

configurations, the D and C arrays, would be the only two

practical configurations to use for a reasonable amount of

observing time. The D array would ensure that no low

amplitude large scale structure emission was missed, whereas

the C array would resolve the-smaller scale structure. Using

only these two arrays means that some small scale structure

below the resolution limit of the C array will be missed,

but will ensure that the majority of the emission was

observed. As the best peak signal-to-noise ratio observed in

any of the channels was 13.4 this would mean that the best

detection achievable with the next largest array, the B

array, would be, for the same amount of observing time, a

less than "two sigma" detection.








In spectral line observations the co rrel1ato r must

multiply the signals from 2n delay lines for each of

N(N-1)/2 baselines, where n is the number of spectral

channels and N is the number of antennae used. The

correlator thus has an upper limit for the product nN which

necessitates a compromise when choosing n and N. The larger

the value of n, the greater the spectral, and hence

velocity, resolution but the poorer the sensitivity. The

larger N is, the better the sensitivity as more antennae

contribute to the signal Ideally the largest values

possible for n and N are required. However, as n has to be

an integer power of two to allow the Fourier transform of

the lag spectrum to be calculated using Fast Fourier

Transform techniques (FFT), this also places some

restrictions on n.

The choice of n depends upon the velocity range of the

global profile of the galaxy under study and the velocity

resolution desired. Also, a few "line-free" channels on each

end of the spectrum are desirable to allow the continuum

emission to be mapped. Previous studies and single dish

results (Bottinelli et al., 1970) indicate that the global

profile for NGC 1300 has a velocity width (full width at a

l evel1 of 25% of the peak l evel1) of 2 90km/sec The se

observations, coupled with the other considerations above,

lead to a choice of n=32 with a single channel separation of

20.63km/sec, 97.656krHz. This choice of n allowed a maximum







of 25 antennae to be used. The discarded antennae were

chosen simply on the basis of their recent malfunction

performance.

During the observing run the central channel, channel

16, was centered on 1540km/sec, a value equal to the

approximate mean of other previous determinations of the

systemic velocity; Sandage and Tammann (1975) find

1535 +9km/sec; de Vauc ou leurs de Vaucouleurs and Corwin

(1976) find 1502+10km/sec; and Botinelli et al. (1970) find

1573+7km/sec. Channel 32 was chosen as the central channel

in order to avoid using the end channels in the 64 channel

spectrometer. Due to Gibbs phenomenon (oscillations in the

bandpass func ti on at the edge s of the bandpass) a few

channels at either end of the spectrometer are severely

degraded, and it was considered prudent to avoid these

channels. The mean velocity is a heliocentric ve locity

calculated using the definition



V = co p (2-15)



Thirty-one of the channels are narrow line channels

separated by 20.63km/sec, 97.656kI~z, with a full width at

half maximum (FWHM) of 25.2km/sec; the thirty-second is a

pseudo-continuum channel with a total width of 1000km/sec,

4.7MHz. This channel, designated channel zero, contains the

true continuum emission plus the line signal, utilizes ~ 75%






32

of the intermediate 6.25MHz broad band filter, and was used

primarily to calibrate the line channels. As this is a broad

band channel, the sensitivity to the calibration is much

greater (17x) than that for the line channels. Consequently,

the calibration procedure was carried out using channel zero

and then appli ed to the single line channels onc e a

satisfactory solution was found. This procedure is

summarized below.

The flux density for the primary calibrator, 3C48, is

forced to assume some "known" value at the frequency of the

observations (VLA calibration manual based on Baars et al.,

1977). Using the flux densities of the secondary calibrators

as free parameters, a solution for amplitude and phase for

each antenna in the array is computed as a function of time.

All the scans of the secondary calibrators are utilized for

this solution. Baselines with closure errors greater than

some specified limits in amplitude and phase ( -10% in

amplitude and 100 in phase) can then be identified and

rejected. If the assumption is made that the complex gain

for the antenna pair jk, C'jk 't can be represented by

amplitudes g p(t) and g p(t) and phases Oj (t) and 4kp~t
then,


Gjkp~t 9jp(t)exp[i(4 +4kp GIkp~ t)+,jkp (2-16)

where c .P are the closure errors. Thus, the smaller these
closure errors the better the approximation becomes for the

actual complex gain. For the mode of observing employed for








these observations, few baselines had closure errors as
o oad5
large as 10% and 10 ,and most were below the 7 n

range. After rejecting the baselines with unacceptable

closure errors, the antenna solution is repeated. This

iterative procedure is continued until acceptable solutions

have been found for the complex gains.

This procedure utilizes one antenna as a reference

antenna for the array. It is thus worthwhile repeating the

calibration using a different reference antenna to improve

the solution. The reference antenna should be particularly

stable compared with the rest of the array and should have

variations which are as slow as possible and not be

monotonic functions of either space or time. A good stable

antenna usually can be found by repeating the calibration

procedure for a few different antennae.

Once acceptable solutions for the complex gains have

been found using the primary calibration source, fluxes for

the secondary calibrators can be determined. These fluxes

are generally called bootstrappedd" fluxes and their errors

give a good indication of the stability of the atmosphere

during the observing run.

The bootstrapped fluxes can be applied to the entire

dataset, including the program object observations, by a

simple running mean, or "boxcar" interpolation of the

amplitude and phase gains of the individual antennae. At

every step of the process the database is inspected and








suspect signal data are flagged, hopefully leading to a

better solution from the next iteration and not seriously

degrading the overall quality of the dataset. The quality of

the dataset is usually not degraded very much as there is a

large duplication of baselines and rejecting a few data

points does not have a large overall effect on the database.

The final step in the calibration procedure is to calibrate

the bandpass by assuming a flat spectrum for the primary

calibrator over the total spectral-line bandwidth. The

purpose of the bandpass calibration is to correct for the

complex gain variations across the spectral channels. The

bandpass usually varies only slowly with time and usually

has to be measured only once during an observing run. The

data are now ready for Fourier inversion and image

processing.

Generally, the data for this project were unaffected by

any serious problems, and few baselines or scans had to be

flagged in the calibration procedures. However, the data

from Summer 1984, for the second half of the observing run,

exhibited some anomalous records at the beginning of each

sc an The source of the se anomalous records was not

discovered and the records were simply deleted from the

dataset. This improved the antenna solution noticeably and

allowed an acceptable solution to be calculated quickly.

Another problem with the more compact arrays when observing

a source with a low southerly declination, such as NGC 1300






35

(6=-19035') is "shadowing." This occurs when the projected

separation of two antennae is smaller than the physical

diameter of the antennae, 25m. This means that one antenna

is partially blocking the other's view of the source. A

correction for this effect can be applied, or the offending

antenna can simply be removed from the database for the

appropriate timerange. This "shadowing" also causes a more

subtle problem for the calibration procedure. When one

antenna is shadowing" ano the r, even slightly, the data

collected during that time range by the "shadowed" antenna

has a noticeable deterioration in quality. This "crosstalk"

arises when the shadowed antenna detects signals from the

electronics of its neighbour. As thi s effect can be

difficult to detect, the safest method to avoid "crosstalk"

is to flag all data from "shadowed" antennae. For NGC 1300

this amounted to approximately 2% of the data, the majority

being at the beginning and the end of the run,- at large hour

angles, or low elevation angles. The amount of data flagged

did not degrade seriously the overall qu al ity of the

database and allowed a good antenna solution to be

calculated. Apart from these two problems, which were easily

corrected, NGC 1300 showed no unpleasant surprises and a

good solution was arrived at in a few iterations of the

calibration procedure.

The galaxy NGC 1300 was observed using the D/C hybrid

configuration on the 9th and 12th July 1984. A total of 25






36

antennae, evenly distributed over the three arms, was used.

The north arm was in the C array configuration and the

southwest and southeast arms were in the more compact D

array configuration. This hybrid configuration allowed a

nearly circular beam to be synthesized and gave a maximum

unprojected separation of 2106.6m (9982X) and a minimum

unproj ected separation of 44.6m (213 X). Seven hours of

observing time were used on the 9th of July, 1984 and seven

hours on the 12th of July, 1984.

Calibration sources were observed at the beginning of

the session, every 40 minutes during the run, and again at

the end of the session. More frequent observations of the

calibrators were not deemed necessary as the timescale for

phase stability of the atmo sphe re at 21cm ( 1420MHz ) is

considered to be a good deal longer than the intervals

chosen here. The bandpass calibrator source, 3C48, was

observed three times during the session: at the beginning,

in the middle, and at the end. This also provided a check

on the overall stability of the system as it allowed a

comparison of the phase and amplitude response over the

whole session.

The primary calibrator, 3C48, was used to calibrate the

receiver handpass and the flux densities of the secondary

calibrators. Two secondary calibrators, 0237-233 and

0420-014, were needed for NGC 1300 due to the relative

positions of available calibrators and the galaxy itself.








0237-233 was used for the first 4 hours of the observing run

and 0420-014 for the remaining 3 hours of the run. The

transition from one secondary calibrator to the other was

acc omp lished by using the primary calibrator as an

intermediate step between the two.

The 1985 observations employed 25 antennae in the C/B

hybrid configuration. The north arm was once again in the

higher resolution configuration and the antennae were evenly

distributed over the three arms. The configuration gave a

maximum unprojected separation of 6920m (32953 X) and a

minimum unprojected separation of 78m (372X). A total of 6

hours of observing were obtained using this hybrid array on

the 28th of June, 1985 and 7.5 hours on the 1st of July,

1985. The phase and amplitude calibration of the data were

done by using the same sources as for the D/C hybrid array;

the observing strategy was the same for both seasons. The

flux densities of these sources and the receiver bandpass

were once again calibrated using 3C48. Table 2-1 lists

calibrator positions and fluxes.



Map-Making and Image Processing

The fundamental result of the aperture synthe si s

description is the existence of a Fourier transform

relationship between the modified sky brightness and the

visibility observed with an interferometer,



I'(xy) = V'(u,v) exp~i2n(ux+vy)]du dv (2-17)














Calibrator P/S Frequency Epoch Array Flux Density
(1) (2) (3) (4) (5) (6)


3C48 P 1413.251 Jul 84 C/D 15.82
P 1413.240 Jun 85 B/C 15.82


0237-233 S 1413.251 Jul 84 C/D 6.25
S 1413.240 Jun 85 B/C 6.12


0420-014 S 1413.251 Jul 84 C/D 2.03
S 1413.240 Jun 85 B/C 2.22


3C48 01 34 49.8 (1950)
32 54 20.5


0237-233 02 37 52.7 (1950)
-23 22 06.4


0420-014 04 20 43.5 (1950)
-01 27 28.6


(1) Calibrator identification.
(2) Primary (P) or Secondary (S) calibrator.
(3) Frequency of observation (MHz).
(4) Epoch of observation.
(5) Array configuration employed for observations.
(6) Flux adopted for primary or determined for
secondary calibrators.


TABLE 2.1

Properties of Survey Calibrators







where I' is the product of the true bri ghtne ss

di stributi on, Io, and the single dish power pattern, A ,

equation (2-10) .

This result can be used to derive the source brightness

distribution from the observed interferometer visibilities.

These visibilities are observed at a number of discrete

(u,v) points. With a small number of points, model-fitting

of the points is feasible, but as a VLA spectral-line data-

base typically consists of ~ 500,000 points the most

practical way of constructing the brightness distribution is

to use Fourier inversion techniques.

There are two common ways of evaluating the Fourier

transform:

1. By direct evaluation of equation (2-17) at the

individual sample points, Dir~ect Fourier Transform,

DFT.

2. By using a Fast Fourier algorithm, FFT.

The advantages of the DFT are that aliasing and

convolution introduced by the gridding procedure for the FFT

are avoided, but the disadvantage is that the number of

multiplications for an NxN grid of M data points cr2MN 2

which can be substantial for the large datasets usually

considered in spectral line observations. The use of the FFT

reduces the number of multiplications to N210gN2 which can

save a considerable amount of computing time. However, for

the FFT the data points must be on a rectangular grid,mxp,







where m and p are integer powers of two. The use .of FFT

algorithms can lead to the introduction of aliasing in the

maps. This aliasing results from the gridding process. The

gridded visibilities may be represented as


Vr(uIv) = III(u~v)* [C (uIv)RS(uIv)*V'I(uv)]) (2-18)
where III is a two- dimensional Shah function, S is a

sampling function, and C is a convolving function.

Due to the presence of the Shah function and the fact

that the Fourier Transform of C is not exactly zero beyond

the map limits, parts of the brightness distribution that

lie outside the primary map field will be aliased into the

primary field. The simplest way to tell if an image is

aliased is to remap the field with a different cell size.

The aliased source will appear to move while a primary

source will stay the same angular distance from the field

center.

The most common grid for the FFT is a square grid (m=p)

with the (u,v) spacings comparable with the cell size; as

the observed data seldom lie on these grid points, some

interpolation method must be used to specify the

visibilities at the grid points. If a scheme which resembles

a convolution in the (u,v) plane is used, then the image

will have predictable distortions which can be corrected at

later stages of the reduction procedure. A convolution also

smoothes the data, providing a good estimate of the gridded

visibility from noisy input data.







The best way to avoid, or at least reduce, aliasing

problems is to use a convolving function, C, that results in

a fast drop-off beyond the edge of the image. This requires

that C be calculated over a large region in the (u,v) plane,

requiring a large amount of computing time Thu s, in

practice, a compromise between alias rejection and computing

time must be reached. The function C should ideally be flat

out to some distance and then drop off sharply without

having sidelobes beyond the edges of the map. The lack of

high sidelobes helps suppress the aliasing of sources lying

outside the map into the map. Aliasing of sources that lie

off the primary image back into the map is only part of the

problem. A primary image source will1 have sidelobes

extending beyond the edge of the image. These sidelobes will

be aliased back in, effectively raising the background and

resulting in a beam shape that is po si tion invariant

(Sramek, 1985 ). Thu s, the convolving function suppresses

aliasing due to replication of the image in the gridding

process. It suppresses aliasing but not sidelobe or ringlobe

responses from sources outside the area of the map. With

alias suppression of 102 or 10 3 at two or three map radii,

it is these sidelobe responses which may cause the dominant

spurious map features. As C is usually separable

C(u,v) = C' (u) C' (v) (2-19)


where







C'(x) = (1-n (x) /CB I(cen (x)),


ni(x) = x/max


and

(cn) = (1_2-a ) S (Cn.(2-20)
aL,o a,a


The function S (CI,) is a prolate spheroidal wave function

(Schwab, 1980) At the VLA the parameters used are

generally m=6, ar=1, n=0. Figure 2-1 shows the form of this

function.

It is desirable not to have the product Nau so large

that the outer cells are all empty and the inner ones

heavily undersampled, nor so small that many po-ints at large

spacings are rejected. For the VLA spectral-line observing

mode an empirical relationship which produces good sampling

is that the synthesized beam be about three to four times

the cell size of the intensity images,Ae

Once the data have been convolved, the map must be

sampled to produce the gridded values. The sampling function

is a two dimensional Shah function (Bracewell, 1965),


III (u,v) = Au~v Cc 6[(u--j~u),(v--k~v)] (2-21)

where du,6v are the separations between grid points.

Unfo rtunate ly, the s ampli ng in baseline space by a

rotation synthesis array, such as the VLA, is non-uniform.

The projections (u,v) of sample points, with respect to a

reference direction, are therefore non-uniformly distributed


















-015 \Y( o m= e






-2.5


-3.0:-






M~AP RADII


Figure 2-1. Spheroidal Convolving Function. Side-
lobe responses for the gridding function used in this study.





44

with varying density inside an irregular boundary, all of

which depend upon the source declination, see Figure 2-2 for

(u,v) coverage. Therefore some sort of weighting function,

W, is necessary to correct for this effect and to control

the synthesized beam shape. The sampling function can then

be written


III(u,v) = Auav ym W6 [(u-j~u) ,(v-k~v)]i. (2-22)


The weighting function is usually expressed as the

product W=dt where d corrects for the varying number of

observed samples in each gridded cell, and t introduces a

taper to reduce the sidelobes. The beam usually consists of

a Gaussian core with broad sidelobes at a one to ten percent

levels. The shape of the sidelobes is simply the Fourier

transform of the unsampled spacings in the (u,v) plane out

to infinity. The taper, t, weights down the sparsely-sampled

outer region of the (u,v) plane and helps suppress the small

scale sidelobes at the expense of a broader beam. The

tapering function is usually a truncated Gaussian function

(Sramek, 1985).

The other weighting function, d, is generally choose

from one of two extremes, natural or uniform weighting.

Natural weighting weights all observed samples equally: d=1.

Thus, the weight of each gridded visibility is proportional

to the number of observed visibilities contributing to that

samp le. Since the density of observed samples is always

































Figure 2-2. (u,v) Coverage. Schematic representa-
tion of the (u,v) coverage obtained by the observations of
NGC 1300.




46





47

higher for the shorter baselines, this tends to produce a

beam with a broad low-level plateau (Sramek, 1982). However,

this type of weighting gives the best.signal-to-noise ratio

for detecting weak emission. Natural weighting is

undesirable for imaging sources with both large and small

scale structure, such as extended emission from galaxies.

Although the sensitivity is inc reased, the broad beam

degrades the resolution and the small scale structure will

become dependent on the beam shape. To remove the broad

plateau each gridded cell is weighted by the inverse of the

number of observed visibilities contributing to that cell:

d=1/N. This weighting is called uniform weighting and, since

not all visibilities are equally weighted, there will be a

degredation in si gnal -to -noi se ratio. Uni form wei ghti ng

gives the same weight to each cell in the gridded (u,v)

plane and the beam characteristics are controlled largely by

the tapering, t (Sramek, 1985).

In principle the procedure for producing the gridded

visibilities for the application of the FFT is

1. Convolve the observed vi sibili ty data points to

produce a continuous function.

2. Resample this continuous function at the grid points.

3. Apply the weighting and taper to the resampled data.

These gridded visibilities can now be Fourier inverted,

using equation 2-17, to produce an estimate of the source

brightness distribution. For NGC 1300 the Fourier inversion






48

was performed using a 6" cell size with a 7kh taper (1484m)

and uniform weighting producing 32 single channel "dirty

maps" and their associated "dirty beams." These dirty maps

are given by the true brightness distribution convolved with

the dirty beam.

Direct Fourier inversion of the observed visibilities,

with all unsampled visibilities set to zero, gives the

principal solution, or dirty image. Thus, the quality of the

image depends entirely upon the sampling in baseline space.

In general this sampling is non-uniform. It is obvious that

the true image cannot be as complex as this dirty image,

where the visibility vanishes at all positions -not sampled

by the observation. There must be image components invisible

to the instrument with non- ze ro vi sibili ti es at the

unsampled positions. The unsampled points in the (u,v) plane

give rise to the sidelobes of the dirty beam and reflect an

unavoidable confusion over the true brightness distribution.

S ome estimate of these uns amp led or i nvi sible image

components is necessary to augment the principal solution in

order to obtain an astronomically plausible image. The

scheme most widely used is the CLEAN algorithm introduced by

Hogbom (1974). CLEAN performs a func ti on re sembl1i ng

interpolation in the (u,v) plane.

The CLEAN algorithm uses the knowledge that radio

sources can be considered as the sum of a number of point

sources in an otherwise empty field of view. A simple





49

iterative procedure is employed to find the positions and

strengths of these point sources. The final image, or

"cle an" image, is the sum of these point components

convolved with a "clean" beam, usually a Gaussian, to de-

emphasize the higher spatial frequencies which are usually

spuriously extrapolated.

The original Hogbom algorithm proceeds as follows:

1. Find the strength, M, and position of the point

brightest in absolute strength in the dirty image.

2. Convolve the dirty beam with a point source, at this

location, of amplitude yM, where v is the loop gain,

and y<1.

3. Subtract the result of this convolution from the

dirty map.

4. Repeat until the residual is below some predetermined

level.

5. Convolve the point sources with an idealized clean

beam, usually an elliptical Gaussian fitted to the

core of the dirty beam.

6. Add the residuals of the dirty image to the clean

image Keeping the residuals avoids having an

amplitude cut-off in the structure corresponding to

the lowest subtracted component and also it provides

an indication of the level of uncertainty in the

brightness values.








Since the basis of this method is to interpolate

unobserved visibilities, the final image is the consequence

of preconceived astrophysical plausibility. Interpretation

of fine detail in clean maps should recognize this non-

uniqueness of the solution.

Clark (1980) developed a variant of the Hogbom

algorithm. The basic idea is to separate the operation of

peak locating from that of convolution-subtract and perform

the convolution-subtract step on a large number of point

sources simultaneously. The algorithm has a minor cycle in

approximate point source location using a truncated beam

patch, which includes the highest exterior sidelobe, and a

major cycle in proper subtraction of a set of point sources

(Clark, 1985; Cornwell, 1985).

It should be clear that CLEAN provides some sort of

estimate for unsampled (u,v) points. In most cases it does

this reasonably well. However, quite often it underestimates

the "zero-spacing" flux, the integral of the flux over the

clean image. This results in the source appearing to rest in

a "bowl of negative surface bri ghtne ss Provi di ng an

estimate of this flux (from single dish measurements for

example) can sometimes help (Cornwell, 1985).

In using CLEAN a decision has to be made concerning

various parameters:

1. Is the addition of the zero-spacing flux necessary?







2. Over what region of the image should the CLEAN be

done?

3. How deep should the CLEANing go, i.e. at what level

should the cutoff be?

The solution to these que sti ons for NGC 1300 was

arrived at by considering the following:

1. The galaxy was observed using the D array. This array

contains short spacings and thu s, the un samp led

region in the (u,v) plane is small. Owing to this, no

zero- space ing flux was added. The decision was

justified as np evidence for a negative brightness

bowl was seen, meaning that CLEAN had provided a good

estimate for this flux. The total flux measured at

the VLA was 36.53Jy(km/sec) compared with

30.3Jy(km/sec) found by Reif et al. (1982).

2. All the line channels were examined and limits set on

the spatial extent of the signal in each channel.

This allowed only regions containing signal to be

used in CLEANing, thus avoiding the time-consuming

CLEANing of regions containing only random noise.

3. When CLEAN is applied to maps correctly the resultant

"blank" sky should show only random noise and no

sidelobe structure. The rms noise level should be

approximately the same from channel to channel and

should also be approximately equal to the expected

rms noise level for spectral-line maps with natural

weighting (Rots, 1982);








= a[N(N-1) T Av]-1/2 (2-23)

where N is the number of antennae used, a is a

constant, a=620 for 21cm, T. is the total on-source

integration time in hours, and av is the bandwidth in

krHz .

For NGC 1300 using 25 antennae, N=25, Ti =20.58hr,

Av=97.656k~Hz gave an expected rms noise level of

0.6mJy/beam. The rms noise level for the dirty maps is

-0.8mJy/beam and for the clean maps ,0.7mJy/beam and thus

indicates that the CLEAN was acceptable. Table 2-2 shows the

rms noise level for the dirty maps and the rms noise level

for the clean maps. Once the expected rms value has been

reached the CLEANing is stopped; proceeding beyond this

point is tantamount to shuffling the noise around. For NGC

1300 this limit was generally reached after 1000 iterations,

as the loop gain was small, y =0.15.

Before the spectral-line channels are CLEANed some

method of subtracting the continuum emi ssion must be

utilized. Continuum emission usually consists of unresolved

point sources as well as some emission from the central

region of the nucleus. The method used for NGC 1300 was to

average a few "line-free" channels from both ends of the

line spectrum producing a continuum emission map. Thi s

continuum map was then subtracted from the dirty spectral-

line channel maps, producing a set of 18 dirty, continuum-

free, spectral-line maps. It is important to note that, due













Image Velocity rms Noise rms Noise rms Noise Peak Brightness
(km/sec) Dirty Map Clean Map Clean Map Clean Map
(mJ/beam) (mJ/beam) (K) (K)


6 1746.10 0.84 0.82 1.28 5.40
7 1725.49 0.75 0.73 1.14 7.44
8 1704.88 0.86 0.83 1.30 16.95
9 1684.27 0.81 0.78 1.22 14.93
10 1663.66 0.84 0.81 1.27 12.59


11 1643.05 0.79 0.75 1.17 13.60
12 1622.44 0.83 0.83 1.30 9.72
13 1601.83 0.82 0.79 1.24 11.21
14 1581.22 0.91 0.91 1.42 9.52
15 1560.61 0. 85 0.85 1.33 9.18


16 1540.00 0.84 0.83 1.30 8.87
17 1519.39 0.83 0.83 1.30 9.11
18 1498.78 0.78 0.77 1.20 11.08
19 1478.17 0.83 0.80 1.25 12.73
20 1457.56 0.83 0.80 1.25 15.82


21 1436.95 0.78 0.78 1.22 10.17
22 1416.34 0.80 0.78 1.22 5.51
23 1395.73 0.82 0.81 1.27 5.32

Continuum 0.30 0.27 0.43 12.63
Channel O 0.18 0.17 0.19-
Large Field 0.77 --


TABLE 2.2

Image Signal and Noise Characteristics








to the non- lineariti es of the CLEAN algori thm, thi s

continuum subtraction must be performed before the maps are

CLEANed. Subtracting CLEAN maps can introduce noise at the

positions of continuum sources (van Gorkom, 1982). Table 2-2

has the noise levels for these continuum free line channels.

The dirty, continuum-free line channels and the continuum

map are now ready for the CLEANing procedure.

Figure 2-3 (a-s) shows the final CLEANed spectral line

channels and the continuum map. The effective resolution is

20.05"x19.53" (FWHM). The beam is indicated on the continuum

map, Figure 2-3 (s). As the astronomical significance of

these observations will be considered in a later section,

the CLEANed line channel maps are just presented here. The

emission from the galaxy appears to be clumpy and is not

very widespread. This hints at the structure found in the

integrated density map, well-defined arms with an extremely

low level disk component. The rms noise levels for the these

maps can be converted from mJy/beam to brightness

temperature using

-26 2
aSx10 C

v 2ks2



where hT_ is in Kelvin, aS is the rms noise level in

mJy/beam, C is the speed of light, is the frequency of

observation in MHz, k is the Boltzman constant, and R is the

beam solid angle in radians.






















Figure 2-3. Spectral Line Channel Maps. CLEAN,
continuum-free spectral line channels for NGC 1300. The
+ mark the positions of fiducial stars and x the center
of the galaxy. The velocity is indicated in the top
right corner. All maps are plotted in intervals of twice
the rms noise level.

A-R. Spectral line channels 6 through 23.

S. CLEAN continuum map showing the center of the
galaxy (x), fiducial starts (+), H II regions (*) and
the beam~size.











NGC 1300
NGCl300 17L16.



28 L i



-1@ C O
30



32.o r/




30 .

+

36



36 .0 a o



o p
110





C 13 a 3
O .Q O,
70 -


RAF 3 17


Figure 2-3 cont.


(Pa~rt A).









NGC 1300
NGCl300 1725.


28 o



-1930 n O 'b




32

Oa



O

38 0


0 0

0/ o
o a--/C

92+ .

38 L O

40
n 10


RAF 3 17


Figure 2-3 cont.


(Part B).









NGC 1300
NGCl300 1705.



28 L O


I- 9 o a
310 a
30 o

OG

32
c> O






0. +

38 o,

O O

9036 o O 0~'
o
4c *9





CI I


R A 3 17


Figure 2-3 cont.


(Part C).














I1 I


16811.


o


0


m I


d CI


-19"30L


C3


r:+


0

+ 1 .
X.


O


O
O s


O


o /O


D


92



n


r-) o
O


3 1)
r:
,cJ


RA


3 17


Figure 2-3 cont.


(Part D).


NGC 1300


NGC1300





16611.


u
o O


13 3


28



-190
30


r,
0


32 L


39r L


36 C


O o


3 J


DC


O


o >


G O


42 L


G


RA F


3 17


Figure 2-3 cont.


NGC 1300


NGC1300


(Part E).




61




NGC 1300
NGlCl300 1693.


28 -,i Ii o
28 o


- 19.
3 0 _0

coc
32 .


3 4 c o c 0 o



a 9, c
36



38 L o o


O o
Y0


R A 3 17


Figure 2-3 cont.


(Part F).




62




NGC 1300
NGlCl300 1622.


28 o
Oo o





-19.3 ;f o




c Ccr
o- a3 0
39 ? o


+ +
3G (3 o X

o a




On
alo o
o Co
92 O




L90 25 10 55
RAF 3 17


Figure 2-3 cont.


(Part G).












-I 1 I


_ _I


1602.


9 r" 3


OO


-19"30 L


r


32 o"


+t
X
a ,


38 L


0 ,1 3


U y


+~+


u0 L


L02 L


RA


3 17


Figure 2-3 cont.


(Part H).


NGC 1300


NGCl3CO




64




NGC 1300
NGC1300 1581.


28 LO
G co

oa C
1930 -o

3 a

32 o


C
3Y C. 9
oG4` +3 c,
5 + o

X O.
36 "'







tlo o '




a 0 0 r;o
I, I 1 f


RAF 3 17


Figure 2-3 cont.


(Part I).













I


I


1561.


3, o
3 C


28




-19.30


00O


32 L


"I


a 0

X


C

*


3 L~


o a ,


oO


. 1


36 L


;7 ,
~j~ "
+2~O


;O r'


O


38 C


L00




12


o
m


. r


C
o


O


R A


3 17


Figure 2-3 cont.


NGC 1300


NGCl300


(Part J) .









NGC 1300
NGC1300 15110.



28 o



-1930


O


O rO




+J 3
36 0I o



38 -- /




o 90

92 ~o


m1 a


L90 25 10 55
R A 3 17


Figure 2-3 cont.


(Part; K).













0 I i s


1519.


"e O


cJ


32 L


,oo /


O C


36 L_


3a t~


O
3


0-
o


92 L


O o -


3 17


Figure 2-3 cont.


(;Part L).


NGC 1300


NGC1300
















I i


I -:I I


1499.


C


9


O


-19"30 1


r
J
f


o O


32[


7


o


b P/


1,


40 ti


L92


o
rn


RA F


3 17


Figure 2-3 cont.


(Part M).


NGC 1300


NGC1300















r I


L
5
?i c
3 O 3 \i
I I ( .I


11178.


Cz


o
o


28 L


d 0


-19030


D


32 &


c~ L'
o
+ icl"r- ~i i


3 6 L


r C


c *


O
7


'3
i


L92 L


B a


3 17


R A


Figure 2-3 cont.


NGC 1300


NIC1l300


(Part N).









NGC 1300
NGCl300 11958.



2 8 _0C;


303
P o
O o <

300

oo a a
32 so a


o a

oo 3
31 on

36 a
s0
'O O "r



32 -, c


uo a
-0s 0


nL I


R A 3 17


Figure 2-3 cont.


(Part O).














I I


I I I


11137.


D o


0


O r


0 0


30 L


o ai


'"=;~'


O


38 0
'"~5 0


7


L j


O


C-
O


O


? O
i)


I "


I i


3 17


Figure 2-3 cont.


NGC 1300


NGCl300


-19'30




32


(Part P).
















I 1


I


11116.


o0


-19 "30


O


`j


a
+ O


3


o
Ci


So


0$


36 L


O
i7
3


110


i)


n i:


42 W


_I


RA F


3 17


Figure 2-3 cont.


(Part Q) .


NGC 1300


NGC1300










NGC 1300
NGCl300 1396.




28 L '
-19. o a


32 O
i; O O
"- D C
00



30 o



oX c

38 0



0~ 'o


C4 2 C
o0


RAR 3 17


Figure 2-3 cont.


(Part R).









NGC 1300
NGCl300 1575.


28



-19.
30



32



311

+i

36m 1


+ -
38








o O
ca2


3 17


Figure 2-3 cont.


(Part S) .





75

Table 2-2 lists the rms noise levels for the CLEANed

maps in mJy/beam and in Kelvin. As can be seen these values

correspond very closely with the expected rms noise level

from equation 2-23.

In addition to the narrow band line channel maps in

Figure 2-3, several channels spaced over the whole velocity

range were mapped over a large field of view, 1.5ox1.50. The

effective resolution for the se large field maps is

24.25"x22.59" (FWHM). These maps were used to search for any

detections of satellite galaxies of NGC 1300 or any other

objects. An example of the inner portion of one of these

wide field maps is shown in Figure 2-4. This is a map of

channel 16 and is a typical result. The continuum emission

has not been subtracted from this map. No evidence was found

for any 21cm line emission from any source other than NGC

1300 in this or any other wide field map. Figure 2-5 shows a

wide field map of "channel zero" with the continuum emission

still present. Thi s, again, is only the inner portion of

the total field mapped. As no evidence was found for any

satellites or other objects, except unresolved continuum

point sources, only the inner portion is shown as an example

of the type of result obtained. The rms noise levels for

these maps are tabulated in Table 2-2.

In summary the map making and CLEANing parameters used

for NCC 1300 are

1. Map making (Channel and Continuum Maps)













NCC1300


T~


1


15110.


`D \I


I


O


o o


35


O
a


O
Q .


SO O 0


O c



0o o o



e0 a





. C.


oO

a


0 P 0O

S


C O
O o
'3CO
3 a


D


O


O


e


O


co


o a


0


45L


0"
o o


o ,o


I ,


3 17


Figure 2-4. Wide Field Nap. Inner portion of wide
field image of channel 16. The continuum emission is still
present. Contours are at intervals of twice the rms noise
level.


NGC 1300
















r


) ~I 11Y L I


O *


P


.



a o


o

'.




-


00

Oa o '




ac o


3 .*
D d
o B







0


- 1 9 .


25 L


oo


04

o ~d
o O
Oc
os O


o0 .

oo oo

o O~


i
. e
o o a
4 (2


0 Go
o 6 b


o ~

P
0


L 5 1..


a ~"


0' a '


O


D~o
- 8
a


a


o

a


.o

a


o o


a


C


,9


OcC~


o, 1


RA F


3 18


Figure 2-5. Channel Zero. Wide field map of channel
zero. Contour levels are at approximately twice rmrs noise
level.


NGC 1300


NGCl300








a) Weighting:

b) Taper:

c) Convolving:

d) Cell size:

e) Image size:

2. Map Making (Wide

a) Weighting:

b) Taper:

c) Convolving:

d) Cell size:

e) Image size:

3. Clean

a) Flux cutoff:

b) Gain:


Uniform

7k X(1484m) 30% level of Gaussian.

Spheroidal with m=6, n=0, a=1.

6"x6"

256x256

Field Maps)

Uniform

7k X(1484m) 30% level of Gaussian.

Spheroidal with m=6, n=0, a=1.

10"x10"

512x512



0.5mJy/beam

0.15













CHAPTER III
DETERMINATION OF THE NEUTRAL HYDROGEN PROPERTIES



Spectrum Integration Techniqiues

The final product of the acquisition, calibration and

processing of the 21cm VLA visibilities is a set of 18

continuum-free narrow spectral-line channels for NGC 1300.

The set consists of signal-free channels at either end of

the spectrum and a series of signal -ri ch spectral-line

channels. The channel separation is 20.63km/sec and each

channel has a width (FWHM) of 25.2km/sec. These continuum-

free channel maps can be used to infer the neutral hydrogen

distribution and its associated velocity field.

If we assume that the atomic hydrogen is optically

thin, then the column density Nh at some point (x,y) is
given by (Mihalas and Binney, 1981 p489)

18 Jm _xyd 31
N (x'Y) = 1.8226xl0



where the velocity, V, is in km/sec, and TB, the brightness

temperature, is in degrees Kelvin.

The mean temperature-weighted velocity at that point is

given by












= .m (3-2)





These will be easily recognized as the zeroeth and first

moments of the bri ghtne ss temperature with re spec t to

velocity.

In the absence of observational noise the evaluation of

these quantities would be straightforward, being a straight

summation over velocity at each (x,y) point. However, as

noise is always present, a method is required which is

capable of discriminating quickly between noise and line

signal, and rejecting the noise before integration. As the

channels cover only a limited spectral range the noise may

not average to zero and will give a definite contribution to

the summation, if the summation was naively carried out over

the full spectral range. The problem is then to define a

range, or window, in velocity space which contains only line

signal. Various methods have been proposed to define this

window (Bosma, 1978, 1981). Bosma considered four methods:

1. Study each spectrum visually and define limits in

velocity.

2. Fit each spectrum with a preconceived shape.

3. Apply an acceptance level in intensity (the cut-off

method).





81

4. Apply an acceptance level in velocity (the "window"

method).

Bosma (1978) studied these various methods and concluded

that the optimum method is the "window" technique.

The method used here is a variation of the "window"

method. Bosma's procedure is followed with some additional

discriminating features. A narrow window in velocity is

initially defined ~and gradually expanded with the value

outside the window being compared with the value outside the

window calculated in the previous step. When these two

.values agree to within a specified tolerance level then all

the signal is considered to have been found and the

procedure is stopped for that pixel. Using this procedure

implies that the real signal is going to be present in a

single range of contiguous channels and any large spike at a

very discrepant velocity is considered to be noise. Also,

any large spike occurring in only one channel will1 be

rejected. The tolerance level depends upon the rms noise of

the single channel maps and on the number of points

remaining in the empirically defined continuum. Thi s

continuum is the mean level of points outside the window.

Two additional criteria are added to improve the signal

detection and noise rejection capabilities of the procedure.

The procedure requires at least n points in the spectrum to

be above a specified bri ghtne ss temperature If thi s

criterion is not satisfied then no further effort is spent







on that pixel and it is rejected from all further

consideration. However, if this criterion is satisfied then a

further test is applied to reject pixels which have the

required number of points above the specified brightness

temperature but do not actually contain line signal. The

total value at each pixel (equation 3-1) must be above a

specified cut-off l eveli, e.g. three times the rms noise

level. If the integrated value is below this cut-off level

then that pixel is considered not to contain line signal and

is rejected. Usually the procedure tests for at least two

points in the spectrum being above twice the rms noise level

in the single channel maps. The integrated value usually

must lie above three times the rms noise level of the single

channel maps or be discarded.

In an effort to ensure that all the low brightness gas

was used in the integration, various tests were carried out

utilizing different combinations of smoothed single channel

maps for signal discrimination and integration. Combinations

tested included testing for integrable signal on convolved

maps and integrating using Hanning smoothed maps, and

testing for signal on convolved maps and integrating the

same convolved image. Various-sized convolving functions

were tried, all two-dimensional Gaussian functions, in order

to determine the optimum convolving method. The tests also

were carried out using different cut-off values for the

integrated spectrum and different-size boxes surrounding the

region of HI emission.






83

The smoothing function used was a running, three-point

Hanning function


X= 0.25 X + 0.5 X + 0.25 X (3-3)
n n-1 n n+1'

This function was applied in velocity space to each

pixel position. The convolving function is designed to bring

out the low brightness features and to suppress the noise.

Various beam solid angles were tested and the convolution

was applied to each single channel map. Values ranging from

half the synthesized beamwidth (FWHM) to two and a half

times the synthesized beamwidth were tried. Below half the

synthesized beamwidth the convolution had essentially no

effect; whereas, above two and a half times the synthesized

beamwidth, the convolution became so broad as to render the

maps unu sable With this size c onvolIvi ng functi on, the

resolution was so severely degraded that essentially no fine

structure was visible; all that remained was a broad, beam-

smeared, disk-like feature.

The criteria used to determine which combinations of

smoothing and convolving functions, and cut-off values gave

the optimum results were

1. The number of spectra used in the integration.

2. The s signal -to-no ise ratio in the convolved and

integrated maps.

3. The HI mass-integral.







4. The ratio of mass-integral to rms noise level in the

integrated maps.

The mass-integral is defined as (Mihalas and Binney,

1981 p490)


HIas = 2.35 x 105D2 /SdV (3-4)

where S is the flux in Jy, and D) is the distance in Mpc. The

integral is calculated for all pixel points deemed to belong

to the galaxy. The region in which thi s integral is

calculated is cho sen by inspection of the HI density

distribution map produced by the "window" procedure. The

ratio of mass-integral to rms noise level is calculated

using the value found by evaluating equation 3-4 inside the

box surrounding the galaxy, and the rms noise level

calculated outside the box. This ratio should be maximized

for the optimum combination of smoothing, convolving and

cutoff values. Table 3-1 shows some typical values from two

run s during thi s testing procedure Thi s shows quite

clearly that for these tests:

1. The rms noise level clearly goes through a minimum.

2. The mass-integral goes through a maximum.

3. The ratio of mass-integral to rms noise goes through

a maximum.

As a result of these tests the following procedures

were adopted:

1. Hanning smooth, in velocity space, the original

single channel maps with a running three-point

function.







TABLE 3.1

Signal Characteristics for Spectrum Integration



Npo~int Beamwidth rms Noise Mass-integral Ratio
(1) (2) (3) (4) (5)


1 0.5 24.29 1.1430 0.0471
1.0 30.78 1.1781 0.0383
1.5 22.07 1.1777 0.0534
2.0 20.38 1.1788 0.0578
2.5 20.41 1.1784 0.0577


2 0.5 17.68 1.1248 0.0636
1.0 24.75 1.1700 0.0473
1.5 14.92 1.1742 0.0787
2.0 14.67 1.1739 0.0800
2.5 15.00 1.1727 0.0782

(1) Minimum number of points in each spectrum required
to be above the cut-off value.
(2) Convolving beamsize, in units of synthesized
beamwidth.
(3) Rms noise level outside a box surrounding the
galaxy in arbitrary units.
(4) Mass-integral for all points deemed to belong to
the galaxy in arbitrary units.
(5) Ratio of mass-integral to rms noise level.




Full Text
KINEMATICS AND DYNAMICS OF BARRED SPIRAL GALAXIES
BY
MARTIN NICHOLAS ENGLAND
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986

"To the Reader Concerning the Hypothesis of this Work"
Andrew Osiander c!543 in
"De Revolutionibus Orbium Caelestium"
N. Copernicus
It is the job of the astronomer to use painstaking and
skilled observation in gathering together the history of the
celestial movements, and then, since he cannot by any line
of reasoning reach the true cause of these movements to
think up or construct whatever causes or hypotheses he
pleases such that, by the assumption of these causes, those
same movements can be calculated from the principles of
geometry for the past and for the future, too. And if
[mathematical astronomy] constructs and thinks up causes--
and it has certainly thought up a good many--nevertheless it
does not think them up in order to persuade anyone of their
truth but only in order that they may provide a correct
basis for calculation. And as far as hypotheses go, let no
one expect anything in the way of certainty from astronomy,
since astronomy can offer us nothing certain.

Plato:
Timaeus
As being is to becoming, so is truth to belief. If
then, Socrates, amid the many opinions about the gods and
the generation of the universe, we are not able to give
notions which are altogether and in every respect exact and
consistent with one another, do not be surprised.

ACKNOWLEDGEMENTS
It is rather difficult to acknowledge all the people
who in one way or another have contributed to this document
without using the standard oft-repeated phrases so common in
these sections of dissertations.
Dr. Stephen Gottesman led me through the intricacies
of the VLA and extraglactic radio astronomy. This was no
trivial achievement as he was dealing with someone who was
initially a confirmed optical stellar spectroscopist. His
success in this can be measured by the results contained in
the next few hundred pages. Not only was he my dissertation
chairman but a person who was always willing to help in
other matters of general well-being, and above all, a
friend.
Dr. James Hunter, who continually challenged me with
his seemingly "straightforward" problems, acted as
cochairman for the dissertation. He is also responsible for
showing an observational astronomer that theoretical
astronomy is not the great insurmountable barrier that it
was first considered to be. He, probably more than anyone
else, taught me the virtue of sitting down with something,
as with his course work problems (generally unpleasant) and
persevering until it was done. The satisfaction of
completing the problem was worth the effort.
IV

The rest of my committee, Drs. Thomas Carr, Haywood
Smith and Gary Ihas, performed their duties competently and
allowed me the freedom, within guidelines, to do as I
pleased.
The 21cm observations utilized in this dissertation
were obtained at the Very Large Array of the National Radio
Astronomy Observatory. The National Radio Astronomy
Observatory is operated by Associated Universities, Inc.,
under contract with the National Science Foundation. My
thanks to all the staff, especially Drs. Jacqueline van
Gorkom and Patrick Palmer. They not only helped make a
competent spectral line observer out of me but introduced me
to the mountains of southwest New Mexico.
My thanks go also to Drs. Bruce and Debra Elmegreen who
made their surface photometry available and to Drs. C.
Telesco and I. Gatley who allowed me to use their 2.2um
data.
The diagrams and photographs were produced by Paul
Gombola and Hans Schrader.
Computing was done using the facilities of the
Astronomy Department and the Northeast Regional Data Center
(NERDC). I thank the numerous people who provided free
consultation in the hallways and helped with problems as
diverse as image processing and dissertation printing.
Thanks especially to Virginia Hetrick and Jim Parkes. This
dissertation was produced using UFTHESIS on NERDC.
v

Irma Smith typed the equations and the "fiddley bits",
and provided typing services throughout my stay in Florida.
Finally, my heartfelt thanks must go to my parents,
Michael and Maureen England, who supported and actively
encouraged their "professional student." Without their
support none of the next few hundred pages would have been
written. I hope that I can repay them someday for their
sacrifices and dedication.
My wife, Sheila, has been a veritable "Rock of
Gibraltar" and has put up with more and had less than any
wife and woman should reasonably be expected to endure. It
is all over now and it is to her and my parents that this
volume is dedicated.
vi

TABLE OF CONTENTS
PAGE
ACKNOWLEDGEMENTS iv
LIST OF TABLES ix
LIST OF FIGURES x
ABSTRACT xiv
CHAPTER
I. INTRODUCTION 1
Selection Criteria 6
Survey Galaxies 8
NGC 1073 8
NGC 1300 15
NGC 3359 15
NGC 3992 16
II. RADIO OBSERVATIONS 18
HI As A Kinematic Tracer 18
Aperture Synthesis Theory 23
Observing Strategy and Calibration 27
Map-Making and Image Processing 37
III. DETERMINATION OF THE NEUTRAL HYDROGEN PROPERTIES . . 79
Spectrum Integration Techniques 79
Neutral Hydrogen Distribution 86
Continuum 113
Kinematics of the Neutral Hydrogen 115
Mass Models 132
IV. SURFACE PHOTOMETRY 140
Calculation of the Volume Mass Distribution . 142
Surface Photometry of NGC 1300 146
Modeling the I Passband Features 146
Comparisons Between Different Passbands . 165
Triaxial Ellipsoid 175
vi 1

V.MODELING
185
The Beam Scheme 185
Hydrodynamical Modeling of NGC 1300 200
Triaxial Bar Models 200
Oval Distortion Models 207
Composite Models 210
Bulge Models 234
VI. RESULTS FROM OTHER GALAXIES 247
NGC 3359 247
Observational Results 247
Hydrodynamical Models 252
NGC 3992 255
Observational Results 256
Hydrodynamical Models 261
NGC 1073 263
Observational Results 264
Hydrodynamical Models 269
VII. PROPERTIES OF BARRED SPIRAL GALAXIES 272
Observational Comparisons 272
Dynamical Properties 275
VIII. SUMMARY 282
Neutral Hydrogen Results for NGC 1300 .... 282
Hydrodynamical Results 283
Dynamical Properties 285
APPENDIX
A. DERIVATION OF VOLUME BRIGHTNESS DISTRIBUTIONS . 287
B. OVAL DISTORTIONS FOR N=1 TYPE TOOMRE DISKS ... 291
BIBLIOGRAPHY 299
BIOGRAPHICAL SKETCH 305
viii

LIST OF TABLES
TABLE PAGE
1.1. Global Properties of Survey Galaxies 14
2.1. Properties of Survey Calibrators 38
2.2. Image Signal and Noise Characteristics 53
3.1. Signal Characteristics for Spectrum Integration . . 85
3.2. Summary of Neutral Hydrogen Observations for
NGC 1300 139
4.1. Bar Projection Parameters for NGC 1300 183
6.1. Summary of Integrated Properties of NGC 3359 . . 254
6.2. Summary of Integrated Properties of NGC 3992 . . 262
6.3. Summary of Integrated Properties of NGC 1073 . . 270
8.1.Summary of Results for NGC 1300 284
IX

LIST OF FIGURES
FIGURE PAGE
1.1. Survey Galaxies 9
2.1. Spheroidal Convolving Function 43
2.2. (u,v) Coverage 45
2.3. Spectral Line Channel Maps 55
2.4. Wide Field Map 76
2.5. Channel Zero 77
3.1. Neutral Hydrogen Distribution Contour Plot .... 88
3.2. Neutral Hydrogen Distribution with the Optical
Image 89
3.3. Neutral Hydrogen Distribution Gray Scale Image . . 91
3.4. Neutral Hydrogen Distribution False Color
Image 92
3.5. Logarithmic Fit to Spiral Arms 96
3.6. Deprojected Azimuthal Profiles 97
3.7. HI I Regions in NGC 1300 98
3.8. Deprojected HI Surface Density 104
3.9. Profiles Through HI Surface Density
Distribution 107
3.10. Continuum Emission 114
3.11. Velocity Contours 116
3.12. False Color Representation of Velocities .... 117
3.13. Velocity Field Superimposed on Optical Object . 119
x

3.14. Angle-Averaged Rotation Curve 125
3.15. Wedge Rotation Curve 126
3.16. Optical and HI Rotation Curves 129
3.17. Rotation Curve to 6.4 arcmin 131
3.18. Mass Models for NGC 1300 134
3.19. HI Observed Global Profile 138
4.1. NGC 1300 Gray Scale I Passband 147
4.2. Contour Plot of I Plate 148
4.3. Convolved I Passband Image NGC 1300 151
4.4. Bar Brightness Profiles 153
4.5. Disk Surface Brightness 155
4.6. Bulge Component Model 158
4.7. Bulge Subtracted Disk Profile 159
4.8. Bulge Subtracted Contour Plot 160
4.9. I Band Model Isophotes 163
4.10. I Band Model Profiles 164
4.11. Gray Scale of Blue Passband 166
4.12. Contour Plot Blue Passband 167
4.13. Minor-axis Profiles Blue and I Passbands .... 169
4.14. Profile Comparison 171
4.15. Comparison of Blue and I Profiles 172
4.16. Contour Plot 2.2um 176
4.17. False Color Plot 2.2um 177
4.18. Flux Profile 2.2um 179
4.19. Comparison Between Different Wavelengths .... 180
5.1. Dependence of Rotation Curve on Projection
Parameters 198
xi

5.2. Gas Response for Disk and Triaxial 202
5.3. Velocity Field for Bar and Triaxial 204
5.4. Model Rotation Curve 205
5.5. Supermassive Bar Rotation Curve 206
5.6. Oval Distortion Model Gas Response 211
5.7. Oval Distortion Model Velocity Field 212
5.8. Composite Model Gray Scale 215
5.9. Composite Model Contour Plot 216
5.10. Composite Model Velocity Field 217
5.11. Composite Model Rotation Curve 218
5.12. Slow Pattern Speed Model Gray Scale 225
5.13. Velocity Field Vectors • 229
5.14. Velocity Field in Perturbation Frame 230
5.15. Noncircular Velocities 231
5.16. Gas Response for Bulge Model 236
5.17. Density Compared with Observations 237
5.18. Bulge Model Velocity Field 238
5.19. Velocity Compared with Observations 239
5.20. Comparison of Rotation Curves 241
5.21. Velocity Vectors for Bulge Model 242
5.22. Velocity Field in Perturbation Frame 243
5.23. Noncircular Velocities 244
6.1. HI Distribution NGC 3359 249
6.2. Velocity Field NGC 3359 250
6.3. Rotation Curve NGC 3359 253
6.4. HI Distribution NGC 3992 257
6.5. Velocity Field NGC 3992 258
xn

260
6.6. Rotation Curve NGC 3992
6.7. HI Distribution NGC 1073 265
6.8. Velocity Field NGC 1073 266
6.9. Rotation Curve NGC 1073 268
xiii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
KINEMATICS AND DYNAMICS OF BARRED SPIRAL GALAXIES
By
Martin Nicholas England
December 1986
Chairman: S. T. Gottesman
Cochairman: J. H. Hunter, Jr.
Major Department: Astronomy
The kinematics and dynamics of a group of barred spiral
galaxies are analysed. Hydrodynamical models using the
"beam scheme" are calculated and provide a set of dynamical
properties for barred spiral galaxies.
Neutral hydrogen radio observations of NGC 1300 show
the galaxy to be an excellent example of a grand design
spiral system. The HI gas is confined almost entirely to the
spiral arms with very little interarm gas. These HI arms
correlate very well with the position of the optical arms.
The HI arms can be traced through about 310 degrees in
azimuth. The central region, the region occupied by the bar,
is deficient in gas.
xiv

The velocity field shows that circular motion is the
dominant component but that large non-circular motions,
mainly in the arms, are present. The rotation curve rises
to a maximum of 185km/sec at r=2.5' and then remains
essentially flat out to about r=3.2'.
Near infrared surface photometry is used to calculate a
triaxial ellipsoidal figure for the bar. Blue and 2.2um
photometry is analysed and compared with the I band and 21cm
observations.
Hydrodynamical models for NGC 1300 are partially
successful in reproducing the observed morphology and
kinematics of NGC 1300. Various combinations of parameters
are investigated and a composite "best model" presented.
This model consists of an n=l Toomre disk, a triaxial bar,
an 1=2 oval distortion and a halo. The pattern speed of
19.3km/sec/kpc places corotation just outside the end of the
bar.
Hydrodynamical models for NGC 1073, NGC 3359 and NGC
3992 are examined and compared with that for NGC 1300. This
results in a set of dynamical properties for barred spiral
galaxies.
xv

CHAPTER I
INTRODUCTION
Barred spiral galaxies present a very interesting but
very difficult problem for astronomers. De Vaucouleurs
(1963) in his sample of 994 spiral galaxies found that about
37% are pure barred galaxies, while another 28% are mixed
spirals. The remaining galaxies are pure spirals, and are
thus in the minority. Therefore, barred systems are common,
and a good understanding of the physical processes occuring
in them would give insight into the formation and
maintenance of the observed spiral structure.
Until recently the comparison of theoretical models and
observations of barred spiral galaxies has not been very
fruitful for a number of reasons. Hydrodynamical
calculations have indicated that the gas distribution and
kinematics in barred spiral galaxies are very sensitive
tracers of the underlying gravitational potential (Roberts,
Huntley and van Albada, 1979). This is due to the fact that
the gas may respond in a highly non-linear way to even small
deviations from axial symmetry (Sanders and Huntley, 1976).
Theory is capable of producing high resolution models of gas
kinematics and structure. However, the observations have
either not had sufficient spatial resolution for a good
1

2
comparison to be made, or their spatial coverage has been
poor. Traditionally, optical measurements of the kinematics
of spiral galaxies have provided high spatial resolution but
very poor spatial coverage as they have relied upon HI I
regions. The distribution of these regions is patchy; Hodge
(1969) has distributions of HII regions in spiral galaxies.
These regions are not a good tracer of the kinematics of the
gas in barred spiral galaxies. These HII regions are mainly
in the inner regions and spiral arms. However, they would
provide an excellent complement for some other, more global,
gas tracer.
Neutral hydrogen is known to be distributed over large
regions in spiral galaxies and could provide the global
kinematic tracer needed to test the theoretical model
results. However, until recently, observations of the
neutral hydrogen in barred spiral galaxies have been made
using single dish radio telescopes. These observations do
not have the required spatial resolution needed to compare
with the theories, and even have difficulty in isolating the
bar from the underlying disk. The National Radio Astronomy
Observatory Very Large Array (NRAO VLA) is a sensitive
instrument of high resolution, on the order of 20" for the
HI emission from barred spiral systems. The VLA is sensitive
enough that a complete two-dimensional map of the velocity
field can be completed in a reasonable amount of observing
time, even though there are no bright, nearby, easily-

3
observed large barred spirals. Thus, observations of the
gas kinematics and structure can now be made that can
confront theoretical models in a quantitative fashion.
High resolution mapping of the gas kinematics in barred
systems, combined with two-dimensional hydrodynamical
modeling, could address the following questions (Teuben et
al., 1986):
1. What is the radial mass distribution in barred
systems?
2. Are principal resonances present in barred spiral
galaxies? Sanders and Huntley (1976) have shown that
the gas flow changes character at the resonances,
consistent with the dominant periodic orbits. Within
the inner Lindblad resonance, gas flow is on
elliptical streamlines oriented perpendicular to the
bar major-axis. Determining the location of the
resonances, combined with the radial mass
distribution, would allow an estimation of the
pattern speed of the bar.
3. What is the character of the gas motions? Elliptical
streaming is recognizable as a skewing of the
velocity contours along the major-axis (Bosma, 1981).
The degree of skewing is related to the bar strength
(Sanders and Tubbs, 1980).
What is the nature of the parallel, straight dust
lanes in barred spiral galaxies of type SBb? In
4.

4
hydrodynamical calculations, such structures arise
naturally as shocks. These dust lanes often lie along
the leading edge of the rotating bar, for example NGC
1300 and NGC 13 65, and as yet there have been no
unambiguous, kinematic verifications that they are
actually associated with shocks. Ondrechen and van
der Hulst (1983) have shown that for NGC 1097 the
radio continuum emission is enhanced along the dust
lanes, which is to be expected from compression in
shock regions.
Asymmetries in the mass distribution, such as barlike
configurations or oval distortions, play an important role
in the dynamics of galaxies. Various numerical simulations
have indicated that barlike configurations are robust and
long-lived and may be a preferred configuration for
gravitationally interacting particles (Miller, 1971, 1976,
1978; Ostriker and Peebles, 1973; Hohl, 1978; Miller and
Smith, 1979). Evidence, both theoretical (Sanders and
Huntley, 1976) and experimental (Sanders and Huntley, 1976;
Huntley, Sanders and Roberts, 1978; Sanders and Tubbs, 1980)
has been presented that supports the origin of spiral arms
as being the dynamical response of a gaseous disk to a
rotating stellar bar. On the other hand, it may be the case
that spiral arms could result from either the dynamical
response of the gas to a rotating barred-spiral potential
(Liebovitch, 1978; Roberts, Huntley and van Albada, 1979) or

5
from the effects of self-gravity in a bar-driven disk of gas
(Huntley, 1980). Evidence that the gas in barred galaxies
does "sense" the presence of a stellar bar is concluded from
a morphological study of barred systems (Kormendy, 1979).
Other observational features which may have significant
implications for the modeling process are
1. The sharp bending of the bar into spiral arms.
2. The presence of luminous, giant HII regions which
often distinguish the spiral arms from the bar in the
region where the arms break from the bar.
The basic aim of this study is to observe a variety of
barred spiral galaxies and to calculate theoretical models
for each galaxy, using some of the observational parameters
as input quantities for the modeling procedure. The VLA was
used to provide detailed, high resolution observations of
the properties of the atomic hydrogen in each of the
galaxies at the highest possible signal-to-noise ratio.
These observations provide an estimate of the rotation curve
for each galaxy and allow the mapping of the galaxian
velocity field and neutral hydrogen gas distribution.
Observations in the near infrared region (7o=8250&) are
reduced to provide data for an "observed" bar, after some
M/L asumptions. This bar is used as an input parameter for
the modeling procedure. Optical observations of the gas
kinematics, where available, are used to complement the
neutral hydrogen kinematical information.

6
The modeling procedure consists of a hydrodynamical
computer code, the "beam scheme" of Sanders and Prendergast
(1974), kindly provided by Dr. J. M. Huntley. This code
calculates the response of a gaseous disk to an imposed
perturbation, for example a bar figure or an oval
distortion. The results from these models are compared with
the observations of the kinematics and distribution of the
neutral hydrogen gas.
Selection Criteria
The sample of barred spiral galaxies used for this
study was selected using several criteria;
1. The galaxy should be large, with an optical diameter
of at least 5'.
2. The bar should be prominent and large in comparison
with the 15"-30" beam synthesized at the VLA.
3. The HI surface brightness should be reasonably high
to allow observations with good signal-to-noise
ratio.
4. The object should not be too far south.
5. The system should be symmetrical.
6. The inclination of the disk of the galaxy, with
respect to the sky plane, should not be too high.
7. Surface photometry, especially in the near infrared,
I passband (A =8250Á), should be available.

7
8. A variety of types of barred spiral galaxy should be
obtained.
The first four criteria are used to ensure that the
observations are feasible in a reasonable amount of
observing time, and that the signal-to-noise ratio is
optimal. The size of the object and the bar allow good, high
resolution observations to be made and the declination
requirement is imposed to obtain as circular a synthesized
beam as possible. Criterion 5 is used to facilitate the
modeling procedure. If the galaxies are not symmetrical, the
complexity of the modeling procedure is increased greatly.
Criterion 6 avoids the problems associated with observing a
galaxy with a line-of-sight through a disk of finite
thickness. The availability of surface photometry,
especially near infrared (Criterion 7) allows an approximate
determination of the underlying distribution of non-gaseous
luminous matter (stars) in the galaxy. Near infrared
photometry gives valuable information on the distribution of
the bar mass as it can penetrate, to some extent, the dust
lanes. This in turn provides constraints on the non-
axisymmetric bar component of the gravitational potential
which is required as input data for the modeling procedure.
Lastly, a variety of galaxies is needed, spanning a range of
galaxy types. This will allow some general conclusions to be
drawn about barred spiral galaxies as a class of object.

8
The galaxies NGC 1073, NGC 1300, NGC 3359, NGC 3992
satisfy most of the selection criteria.
Survey Galaxies
The four galaxies used in this study are shown in
Figure 1-1 (a-d). These photographs are taken from various
sources. Other photographs of these galaxies which may be of
interest are near infrared exposures in Elmegreen (1981),
yellow and hydrogen alpha images in Hodge (1969), and for
NGC 1073, NGC 1300 and NGC 3359 blue exposures from the
Palomar 200" in Sandage (1961). Table 1-1 lists some global
properties of these galaxies compiled from a variety of
sources. No independent effort has been made to verify
these parameters. As can be seen from Figure 1-1 these
galaxies all have rather different morphologies and each
should present different problems for the modeling
procedure. Thus, a wide range of morphological types is
represented by this sample and should allow some general
conclusions to be drawn.
NGC 1073
This galaxy, shown in Figure 1-1 (a), is classified as
an SBT5 by de Vaucouleurs, de Vaucouleurs and Corwin (1976)
and as an SBc(sr) by Sandage (1961). The two prominent
spiral arms do not begin at the ends of the bar, but at 3CP
from the ends. The bar has a bright, central, elliptical

Figure 1-1. Survey Galaxies. Optical photographs
of the four galaxies used in this survey.
A. NGC 1073
B. NGC 1300
C. NGC 3359
D. NGC 3992
(Arp and Sulentic, 1979).
(National Geographic--Palomar Sky Survey).
(National Geographic--Palomar Sky Survey).
(National Geographic—Palomar Sky Survey).
In all photographs north is to the top and east is
to the left except for NGC 3359 where north is to the top
and west is to the left.

1G
N
Picure 1-1 cont
(Part A)

11
Figure 1-1 cont.
(Part B).

12
Figure 1-1 cent.
(Part C).

13
Figure 1-1 cont. (Part D)

14
TABLE 1.1
Global Properties of Survey Galaxies
Parameter
NGC 1300
NGC 1073
Right Ascension3
3
17 25.2
2
41 09.0
Declinatiorf
-19
35 29.0
1
09 54.0
Morphological Type*3
SBT4
SBT5
Distance (Mpc)c
17.1
13.6
Photometric Diameter^D^^(arcmin)
6.5
4.9
Photometric Diameter (kpc)
32.3
19.4
Dimensions of Optical Bar (arcmin)
2.3x0.5
1.2x0.2
Corrected Blue Luminosity^(10^ Lo)
2.39
0.93
Corrected Blue Magnitude
10.7
11.2
Parameter
NGC 3359
NGC 3992
Right Ascensioif
10
43 20.7
11
55 01.0
Declinatiorf
63
29 12.0
53
39 13.0
Morphological Type*3
SBT5
SBT4
Distance (Mpc)c
11.0
14.2
Photometric Diameter*3 D^j- ( arcmin)
6.3
7.6
Photometric Diameter (kpc)
20.2
31.4
Dimensions of Optical Bar (arcmin)
1.7x0.6
1.7x0.5
Corrected Blue Luminosity^(10^ Lo)
1.08
2.40
Corrected Blue Magnitude
10.6
10.22
a Gallouet, Heidmann and Dampierre (1973).
b De Vaucouleurs, de Vaucouleurs and Corwin (1976).
c De Vaucouleurs and Peters (1981).
d Calculated using above values of distance and magnitude,
and using Mg(o)=+5.48 (Allen, 1973).

15
region, decreasing in brightness noticeably before meeting
the arms. The ring is not complete and there are no straight
absorption lanes. Both the arms and the bar can be resolved
into many knots. The west arm appears to bifurcate at about
the end of the bar. Arp and Sulentic (1979) identified three
quasars in the field of NGC 1073, namely objects 1,2 and 3
in Figure 1-1 (a).
NGC 1300
NGC 1300, Figure 1-1 (b), is described by Sandage
(1961) as the prototype of the pure SBb(s) system. It is
classified as an SBT4 by de Vaucouleurs, de Vaucouleurs and
Corwin (1976). The bar is very prominent, distinct and
smooth in texture, with two straight dust lanes emerging at
an angle from the nucleus and following the bar to its ends
and turning sharply and following the inside of the spiral
arms. The two arms start abruptly at the ends of the bar
each forming almost complete ellipses with the nucleus and
the other end of the bar being the approximate foci. They
can be traced through almost 340 °.
NGC 3359
This galaxy, Figure 1-1 (c), described by Sandage
(1961) as being a broken ring galaxy, is classified an
SBc(rs), and as an SBT5 by de Vaucouleurs, de Vaucouleurs
and Corwin (1976). A fairly prominent two-armed pattern

16
emerges from a strong central bar. The arms are asymmetric,
with the arm beginning at the southern end of the bar being
far less structured than the other. This arm appears to
break up into two or more segments whereas the other arm
more closely follows a "grand design" spiral pattern. There
is a high degree of resolution of both bar and arms into
knots.
NGC 3992
Significant spiral structure (two bifurcated arms or
possibly even a three-arm pattern) emerges from an
incomplete ring surrounding the bar in NGC 3992 (Figure 1-1
(d) ) . De Vaucouleurs, de Vaucouleurs and Corwin (1976)
classify this galaxy as an SBT4. Two absorption lanes are
visible emerging from a bright, central nuclear region. The
bar is smooth in texture but the arms can be resolved easily
into knots.
This dissertation will describe in detail, the
observations, reduction and analysis, and hydrodynamical
modeling of NGC 1300. Data for NGC 1073, NGC 3359 (Ball,
1984, 1986) and NGC 3992 (Hunter et al., 1986) are published
elsewhere and only the conclusions are utilized here. The
neutral hydrogen data collection, reduction and analysis are
described in Chapters 2 and 3. Surface photometry in the
blue, near infrared and 2.2um passbands is discussed in
Chapter 4, with the results from Chapters 3 and 4 being used

17
in the hydrodynamical modeling in Chapter 5. The
observational and modeling results for NGC 1073, NGC 3359
and NGC 3992 are summarized in Chapter 6 and comparisons
between these galaxies are made in Chapter 7. A summary of
all the results is presented in Chapter 8.

CHAPTER II
RADIO OBSERVATIONS
HI As A Kinematic Tracer
To successfully model and understand the dynamics of a
barred spiral galaxy, some sort of tracer of the dynamics of
the system is needed. Any tracer which is closely associated
with the gas may be used. Several components are available
for use as this tracer. Observations of the optical Hydrogen
alpha line provide velocities for HII regions, which are
associated with hot young stars which have recently formed
from the gas. Observations of the other Population I
component, molecular gas clouds, also could provide the
kinematical information needed. However, both these
measurements have serious drawbacks. The HII observations
have high spatial resolution but generally very incomplete
coverage. This is due to the dumpiness of these regions
which means that only velocities near the hottest stars can
be measured. Molecular hydrogen, which presumably makes up a
significant portion of the molecular clouds, is difficult to
detect. Carbon monoxide, CO, the second most abundant
interstellar molecule, coexists with molecular hydrogen and
can be used to map the molecular regions in galaxies and
elucidate the varying rates of star formation (Black, 1985;
18

19
Dalgano, 1985). CO is usually far more concentrated in the
inner disk (Morris and Rickard, 1982), although it does
appear to follow the intensity distribution of the blue
light (Young et al., 1984; Young, 1985). The CO transitions
are fairly easy to excite and lie in the millimeter
wavelength region.
A dominant component of the gas of the interstellar
medium consists of neutral hydrogen, HI, in its ground
state. It is well-distributed spatially and is relatively
easy to detect. This gas has a spin temperature, T^ , of
approximately 100K (Mihalas and Binney, 1981 p485). The
ground state is split into two hyperfine levels separated by
6xl0"6 eV. This energy difference is extremely small; it
corresponds to a temperature T=0.07K (through E=kT), well
below the ambient temperature of the surrounding medium,
and, consequently, much of the gas is in the upper level.
The upper level, or ortho-state, has the dipole moments of
the electron and nucleus parallel and the lower level, the
para-state, has the dipole moments anti-parallel. The
probability of the forbidden ortho-para radiative
transition, the F=1 to F=0 spin-flip transition, is so low
7
that the mean lifetime of the excited level is 1.1x10 yrs.
In contrast, the collisional de-excitation timescale is much
shorter, 400yrs at N =20atoms/cm than the radiative de¬
excitation timescale, even in the low densities typical of
the interstellar medium. This implies that collisions can

20
establish equilibrium populations in the two levels, which
means that there will be nearly three atoms in the upper
level (which is threefold degenerate) to every one in the
lower level.
Because the collisional excitation and de-excitation
rates are so much faster than the rate of radiative decay,
the atomic populations n^ and in the two levels will be
essentially the same as those expected in thermodynamic
equilibrium. Thus,
n2/ni = (g2/9i) exP (-hv/kTs) (2-1)
where g2/g^=3 is the ratio of the degeneracies of the two
-4
levels. In a typical cloud T =100K, so (hv/kT =6.8x10 and
8 S
exp (~h v/kTs^0.9993, giving,
n2/ni : g2/gi = 3* (2-2)
In terms of probability coefficients,
nlC12 = n2 (2-3)
where C^2 and C2^ are collisional probabilities and ^2^ is
the Einstein probability coefficient for spontaneous
radiative decay from level 2 to level 1. As a2^ is small,
nlC12 = n2C21
(2-4)
and approximate equilibrium is established. Although ^ is
small -2.868xl0"g^ sec--*-, radiative decay is the observable
transition mechanism. The large column densities along a
typical line-of-sight in a galaxy make this radiative

21
transition detectable. This transition is observable at a
frequency of 1420.40575MHz (Ao=21.105cm) . Its observation
was predicted by van de Hulst (1945) and first measured by
Ewen and Purcell (1951). Muller and Oort (1951) and
Christiansen and Hindman (1952) confirmed the measurement.
Neutral hydrogen generally covers a region larger than
the observed optical object and thus provides good coverage
of the whole disk of the galaxy and not just selected
regions, as do Hydrogen alpha observations. If the outermost
regions are excluded, then HI is among the flattest and
thinnest of the disk components of ours and other galaxies
(Jackson and Kellerman, 1974). This allows the
determination, with a resonable degree of confidence, of the
two-dimensional location of any observed emission. This gas
is pervasive enough that the emission recorded by radio
telescopes appears to be continuously distributed.
If the neutral hydrogen gas is assumed to be optically
thin, a simple integration of the brightness temperature,
T , over velocity, V, determines the column density, N , of
B h
the gas at that point (Mihalas and Binney, 1981 p489):
N (x,y)
h
1.8226 x 1018 T (x,y) dV,
B
(2-5)
where V is in km/s, T is in Kelvin,and, N
B
h
• O
in atoms/cra .
The mean temperature-weighted velocity at a point is
given by the first moment with respect to velocity

22

r00
lTB(x,y) V(x,y)dV
T0(x,y) dV
(2-6)
If the neutral hydrogen gas is not optically thin this
will lead to an underestimate of the surface density. In
this case the observed brightness temperature, , would
approach the physical, spin temperature of the gas, T g.
In general,
tb = Ts(1'e’t)' <2-7)'
and, for an optically thin gas, t< S
optically thick gas, T =T0 (Mihalas and Binney, 1981 p487).
.D O
The highest observed brightness temperature for NGC
1300, averaged over the beam, was 16.95K. Assuming a mean
temperature for the gas of 100K (McKee and Ostriker, 1977;
Spitzer, 1978) gives an approximate optical depth of t=0.19,
thereby justifying the optically thin assumption. Although
this leads to an underestimate of the column density the
effect is <15% at the peak emission and will be less at
other points. As the "optical depth structure" of the medium
is not known, the assumption of an optically thin medium
will be retained.

23
Thus, in summary, neutral hydrogen provides a good
tracer for the kinematics of the gas in a galaxy;
1. It is well distributed spatially.
2. It is relatively easy to observe.
3. Assuming it is optically thin, the above simple
expressions hold for the column density of the gas
and the mean velocity of the gas at an observed
location, equations 2-5 and 2-6.
Aperture Synthesis Theory
The neutral hydrogen content of NGC 1300 was observed
using the Very Large Array (VLA) of the National Radio
Astronomy Observatory (NRAO). The VLA is the largest and
most sensitive radio telescope which exploits the principle
of earth-rotation aperture synthesis. The array is a
multiple-interferometer instrument using a maximum of 27
antennae. As the basic theory of interferometry and earth-
rotation aperture synthesis is well covered in Fomalont and
Wright (1974), Hjellming and Basart (1982), Thompson (1985),
D'Addario (1985), Clark (1985) and, from an electrical
engineer's perspective in Swenson and Mathur (1968), only a
brief discussion will be given here and some fundamental
results quoted.
The basic process of interferometry is the cross¬
correlation of signals from two antennae observing the same
source. The resulting signal is analogous to the

24
interference pattern in the classical optical double slit
experiment. The cross-correlation of these two signals
produces information on both the intensities of sources in
the beam of the antennae and on their positions relative to
the pointing position of the antennae. Any distribution of
radio emission in the beam of an antenna can be considered
as a superposition of a large number of components of
different sizes, locations and orientations. As the
relationship between intensity distributions and the
components can be described in terms of a Fourier integral,
it follows that an interferometer pair, at any instant,
measures a single Fourier component of the angular
distribution of sources in the beam pattern. The essential
goal in radio aperture synthesis observations is to measure
a large number of these Fourier components. This procedure
allows the reconstruction of an image of the spatial
intensity distribution of sources in the beam. The VLA
achieves the measurement of a large number of Fourier
components by using multiple interferometer pairs and
allowing their geometric relationships with the sources in
the sky to change by utilizing the rotation of the earth,
hence the term earth-rotation aperture synthesis. For
multiple interferometer pairs, N antennae, there are
N(N-l)/2 different baselines, or samples of the Fourier
components, at any one instant. The VLA has a maximum of 27
antennae or 351 samples of the Fourier components. These

25
samples are not all unique as there is redundancy in the
baselines.
The output from a two element interferometer can be
shown to be
V (u,v)
oo
I'(X,y)
exp[-i2-rr (ux+vy) ]dx dy
(2-8)
where I'(x,y) is the observed brightness distribution,
V (u,v)is the observed complex visibility, and u,v are
projected spacings in east and north directions
respectively, sometimes called spatial frequencies
(Hjellming and Basart, 1982).
This shows that a single measurement of the complex
visibility, v' > corresponding to a particular projected
baseline, or particular (u,v) point, gives a single Fourier
component of I', the observed brightness distribution. The
similarity theorem of Fourier transforms (Bracewell, 1965)
shows that large extent in the (x,y) plane means small
extent in the (u,v) plane and vice versa. Thus, achievement
of high spatial resolution requires large spacings between
the antennae in an interferometer pair, and conversely,
large scale structure requires low spatial frequencies,
short spacings.
Equation 2-8 can be inverted to give the observed
brightness distribution I' as a function of the measured
complex visibilities, v' ,

26
I’ V (u,v) exp[i2ir (ux+vy) ]du dv
(2-9)
where I' is the product of the true brightness distribution
I and the single antenna power pattern A,
I'(x,y) = A(x,y) IQ(x,y)
(2-10)
These results have been calculated in the absence of
noise. Since all observations measure only a finite number
of (u,v) points and all contain noise, 11 cannot be
determined uniquely or without error. A later section deals
with the problem of missing complex visibilities and the
non-uniqueness of the solution of equation 2-9.
The extension of these results to spectral line
observations introduces several complications. The signal
has to be divided into a number of independent, narrow-band
spectral channels. At the VLA this is achieved by
introducing an additional delay, tj , into the signal path.
This delay destroys the coherence of the received signals
except for those in a narrow frequency range centered on
some frequency v_. . Changing this delay changes the frequency
v and allows the signal to be divided into a number of
independent, narrow-band channels. The integration of
equation 2-8 over bandwidth gives
V(u,v,t)

27
where F(v)is the frequency bandpass function.
Due to the symmetry of the delays introduced, only the
real part needs to be Fourier transformed, giving (Hjellming
and Basart, 1982)
r"
Re [V1 (u, v, t) ] exp (i 2 -rr v t) dt =
oo
oo
|jl'(x,y) F (v) exp[i2-rrv (ux+vy) ]dx dv. (2-12)
— oo
This is the Fourier transform at one of the frequencies
and contains all the visibility information necessary to map
the source at that frequency. Equivalently, as the number of
delays t^ is finite, this procedure allows the mapping of
the narrow-band channels. The right hand side of equation
2-11 contains the bandpass function, f (v) , which must be
calibrated. This is done by observing a strong continuum
source, which is assumed to exhibit no spectral variation
over the quite narrow total bandpass normally used for
spectral line work.
Observing Strategy and Calibration
In an interferometer, such as the VLA, high resolution
is achieved by using large separations of the antennae.
Conversely, broad structure requires relatively small
spacings; thus, both long and short spacings are required to

28
measure both the small scale and the extended structure in a
galaxy. However, the higher the resolution, the poorer the
brightness sensitivity. This conflict demands that a
compromise be made between sensitivity and resolution.
The minimum detectable flux density, AS . , depends
min
only upon system temperature, bandwidth, integration time
and effective collecting area, viz.,
(2-13)
where T is the system temperature in Kelvin, A is the
SYS o
effective collecting area, Av is the bandwidth in Hz, and, t
is the integration time in hours.
The effective collecting area A where A^ is the
total area and n is the aperture efficiency.
However, for resolved sources the detectable brightness
temperature is the important quantity, and
(2-14)
where is the synthesized beam solid angle.
The synthesized beam is the power pattern of the array
as a whole, rather than the power pattern of an individual
antenna. Thus, for a point source, the synthesized beam is
the observed normalised brightness distribution.
Consequently, as resolution is improved the brightness
sensitivity is degraded, and vice versa.

29
If observing time were unlimited, the choice of arrays
would be an easy undertaking. The resolution required would
dictate the largest separation of the antennae, and the
required signal-to-noise ratio would dictate the amount of
integration time needed. However, as observing time is
limited, in order to determine which array configurations
were practical to use for this project required
consideration of both the resolution needed to observe the
structure and the sensitivity needed to ensure that the
majority of the gas was observed. Another factor which had
to be considered was that, as the VLA was used as a
spectrometer, the sensitivity in each narrow line channel is
relatively poor. With these considerations in mind, it soon
became evident that the two lowest resolution
configurations, the D and C arrays, would be the only two
practical configurations to use for a resonable amount of
observing time. The D array would ensure that no low
amplitude large scale structure emission was missed, whereas
the C array would resolve the smaller scale structure. Using
only these two arrays means that some small scale structure
below the resolution limit of the C array will be missed,
but will ensure that the majority of the emission was
observed. As the best peak signal-to-noise ratio observed in
any of the channels was 13.4 this would mean that the best
detection achievable with the next largest array, the B
array, would be, for the same amount of observing time, a
less than "two sigma" detection.

30
In spectral line observations the correlator must
multiply the signals from 2n delay lines for each of
N(N-l)/2 baselines, where n is the number of spectral
channels and N is the number of antennae used. The
correlator thus has an upper limit for the product nN which
necessitates a compromise when choosing n and N. The larger
the value of n, the greater the spectral, and hence
velocity, resolution but the poorer the sensitivity. The
larger N is, the better the sensitivity as more antennae
contribute to the signal. Ideally the largest values
possible for n and N are required. However, as n has to be
an integer power of two to allow the Fourier transform of
the lag spectrum to be calculated using Fast Fourier
Transform techniques (FFT), this also places some
restrictions on n.
The choice of n depends upon the velocity range of the
global profile of the galaxy under study and the velocity
resolution desired. Also, a few "line-free" channels on each
end of the spectrum are desirable to allow the continuum
emission to be mapped. Previous studies and single dish
results (Bottinelli et al. , 1970) indicate that the global
profile for NGC 1300 has a velocity width (full width at a
level of 25% of the peak level) of 290km/sec. These
observations, coupled with the other considerations above,
lead to a choice of n=32 with a single channel separation of
20.63km/sec, 97.656kHz. This choice of n allowed a maximum

31
of 25 antennae to be used. The discarded antennae were
chosen simply on the basis of their recent malfunction
performance.
During the observing run the central channel, channel
16, was centered on 1540km/sec, a value equal to the
approximate mean of other previous determinations of the
systemic velocity; Sandage and Tammann (1975) find
1535±9km/sec; de Vaucouleurs, de Vaucouleurs and Corwin
(1976) find 1502+10km/sec; and Botinelli et al. (1970) find
1573±7km/sec. Channel 32 was chosen as the central channel
in order to avoid using the end channels in the 64 channel
spectrometer. Due to Gibbs phenomenon (oscillations in the
bandpass function at the edges of the bandpass) a few
channels at either end of the spectrometer are severely
degraded, and it was considered prudent to avoid these
channels. The mean velocity is a heliocentric velocity
calculated using the definition
V
AA
(2-15)
Thirty-one of the channels are narrow line channels
separated by 20.63km/sec, 97.656kHz, with a full width at
half maximum (FWHM) of 25.2km/sec; the thirty-second is a
pseudo-continuum channel with a total width of lOOOkm/sec,
4.7MHz. This channel, designated channel zero, contains the
true continuum emission plus the line signal, utilizes ~75%

32
of the intermediate 6.25MHz broad band filter, and was used
primarily to calibrate the line channels. As this is a broad
band channel, the sensitivity to the calibration is much
greater (~7x) than that for the line channels. Consequently,
the calibration procedure was carried out using channel zero
and then applied to the single line channels once a
satisfactory solution was found. This procedure is
summarized below.
The flux density for the primary calibrator, 3C48, is
forced to assume some "known" value at the frequency of the
observations (VLA calibration manual based on Baars et al.,
1977). Using the flux densities of the secondary calibrators
as free parameters, a solution for amplitude and phase for
each antenna in the array is computed as a function of time.
All the scans of the secondary calibrators are utilized for
this solution. Baselines with closure errors greater than
some specified limits in amplitude and phase ( ~10% in
amplitude and 10° in phase) can then be identified and
rejected. If the assumption is made that the complex gain
for the antenna pair jk, G_.^t), can be represented by
amplitudes g. (t) and g^ (t) and phases . (t) and ^ (t)
then,
Gjkp(t) = gjp(t)exp[1('tljp+V]9kp(t) + Ejkp (2-16
where e are the closure errors. Thus, the smaller these
jkp
closure errors the better the approximation becomes for the
actual complex gain. For the mode of observing employed for

33
these observations, few baselines had closure errors as
o o
large as 10% and 10 , and most were below the 7% and 5
range. After rejecting the baselines with unacceptable
closure errors, the antenna solution is repeated. This
iterative procedure is continued until acceptable solutions
have been found for the complex gains.
This procedure utilizes one antenna as a reference
antenna for the array. It is thus worthwhile repeating the
calibration using a different reference antenna to improve
the solution. The reference antenna should be particularly
stable compared with the rest of the array and should have
variations which are as slow as possible and not be
monotonic functions of either space or time. A good stable
antenna usually can be found by repeating the calibration
procedure for a few different antennae.
Once acceptable solutions for the complex gains have
been found using the primary calibration source, fluxes for
the secondary calibrators can be determined. These fluxes
are generally called "bootstrapped" fluxes and their errors
give a good indication of the stability of the atmosphere
during the observing run.
The bootstrapped fluxes can be applied to the entire
dataset, including the program object observations, by a
simple running mean, or "boxcar" interpolation of the
amplitude and phase gains of the individual antennae. At
every step of the process the database is inspected and

34
suspect signal data are flagged, hopefully leading to a
better solution from the next iteration and not seriously
degrading the overall quality of the dataset. The quality of
the dataset is usually not degraded very much as there is a
large duplication of baselines and rejecting a few data
points does not have a large overall effect on the database.
The final step in the calibration procedure is to calibrate
the bandpass by assuming a flat spectrum for the primary
calibrator over the total spectral-line bandwidth. The
purpose of the bandpass calibration is to correct for the
complex gain variations across the spectral channels. The
bandpass usually varies only slowly with time and usually
has to be measured only once during an observing run. The
data are now ready for Fourier inversion and image
processing.
Generally, the data for this project were unaffected by
any serious problems, and few baselines or scans had to be
flagged in the calibration procedures. However, the data
from Summer 1984, for the second half of the observing run,
exhibited some anomalous records at the beginning of each
scan. The source of these anomalous records was not
discovered and the records were simply deleted from the
dataset. This improved the antenna solution noticeably and
allowed an acceptable solution to be calculated quickly.
Another problem with the more compact arrays when observing
a source with a low southerly declination, such as NGC 1300

35
( <5=-19°35' ) is "shadowing." This occurs when the projected
separation of two antennae is smaller than the physical
diameter of the antennae, 25m. This means that one antenna
is partially blocking the other's view of the source. A
correction for this effect can be applied, or the offending
antenna can simply be removed from the database for the
appropriate timerange. This "shadowing" also causes a more
subtle problem for the calibration procedure. When one
antenna is "shadowing" another, even slightly, the data
collected during that time range by the "shadowed" antenna
has a noticeable deterioration in quality. This "crosstalk"
arises when the shadowed antenna detects signals from the
electronics of its neighbour. As this effect can be
difficult to detect, the safest method to avoid "crosstalk"
is to flag all data from "shadowed" antennae. For NGC 1300
this amounted to approximately 2% of the data, the majority
being at the beginning and the end of the run, at large hour
angles, or low elevation angles. The amount of data flagged
did not degrade seriously the overall quality of the
database and allowed a good antenna solution to be
calculated. Apart from these two problems, which were easily
corrected, NGC 1300 showed no unpleasant surprises and a
good solution was arrived at in a few iterations of the
calibration procedure.
The galaxy NGC 1300 was observed using the D/C hybrid
configuration on the 9th and 12th July 1984. A total of 25

36
antennae, evenly distributed over the three arms, was used.
The north arm was in the C array configuration and the
southwest and southeast arms were in the more compact D
array configuration. This hybrid configuration allowed a
nearly circular beam to be synthesized and gave a maximum
unprojected separation of 2106.6m (9982X) and a minimum
unprojected separation of 44.6m (213X). Seven hours of
observing time were used on the 9th of July, 1984 and seven
hours on the 12th of July, 1984.
Calibration sources were observed at the beginning of
the session, every 40 minutes during the run, and again at
the end of the session. More frequent observations of the
calibrators were not deemed necessary as the timescale for
phase stability of the atmosphere at 21cm (1420MHz) is
considered to be a good deal longer than the intervals
chosen here. The bandpass calibrator source, 3C48, was
observed three times during the session: at the beginning,
in the middle, and at the end. This also provided a check
on the overall stability of the system as it allowed a
comparison of the phase and amplitude response over the
whole session.
The primary calibrator, 3C48, was used to calibrate the
receiver bandpass and the flux densities of the secondary
calibrators. Two secondary calibrators, 0237-233 and
0420-014, were needed for NGC 1300 due to the relative
positions of available calibrators and the galaxy itself.

37
0237-233 was used for the first 4 hours of the observing run
and 0420-014 for the remaining 3 hours of the run. The
transition from one secondary calibrator to the other was
accomplished by using the primary calibrator as an
intermediate step between the two.
The 1985 observations employed 25 antennae in the C/B
hybrid configuration. The north arm was once again in the
higher resolution configuration and the antennae were evenly
distributed over the three arms. The configuration gave a
maximum unprojected separation of 6920m (32953a) and a
minimum unprojected separation of 78m (372a). A total of 6
hours of observing were obtained using this hybrid array on
the 28th of June, 1985 and 7.5 hours on the 1st of July,
1985. The phase and amplitude calibration of the data were
done by using the same sources as for the D/C hybrid array;
the observing strategy was the same for both seasons. The
flux densities of these sources and the receiver bandpass
were once again calibrated using 3C48. Table 2-1 lists
calibrator positions and fluxes.
Map-Making and Image Processing
The fundamental result of the aperture synthesis
description is the existence of a Fourier transform
relationship between the modified sky brightness and the
visibility observed with an interferometer,
f°r
I'(x,v) =
J J
— oo
V' (u,v) exp[i2-rr (ux+vy) ]du dv
(2-17)

TABLE 2.1
Properties of Survey Calibrators
Calibrator
(1)
P/S
(2)
Frequency
(3)
Epoch
(4)
Array
(5)
Flux Density
(6)
3C48
P
1413.251
Jul 84
C/D
15.82
P
1413.240
Jun 85
B/C
15.82
0237-233
S
1413.251
Jul 84
C/D
6.25
S
1413.240
Jun 85
B/C
6.12
0420-014
s
1413.251
Jul 84
C/D
2.03
s
1413.240
Jun 85
B/C
2.22
3C48
01
34 49.8
(1950)
32
54 20.5
0237-233
02
37 52.7
(1950)
-23
22 06.4
0420-014
04
20 43.5
(1950)
-01
27 28.6
(1) Calibrator identification.
(2) Primary (P) or Secondary (S) calibrator.
(3) Frequency of observation (MHz).
(4) Epoch of observation.
(5) Array configuration employed for observations.
(6) Flux adopted for primary or determined for
secondary calibrators.

39
where I' is the product of the true brightness
distribution, I0, and the single dish power pattern, A ,
equation (2-10) •
This result can be used to derive the source brightness
distribution from the observed interferometer visibilities.
These visibilities are observed at a number of discrete
(u,v) points. With a small number of points, model-fitting
of the points is feasible, but as a VLA spectral-line data¬
base typically consists of -500,000 points the most
practical way of constructing the brightness distribution is
to use Fourier inversion techniques.
There are two common ways of evaluating the Fourier
transform:
1. By direct evaluation of equation (2-17) at the
individual sample points, Direct Fourier Transform,
DFT.
2. By using a Fast Fourier algorithm, FFT.
The advantages of the DFT are that aliasing and
convolution introduced by the gridding procedure for the FFT
are avoided, but the disadvantage is that the number of
multiplications for an NxN grid of M data points a 2MN ,
which can be substantial for the large datasets usually
considered in spectral line observations. The use of the FFT
2 2
reduces the number of multiplications to N logN , which can
save a considerable amount of computing time. However, for
the FFT the data points must be on a rectangular grid,mxp,

40
where m and p are integer powers of two. The use of FFT
algorithms can lead to the introduction of aliasing in the
maps. This aliasing results from the gridding process. The
gridded visibilities may be represented as
V(u,v) = III(u,v)• [c(u,v)*S(u,v)•V (u,v)] (2-18)
where III is a two-dimensional Shah function, S is a
sampling function, and C is a convolving function.
Due to the presence of the Shah function and the fact
that the Fourier Transform of C is not exactly zero beyond
the map limits, parts of the brightness distribution that
lie outside the primary map field will be aliased into the
primary field. The simplest way to tell if an image is
aliased is to remap the field with a different cell size.
The aliased source will appear to move while a primary
source will stay the same angular distance from the field
center.
The most common grid for the FFT is a square grid (m=p)
with the (u,v) spacings comparable with the cell size; as
the observed data seldom lie on these grid points, some
interpolation method must be used to specify the
visibilities at the grid points. If a scheme which resembles
a convolution in the (u,v) plane is used, then the image
will have predictable distortions which can be corrected at
later stages of the reduction procedure. A convolution also
smoothes the data, providing a good estimate of the gridded
visibility from noisy input data.

41
The best way to avoid, or at least reduce, aliasing
problems is to use a convolving function, C, that results in
a fast drop-off beyond the edge of the image. This requires
that C be calculated over a large region in the (u,v) plane,
requiring a large amount of computing time. Thus, in
practice, a compromise between alias rejection and computing
time must be reached. The function C should ideally be flat
out to some distance and then drop off sharply without
having sidelobes beyond the edges of the map. The lack of
high sidelobes helps suppress the aliasing of sources lying
outside the map into the map. Aliasing of sources that lie
off the primary image back into the map is only part of the
problem. A primary image source will have sidelobes
extending beyond the edge of the image. These sidelobes will
be aliased back in, effectively raising the background and
resulting in a beam shape that is position invariant
(Sramek, 1985). Thus, the convolving function suppresses
aliasing due to replication of the image in the gridding
process. It suppresses aliasing but not sidelobe or ringlobe
responses from sources outside the area of the map. With
alias suppression of 10^ or 10 ^ at two or three map radii,
it is these sidelobe responses which may cause the dominant
spurious map features. As C is usually separable
C(u,v) = C (u) C (v) (2-19)
where

42
C (x) = J 1-n2 (x) | % (c,n (x))
a . o
,o
n(x) = x/mAx
and
4» (c,n) = (1-n )
a ,o
2.-a/2
(2-20)
The function s (C,n) is a prolate spheroidal wave function
a r a.
(Schwab, 1980). At the VLA the parameters used are
generally m=6, a=l, n=0. Figure 2-1 shows the form of this
function.
It is desirable not to have the product NAu so large
that the outer cells are all empty and the inner ones
heavily undersampled, nor so small that many points at large
spacings are rejected. For the VLA spectral-line observing
mode an empirical relationship which produces good sampling
is that the synthesized beam be about three to four times
the cell size of the intensity images,ag •
Once the data have been convolved, the map must be
sampled to produce the gridded values. The sampling function
is a two dimensional Shah function (Bracewell, 1965),
HI(u,v) = AuAv EE 6 [ (u-jAu) , (v-kAv) ] (2-21)
where Au,Av are the separations between grid points.
Unfortunately, the sampling in baseline space by a
rotation synthesis array, such as the VLA, is non-uniform.
The projections (u,v) of sample points, with respect to a
reference direction, are therefore non-uniformly distributed

Log (WEIGHT)
43
Figure 2-1. Spheroidal Convolving Function. Side-
lobe responses for the gridding function used in this study.

44
with varying density inside an irregular boundary, all of
which depend upon the source declination, see Figure 2-2 for
(u,v) coverage. Therefore some sort of weighting function,
W, is necessary to correct for this effect and to control
the synthesized beam shape. The sampling function can then
be written
00
III (u,v) = AuAv T.J. W6 [ (u-j Au) , (v-kAv) ] . (2-22)
The weighting function is usually expressed as the
product W=dt where d corrects for the varying number of
observed samples in each gridded cell, and t introduces a
taper to reduce the sidelobes. The beam usually consists of
a Gaussian core with broad sidelobes at a one to ten percent
level. The shape of the sidelobes is simply the Fourier
transform of the unsampled spacings in the (u,v) plane out
to infinity. The taper, t, weights down the sparsely-sampled
outer region of the (u,v) plane and helps suppress the small
scale sidelobes at the expense of a broader beam. The
tapering function is usually a truncated Gaussian function
(Sramek, 1985).
The other weighting function, d, is generally choosen
from one of two extremes, natural or uniform weighting.
Natural weighting weights all observed samples equally: d=l.
Thus, the weight of each gridded visibility is proportional
to the number of observed visibilities contributing to that
sample. Since the density of observed samples is always

Figure 2-2. (u,v) Coverage. Schematic representa¬
tion of the (u,v) coveraae obtained by the observations of
NGC 1300.


47
higher for the shorter baselines, this tends to produce a
beam with a broad low-level plateau (Sramek, 1982). However,
this type of weighting gives the best.signal-to-noise ratio
for detecting weak emission. Natural weighting is
undesirable for imaging sources with both large and small
scale structure, such as extended emission from galaxies.
Although the sensitivity is increased, the broad beam
degrades the resolution and the small scale structure will
become dependent on the beam shape. To remove the broad
plateau each gridded cell is weighted by the inverse of the
number of observed visibilities contributing to that cell:
d=l/N. This weighting is called uniform weighting and, since
not all visibilities are equally weighted, there will be a
degredation in signal-to-noise ratio. Uniform weighting
gives the same weight to each cell in the gridded (u,v)
plane and the beam characteristics are controlled largely by
the tapering, t (Sramek, 1985).
In principle the procedure for producing the gridded
visibilities for the application of the FFT is
1. Convolve the observed visibility data points to
produce a continuous function.
2. Resample this continuous function at the grid points.
3. Apply the weighting and taper to the resampled data.
These gridded visibilities can now be Fourier inverted,
using equation 2-17, to produce an estimate of the source
brightness distribution. For NGC 1300 the Fourier inversion

48
was performed using a 6" cell size with a 7kA taper (1484m)
and uniform weighting producing 32 single channel "dirty
maps" and their associated "dirty beams." These dirty maps
are given by the true brightness distribution convolved with
the dirty beam.
Direct Fourier inversion of the observed visibilities,
with all unsampled visibilities set to zero, gives the
principal solution, or dirty image. Thus, the quality of the
image depends entirely upon the sampling in baseline space.
In general this sampling is non-uniform. It is obvious that
the true image cannot be as complex as this dirty image,
where the visibility vanishes at all positions not sampled
by the observation. There must be image components invisible
to the instrument with non-zero visibilities at the
unsampled positions. The unsampled points in the (u,v) plane
give rise to the sidelobes of the dirty beam and reflect an
unavoidable confusion over the true brightness distribution.
Some estimate of these unsampled or invisible image
components is necessary to augment the principal solution in
order to obtain an astronomically plausible image. The
scheme most widely used is the CLEAN algorithm introduced by
Hogbom (1974). CLEAN performs a function resembling
interpolation in the (u,v) plane.
The CLEAN algorithm uses the knowledge that radio
sources can be considered as the sum of a number of point
sources in an otherwise empty field of view. A simple

49
iterative procedure is employed to find the positions and
strengths of these point sources. The final image, or
"clean" image, is the sum of these point components
convolved with a "clean" beam, usually a Gaussian, to de-
emphasize the higher spatial frequencies which are usually
spuriously extrapolated.
The original Hogbom algorithm proceeds as follows:
1. Find the strength, M, and position of the point
brightest in absolute strength in the dirty image.
2. Convolve the dirty beam with a point source, at this
location, of amplitude yM, where y is the loop gain,
and y<1.
3. Subtract the result of this convolution from the
dirty map.
4. Repeat until the residual is below some predetermined
level.
5. Convolve the point sources with an idealized clean
beam, usually an elliptical Gaussian fitted to the
core of the dirty beam.
6. Add the residuals of the dirty image to the clean
image. Keeping the residuals avoids having an
amplitude cut-off in the structure corresponding to
the lowest subtracted component and also it provides
an indication of the level of uncertainty in the
brightness values.

50
Since the basis of this method is to interpolate
unobserved visibilities, the final image is the consequence
of preconceived astrophysical plausibility. Interpretation
of fine detail in clean maps should recognise this non¬
uniqueness of the solution.
Clark (1980) developed a variant of the Hogbom
algorithm. The basic idea is to separate the operation of
peak locating from that of convolution-subtract and perform
the convolution-subtract step on a large number of point
sources simultaneously. The algorithm has a minor cycle in
approximate point source location using a truncated beam
patch, which includes the highest exterior sidelobe, and a
major cycle in proper subtraction of a set of point sources
(Clark, 1985; Cornwell, 1985).
It should be clear that CLEAN provides some sort of
estimate for unsampled (u,v) points. In most cases it does
this reasonably well. However, quite often it underestimates
the "zero-spacing" flux, the integral of the flux over the
clean image. This results in the source appearing to rest in
a "bowl" of negative surface brightness. Providing an
estimate of this flux (from single dish measurements for
example) can sometimes help (Cornwell, 1985).
In using CLEAN a decision has to be made concerning
various parameters:
1. Is the addition of the zero-spacing flux necessary?

51
2. Over what region of the image should the CLEAN be
done?
3. How deep should the CLEANing go, i.e. at what level
should the cutoff be?
The solution to these questions for NGC 1300 was
arrived at by considering the following:
1. The galaxy was observed using the D array. This array
contains short spacings and thus, the unsampled
region in the (u,v) plane is small. Owing to this, no
zero-spacing flux was added. The decision was
justified as np evidence for a negative brightness
bowl was seen, meaning that CLEAN had provided a good
estimate for this flux. The total flux measured at
the VLA was 36.53Jy(km/sec) compared with
30.3Jy(km/sec) found by Reif et al. (1982).
2. All the line channels were examined and limits set on
the spatial extent of the signal in each channel.
This allowed only regions containing signal to be
used in CLEANing, thus avoiding the time-consuming
CLEANing of regions containing only random noise.
3. When CLEAN is applied to maps correctly the resultant
"blank" sky should show only random noise and no
sidelobe structure. The rms noise level should be
approximately the same from channel to channel and
should also be approximately equal to the expected
rms noise level for spectral-line maps with natural
weighting (Rots, 1982);

52
a = a[N(N-l) T^v]"1/2 (2-23)
where N is the number of antennae used, a is a
constant, a=620 for 21cm, T. is the total on-source
i
integration time in hours, and Av is the bandwidth in
kHz.
For NGC 1300 using 25 antennae, N=25, T^ =20.58hr,
A v =97.656kHz gave an expected rms noise level of
0.6mJy/beam. The rms noise level for the dirty maps is
~0.8mJy/beam and for the clean maps .. 0.7mJy/beam and thus
indicates that the CLEAN was acceptable. Table 2-2 shows the
rms noise level for the dirty maps and the rms noise level
for the clean maps. Once the expected rms value has been
reached the CLEANing is stopped; proceeding beyond this
point is tantamount to shuffling the noise around. For NGC
1300 this limit was generally reached after 1000 iterations,
as the loop gain was small, y=0.15.
Before the spectral-line channels are CLEANed some
method of subtracting the continuum emission must be
utilized. Continuum emission usually consists of unresolved
point sources as well as some emission from the central
region of the nucleus. The method used for NGC 1300 was to
average a few "line-free" channels from both ends of the
line spectrum producing a continuum emission map. This
continuum map was then subtracted from the dirty spectral-
line channel maps, producing a set of 18 dirty, continuum-
free, spectral-line maps. It is important to note that, due

53
TABLE 2.2
Image Signal and Noise Characteristics
Image
Velocity
(km/sec)
rms Noise
Dirty Map
(mJ/beam)
rms Noise
Clean Map
(mJ/beam)
rms Noise
Clean Map
(K)
Peak Brightne
Clean Map
(K)
6
1746.10
0.84
0.82
1.28
5.40
7
1725.49
0.75
0.73
1.14
7.44
8
1704.88
0.86
0.83
1.30
16.95
9
1684.27
0.81
0.78
1.22
14.93
10
1663.66
0.84
0.81
1.27
12.59
11
1643.05
0.79
0.75
1.17
13.60
12
1622.44
0.83
0.83
1.30
9.72
13
1601.83
0.82
0.79
1.24
11.21
14
1581.22
0.91
0.91
1.42
9.52
15
1560.61
0.85
0.85
1.33
9.18
16
1540.00
0.84
0.83
1.30
8.87
17
1519.39
0.83
0.83
1.30
9.11
18
1498.78
0.78
0.77
1.20
11.08
19
1478.17
0.83
0.80
1.25
12.73
20
1457.56
0.83
0.80
1.25
15.82
21
1436.95
0.78
0.78
1.22
10.17
22
1416.34
0.80
0.78
1.22
5.51
23
1395.73
0.82
0.81
1.27
5.32
Continuum
0.30
0.27
0.43
12.63
Channel 0
0.18
0.17
0.19
-
Large Field
0.77
-
-
-

54
to the non-linearities of the CLEAN algorithm, this
continuum subtraction must be performed before the maps are
CLEANed. Subtracting CLEAN maps can introduce noise at the
positions of continuum sources (van Gorkom, 1982). Table 2-2
has the noise levels for these continuum free line channels.
The dirty, continuum-free line channels and the continuum
map are now ready for the CLEANing procedure.
Figure 2-3 (a-s) shows the final CLEANed spectral line
channels and the continuum map. The effective resolution is
20.05"xl9.53" (FWHM). The beam is indicated on the continuum
map, Figure 2-3 (s). As the astronomical significance of
these observations will be considered in a later section,
the CLEANed line channel maps are just presented here. The
emission from the galaxy appears to be clumpy and is not
very widespread. This hints at the structure found in the
integrated density map, well-defined arms with an extremely
low level disk component. The rms noise levels for the these
maps can be converted from mJy/beam to brightness
temperature using
4Sx10_26C2
4TB =
v ¿2kfi
where at is in Kelvin, as is the rms noise level in
B
mJy/beam, c is the speed of light, v is the frequency of
observation in MHz, k is the Boltzman constant, and Í2 is the
beam solid angle in radians.

Figure 2-3. Spectral Line Channel Maps. CLEAN,
continuum-free spectral line channels for NGC 1300. The
+ mark the positions of fiducial stars and x the center
of the galaxy. The velocity is indicated in the top
right corner. All maps are plotted in intervals of twice
the rms noise level.
A-R. Spectral line channels 6 through 23.
S. CLEAN continuum map showing the center of the
galaxy (x), fiducial starts (+), H II regions (*) and
the beamsize.

DEC
56
NGC 1300
NGC 1 300 1 746.
Figure 2-3 cont. (Part A)

DEC
57
NGC 1300
NGC 1300 1725.
Figure 2-3 cont. (Part B).

DEC
58
-19
NGC 1300
NGC 1300 1705.
Figure 2-3 cont. (Part C).

DEC
59
- 1 9
NGC 1300
NGC 1300
1684.
Figure 2-3 cont. (Part D).

DEC
60
-19
NGC 1300
NGC 1 300 1664.
Figure 2-3 cont. (Part E).

DEC
61
-19
NGC 1300
NGC 1300 1643.
Figure 2-3 cont. (Part F).

DEC
62
-19
NGC 1300
NGC 1300 1622.
Figure 2-3 cont. (Part G)

DEC
63
-19
NGC 1300
NGC 1300 1602.
Figure 2-3 cont. (Part H)

DEC
64
-19
NGC 1300
NGC 1 300 1581 .
Figure 2-3 cont. (Part I).

DEC
NGC 1 300
NGC 1300
1561.
Figure 2-3 cont. (Part J).

DEC
66
19
NGC 1300
NGC 1300 1540.
Figure 2-3 cont. (Part K)

DEC
67
NGC 1300
NGC 1300 1519.
Figure 2-3 cont. (Part L).

DEC
68
-19
NGC 1300
NGC 1300 1499.
i i 1 £ Li l
40 25 10 55
R fi 3 17
Figure 2-3 cont. (Part M)

DEC
69
-19
NGC 1300
NGC 1300 1478.
Figure 2-3 cont. (Part N).

DEC
NGC 1300
1458
NGC 1300
Figure 2-3 cont. (Part O)

DEC
71
- 1 9
NGC 1300
NGC 1300 1437.
Figure 2-3 cont. (Part P)

DEC
72
- 1 9
NGC 1300
NGC 1300 1416.
Figure 2-3 cont. (Part Q).

DEC
73
1 9
NGC 1300
NGC 1300 1396.
Figure 2-3 cont. (Part R) .

DEC
74
-19
NGC 1300
NGC 1300 1575.
Figure 2-3 cont. (Part S).

75
Table 2-2 lists the rms noise levels for the CLEANed
maps in mJy/beam and in Kelvin. As can be seen these values
correspond very closely with the expected rms noise level
from equation 2-23.
In addition to the narrow band line channel maps in
Figure 2-3, several channels spaced over the whole velocity
range were mapped over a large field of view, 1.5°xl.5°. The
effective resolution for these large field maps is
24.25"x22.59" (FWHM). These maps were used to search for any
detections of satellite galaxies of NGC 1300 or any other
objects. An example of the inner portion of one of these
wide field maps is shown in Figure 2-4. This is a map of
channel 16 and is a typical result. The continuum emission
has not been subtracted from this map. No evidence was found
for any 21cm line emission from any source other than NGC
1300 in this or any other wide field map. Figure 2-5 shows a
wide field map of "channel zero" with the continuum emission
still present. This, again, is only the inner portion of
the total field mapped. As no evidence was found for any
satellites or other objects, except unresolved continuum
point sources, only the inner portion is shown as an example
of the type of result obtained. The rms noise levels for
these maps are tabulated in Table 2-2.
In summary the map making and CLEANing parameters used
for NGC 1300 are
1. Map making (Channel and Continuum Maps)

DEC
76
NGC 1300
NGC 1300 1540.
Figure 2-4. Wide Field Map. Inner portion of wide
field image of channel 16. The continuum emission is still
present. Contours are at intervals of twice the rms noise
level.

DEC
77
NGC 1300
NGC 1300
Figure 2-5. Channel Zero. Wide field map of channel
zero. Contour levels are at approximately twice rms noise
level.

Uniform
78
a) Weighting:
Uniform
b) Taper:
7k -\ (1484m) 30% level of Gaussian
c) Convolving:
Spheroidal with m=6, n=0, a=l.
d) Cell size:
6"x6"
e) Image size:
256x256
2. Map Making (Wide Field Maps)
a) Weighting:
Uniform
b) Taper:
7k \(1484m) 30% level of Gaussian
c) Convolving:
Spheroidal with m=6, n=0, a=l.
d) Cell size:
10"xl0"
e) Image size:
512x512
3. Clean
a) Flux cutoff:
0.5mJy/beam
b) Gain:
0.15

CHAPTER III
DETERMINATION OF THE NEUTRAL HYDROGEN PROPERTIES
Spectrum Integration Techniques
The final product of the acquisition, calibration and
processing of the 21cm VLA visibilities is a set of 18
continuum-free narrow spectral-line channels for NGC 1300.
The set consists of signal-free channels at either end of
the spectrum and a series of signal-rich spectral-line
channels. The channel separation is 20.63km/sec and each
channel has a width (FWHM) of 25.2km/sec. These continuum-
free channel maps can be used to infer the neutral hydrogen
distribution and its associated velocity field.
If we assume that the atomic hydrogen is optically
thin, then the column density N at some point (x,y) is
b
given by (Mihalas and Binney, 1981 p489)
(3-1)
where the velocity, V, is in km/sec, and T , the brightness
B
temperature, is in degrees Kelvin.
The mean temperature-weighted velocity at that point is
given by
79

80
j -3(x#y)V(xfy)d V
= . (3-2)
â–  00
T (x,y)dV
B
oo
These will be easily recognised as the zeroeth and first
moments of the brightness temperature with respect to
velocity.
In the absence of observational noise the evaluation of
these quantities would be straightforward, being a straight
summation over velocity at each (x,y) point. However, as
noise is always present, a method is required which is
capable of discriminating quickly between noise and line
signal, and rejecting the noise before integration. As the
channels cover only a limited spectral range the noise may
not average to zero and will give a definite contribution to
the summation, if the summation was naively carried out over
the full spectral range. The problem is then to define a
range, or window, in velocity space which contains only line
signal. Various methods have been proposed to define this
window (Bosma, 1978, 1981). Bosma considered four methods:
1. Study each spectrum visually and define limits in
velocity.
2. Fit each spectrum with a preconceived shape.
Apply an acceptance level in intensity (the cut-off
method).
3.

81
4. Apply an acceptance level in velocity (the "window"
method).
Bosma (1978) studied these various methods and concluded
that the optimum method is the "window" technique.
The method used here is a variation of the "window"
method. Bosma's procedure is followed with some additional
discriminating features. A narrow window in velocity is
initially defined and gradually expanded with the value
outside the window being compared with the value outside the
window calculated in the previous step. When these two
values agree to within a specified tolerance level then all
the signal is considered to have been found and the
procedure is stopped for that pixel. Using this procedure
implies that the real signal is going to be present in a
single range of contiguous channels and any large spike at a
very discrepant velocity is considered to be noise. Also,
any large spike occurring in only one channel will be
rejected. The tolerance level depends upon the rms noise of
the single channel maps and on the number of points
remaining in the empirically defined continuum. This
continuum is the mean level of points outside the window.
Two additional criteria are added to improve the signal
detection and noise rejection capabilities of the procedure.
The procedure requires at least n points in the spectrum to
be above a specified brightness temperature. If this
criterion is not satisfied then no further effort is spent

82
on that pixel and it is rejected from all further
consideration. However, if this criterion is satisfed then a
further test is applied to reject pixels which have the
required number of points above the specified brightness
temperature but do not actually contain line signal. The
total value at each pixel (equation 3-1) must be above a
specified cut-off level, e.g. three times the rms noise
level. If the integrated value is below this cut-off level
then that pixel is considered not to contain line signal and
is rejected. Usually the procedure tests for at least two
points in the spectrum being above twice the rms noise level
in the single channel maps. The integrated value usually
must lie above three times the rms noise level of the single
channel maps or be discarded.
In an effort to ensure that all the low brightness gas
was used in the integrations, various tests were carried out
utilizing different combinations of smoothed single channel
maps for signal discrimination and integration. Combinations
tested included testing for integrable signal on convolved
maps and integrating using Hanning smoothed maps, and
testing for signal on convolved maps and integrating the
same convolved image. Various-sized convolving functions
were tried, all two-dimensional Gaussian functions, in order
to determine the optimum convolving method. The tests also
were carried out using different cut-off values for the
integrated spectrum and different-size boxes surrounding the
region of HI emission.

83
The smoothing function used was a running, three-point
Hanning function
X = 0.25 X , + 0.5 X + 0.25 X .. (3-3)
n n-1 n n+1
This function was applied in velocity space to each
pixel position. The convolving function is designed to bring
out the low brightness features and to suppress the noise.
Various beam solid angles were tested and the convolution
was applied to each single channel map. Values ranging from
half the synthesized beamwidth (FWHM) to two and a half
times the synthesized beamwidth were tried. Below half the
synthesized beamwidth the convolution had essentially no
effect; whereas, above two and a half times the synthesized
beamwidth, the convolution became so broad as to render the
maps unusable. With this size convolving function, the
resolution was so severly degraded that essentially no fine
structure was visible; all that remained was a broad, beam-
smeared, disk-like feature.
The criteria used to determine which combinations of
smoothing and convolving functions, and cut-off values gave
the optimum results were
1. The number of spectra used in the integration.
2. The signal-to-noise ratio in the convolved and
integrated maps.
3. The HI mass-integral.

84
4. The ratio of mass-integral to rms noise level in the
integrated maps.
The mass-integral is defined as (Mihalas and Binney,
1981 p490)
HI = 2.35 x 105D2 /SdV (3-4)
mass
where S is the flux in Jy, and D is the distance in Mpc. The
integral is calculated for all pixel points deemed to belong
to the galaxy. The region in which this integral is
calculated is chosen by inspection of the HI density
distribution map produced by the "window" procedure. The
ratio of mass-integral to rms noise level is calculated
using the value found by evaluating equation 3-4 inside the
box surrounding the galaxy, and the rms noise level
calculated outside the box. This ratio should be maximized
for the optimum combination of smoothing, convolving and
cutoff values. Table 3-1 shows some typical values from two
runs during this testing procedure. This shows quite
clearly that for these tests:
1. The rms noise level clearly goes through a minimum.
2. The mass-integral goes through a maximum.
3. The ratio of mass-integral to rms noise goes through
a maximum.
As a result of these tests the following procedures
were adopted:
1. Hanning smooth, in velocity space, the original
single channel maps with a running three-point
function.

TABLE 3.1
Signal Characteristics for Spectrum Integration
Npoint
(1)
Beamwidth
(2)
rms Noise
(3)
Mass-integral
(4)
Ratio
(5)
1
0.5
24.29
1.1430
0.0471
1.0
30.78
1.1781
0.0383
1.5
22.07
1.1777
0.0534
2.0
20.38
1.1788
0.0578
2.5
20.41
1.1784
0.0577
2 0.5
17.68
1.1248
0.0636
1.0
24.75
1.1700
0.0473
1.5
14.92
1.1742
0.0787
2.0
14.67
1.1739
0.0800
2.5
15.00
1.1727
0.0782
(1) Minimum number of points in each spectrum required
to be above the cut-off value.
(2) Convolving beamsize, in units of synthesized
beamwidth.
(3) Rms noise level outside a box surrounding the
galaxy in arbitrary units.
(4) Mass-integral for all points deemed to belong to
the galaxy in arbitrary units.
(5) Ratio of mass-integral to rms noise level.

86
2. Convolve the smoothed channel maps using a Gaussian
with a beamwidth (FWHM) twice the synthesized beam.
3. Test for line signal on the convolved maps using a
two point test and a cut-off of twice the rms noise
level.
4. Integrate the smoothed maps using three times the rms
noise level as a cut-off.
This procedure produces maps of the beam-smoothed
column density of the HI gas distribution and temperature-
weighted mean velocities of the gas.
Neutral Hydrogen Distribution
The spectrum integration procedure described above was
used to produced the beam-smoothed column density of the
observed HI gas, assuming a small optical depth, shown in
Figures 3-1 to 3-4. The maximum observed density is
1.59x102latoms/cm2 Generally, the signals are not spread
over more than 4 or 5 channels. This gives an rms noise
level of about 5x10 ^atoms/cm ^ or approximately 3% of the
peak density. Various methods of presenting these data are
shown in these diagrams in an attempt to get a clear
understanding of the neutral hydrogen distribution. Figure
3-1 shows a contour plot of the data for NGC 1300. This
diagram is rather confused and difficult to interpret. By
superimposing the contour plot on an optical photograph of
the galaxy, Figure 3-2, the structure of the hydrogen

87
distribution can be discerned. A gray scale of the
distribution, Figure 3-3, shows the regions of high density
gas and low density gas; but a better method to display the
structural detail of the neutral hydrogen gas distribution
is to use a false color display where each color represents
a range of values. Figure 3-4 is a false color image of the
gas distribution in NGC 1300. This diagram vividly
illustrates the structural detail of the galaxy.
Before interpretation of the observed column density,
all pixels had their spectra examined for any anomalous
effects, a beam-smoothed noise spike at an unlikely
velocity, for example. Any such anomalous spectra were
discarded and corrections applied by hand to the dataset. If
a pixel obviously had a weak signal but had been discarded
by the automated routine as the integrated value was not
three times the rms noise level, it was added into the
dataset. Very few, <1%, of the spectra examined required
corrections; a few pixels in the center of the galaxy and
some at the outer edges of the arms were all that required
corrections.
The most noticeable features in the HI distribution are
1. The very prominent and strong spiral arms.
2. The lack of gas in the central bar region.
The contrast between the spiral arms and the background
region is high as there is essentially no gas in the
interarm regions. The observed gas is confined almost
exclusively to the spiral arms, making NGC 1300 an excellent

DEC
88
NGC 1300
DENSITY
R A 3 17
Figure 3-1. tJeutral Hydrogen Distribution Contour
Plot. The center of the galaxy (x) and fiducial stars
(+) are marked. The contour levels are in intervals of
10% of the peak observed density. Peak observed density
is 1.59 x 1021 cm-2.

Figure 3-2. Neutral Hydrogen Distribution with
the Optical Image. HI gas distribution superimposed upon
an image of KGC 1300 from the National Geographic-Palomar
Sky Survey.

DEC
90
NGC 1300
DE NS IT T
R fi
3 17

91
NGC 1300 HI OENSITT
¿i
Figure 3-3.
Scale Image.
Neutral Hydrogen
Distribution Gray

Figure 3-4. Neutral Hydrogen Distribution False
Color Image. Blue represents low density gas and red high
density gas.


94
example of a grand design spiral. There is some evidence for
gas in the nuclear region of the galaxy but this is very low
density gas and confined to a few pixels. The inner region
of the galaxy was convolved in an attempt to enhance the low
level gas in the nuclear region. No extra, low density gas
was found, thus indicating that the gas is probably hidden
in the noise, if it exists.
Comparing the observed HI spiral structure with the
optical spiral arms shows that the two features correspond
very well. The optical arms can be reliably traced through
approximately 20CP in azimuth whereas the HI arms can be
traced through about 310° in azimuth. Noticeable features in
the optical image of the system are also evident in the HI
gas distribution image. The breaks in the optical arms at
position angles 0° and 175° are also prominent in the HI gas
distribution. Also, at position angles 0° and 175°, breaks
in the outer regions of the gas arms may be evident.
However, the gas density in these regions is low, and these
breaks may only be the result of the low density and not
actually physical breaks, as in the inner regions. These
breaks may be manifestations of stellar orbital resonances.
The region of maximum brightness in the northern section of
the western arm, in the optical image, shows a definite
shift in position before and after the break in the arm.
The HI gas arm does not show this shift in position, with
the gas maximum being slightly closer to the nucleus than

95
the optical maximum before the break, and slightly farther
from the nucleus than the optical maximum after the break.
Thus, the optical arm lies slightly outside the gas arm,
whereas after the break the optical arm lies inside the gas
arm. The situation is not as pronounced in the southern
section of the east arm where the gas and optical arms are
more nearly coincident.
The arms may be described by a simple logarithmic form
0 (R) = £n (R/R ) /tan a (3-5)
where R, and 8 are measured in the plane of the galaxy.
The pitch angle of the spiral and RQ are constants.
However, the values for a and R do not remain constant
along the arms. The east arm shows a change in a and RQ at
° o ,
an azimuthal angle of ~195 , changing from a=5 and Rq=1.73
to a=25° and Rq =0.46 ' ; thus it becomes less tighly wound in
the outer regions than in the inner regions. The west arm
shows the same pattern; a=5° and R =1.5' and changes to a=25°
o
and Rq=0.6' at an azimuthal angle of - 145 . These
logarithmic spirals are shown in Figure 3-5, along with the
deprojected observations. The observed spiral pattern is
calculated using the peak observed densities in a small
region at each azimuthal angle. Profiles along the arms are
shown in Figure 3-6. The overall appearance of the gas
distribution in NGC 1300 shows this to be an excellent grand
design spiral system.

96
N
6b:
<5 ! !
' *«
x\
a#
acp-e*-*^
Q-
\
XX
\X
\
*
\
*
\
s *
\ l
\ X
b '
\
+
^ k
6 '
Vx
x
<>
ó
4
6
\
9
x
*x
.XXx
'--x..x.x>x
\o
\o
\o
\o
\
X EAST ARM HI
o WEST ARM HI
Figure 3-5. Logarithmic Fit to Spiral Arms. Two
component logarithmic spiral representation of the depro-
jected, observed HI arms. The observations are (x) for the
east arm and (o) for the west arm. The inner components
have a=5° and the outer components have a=25°.

97
12
o
S io
o
x
w 8
>
t 6
LÜ
O 4
LU
O
< 2
3-6. Deprojected Azimuthal Profiles,
of the HI gas along the spiral arms.
li¬
ar
Z)
CO
Figure
face density
X
o
O-o EAST arm
X X WEST ARM
1 1 1 1 1—
50 100 150 200 250
AZIMUTHAL ANGLE (°)
Sur-

DEC
98
NGC 1300
DENSITY
R A 3 17
Figure 3-7. HII Regions in NGC 1300. Positions
of the HII regions compared with the contour levels of
25%, 50% and 75% of the peak density. HII regions from
Hodge (1969).

99
Hodge (1969) observed HI I regions in NGC 1300. These
regions are plotted in Figure 3-7. Also plotted are
contours of the gas density at levels of 25%, 50% and 75% of
the peak density. The positions of the HI I regions
correspond with the positions of regions of high HI gas
density and are concentrated in regions of high brightness
in the optical image. The regions in the west arm are
clumped at the beginning of the spiral arm and in the region
immediately following the break. Both these regions also
show evidence for dust lanes and could possibly indicate
shock regions in the galaxy. The HII emission in the east
arm is located after the break in the arm. Again, the
optical image shows some bright knots and some evidence for
dust lanes. This, again, could be evidence for shock fronts.
Also very noticeable in the gas distribution is the HI
gas poor region in the center of the galaxy. This region
corresponds closely to the bar region and is possibly caused
by dynamical effects of the rotating bar. There is some
evidence for gas at the center of the galaxy, but as
mentioned earlier, this is very low density gas. There is
also some evidence for gas at the positions of the dust
lanes in the bar region, but again, this is low density gas
and cannot be regarded as conclusive evidence for shock
regions; however, the suggestion is certainly strong. Low
resolution observations indicated that there may be gas in
this depleted region, but in the combined C/D array dataset

100
this gas, if it exists, probably lies below the rms noise
level. In an attempt to recover any low level gas, the full
resolution dataset was convolved to a resolution comparable
to that of the D array and the integrations repeated. Some
extra low level gas was brought out in the interarm regions
but no significant enhancement of the gas was found in the
depleted bar region. This depletion in the bar region has
been observed in other barred spiral galaxies. The galaxy
NGC 3992 (Gottesman et al., 1984) shows a similar depletion
in the bar region whereas NGC 3359 (Ball, 1984) and NGC 1073
show a little depletion but not as markedly as do NGC 1300
and NGC 3992.
The extent of the depleted region, although somewhat
irregular, can be approximated by an ellipse of semi-major
axis a=l.1' and position angle -80°. When deprojected into a
circle this ellipse gives an inclination angle i=51°. This
is the same as the inclination angle for the galaxy deduced
using 21cm radial velocities (see next section for details).
The size of the semi-major axis of this ellipse, 1.1',
corresponds well with the semi-major axis of the bar, 1.28',
and thus possibly indicates that the region is depleted due
to dynamical effects of the bar. Inside the bar region the
bar has an angular velocity less than the angular velocity
of the gas. Any interaction between the bar and the gas is
likely to result in a loss of angular momentum of the gas.
This will cause the gas to migrate towards the center of the

101
galaxy and cause a gas buildup. However, this gas
enhancement is not seen in the HI, although, as will be seen
in the modeling, section there is a gas buildup in the
models.
Alternatively, molecular gas may be the dominant
component in this region. Carbon monoxide has been shown to
be a good tracer of H^ in molecular cloud complexes (see for
example Thaddeus, 1977; Bloemen et al. , 1986) and thus,
detection of CO in the central region of NGC 1300 would give
some estimate for the amount of molecular gas present. As no
CO observations have been made of NGC 1300 some other method
is needed to estimate the amount of molecular gas in the
central region. Various studies have indicated that the CO
emission is almost always enhanced in regions of suspected
star formation (Thaddeus, 1977; Rieke et al., 1980; Telesco
and Harper, 1980). Thus, if an estimate for the amount of
star formation in the central region of NGC 1300 can be
made, this will give some indication of the amount of
molecular gas present in this region. Examination of IRAS
fluxes for the inner 1.5* of the system will give an
indication of the star-formation activity in the nuclear
region and thus, an estimate for the amount of gas in the
center. Following the discussion of Hawarden et al. (1985),
the ratios of the lOOum flux to the 25um flux, and of the
25um flux to the 12um flux give an indication of the star¬
forming activity in the center. If R( 100um/25um) < 20 and

102
R(25um/12um) > 2, then there is very likely vigorous star
formation in the center, and consequently, there may be
large amounts of gas present, but unseen by the 21cm
observations. The IRAS point source fluxes for NGC 1300 are
12um < 0.25 Jy.
25um < 0.31 Jy.
60um 2.39 Jy.
lOOum 10.78 Jy.
Thus, as there is no indication of vigorous star
formation in the center, it seems unlikely that massive
amounts of either ionized gas or molecular gas exist in the
inner 1.5' of the galaxy. A dilemma therefore exists. On one
hand we have the possible loss of angular momentum of the
gas causing a gas buildup in the center, and on the other
hand, all available data on gas tracers, at present, show no
large amounts of gas in the center. What has happened to the
gas? Perhaps it will show up in the CO observations but the
present evidence indicates that this is unlikely. Another
possible explanation is that this gas has become associated
with the nuclear non-thermal continuum source. Further
observations of molecular components might help resolve this
problem.
The HI gas has a fairly-well defined extent with a
major-axis diameter of about 7.6' at a level of
20 2
2x10 atoms/cm . The optical major-axis diameter, at a level
of 25.Omag/arcsecis 6.5' (de Vaucouleurs, de Vaucouleurs

103
and Corwin, 1976). The radial extent of the galaxy is
determined by the outer sections of the spiral arms. Very
little gas is seen as a broad disk-like feature. In fact the
observed gas seems to be almost entirely confined to the
spiral arm region. Any disk gas is below the rms noise level
19 ?
for this map. The rms noise level is 5x10 atoms/cm . Figure
3-8 shows the radial dependence of the deprojected HI
surface density.
The depletion of the gas in the center is evident from
the low surface densities for the inner 1.0' of the galaxy.
The tail of the distribution has very low surface densities
from about r=3.8' outwards. The line joining the two points
plotted for each position indicates the upper and lower
bounds for the surface density. Thus, this tail indicates
that at r>3.8' the values are very uncertain due to low
signal-to-noise ratio. Points in this region are determined
from a few lumpy patches. All values for the surface density
have upper and lower bounds indicated. In the inner 1.0' of
the galaxy this is mainly due to the lack of gas whereas,
for the regions encompassing the arms, this range is due to
the lack of interarm gas. The HI distribution is patchy,
being confined largely to the arm region, and thus, as each
point in Figure 3-8 represents the annulus-averaged value at
a particular deprojected radius, there will be some regions
in the annulus which contain only very low surface density
gas, the interarm regions for example. The nature of the

SURFACE DENSITY ( xl020/cm2 )
104
Figure 3-8. Deprojected HI Surface Density.
Annulus-averaged surface density of HI gas in NGC 1300.

105
surface density distribution is well-illustrated by
considering Figure 3-9 (a-e) which shows profiles at various
positions of constant right ascención and declination.
Figure 3-9 (a) shows the positions of these profiles and
Figure 3-9 (b-e) shows the profiles. Very noticeable in
Figure 3-9 (b) are the four peaks in the profile. In order
of decreasing declination these peaks correspond to the
outer region of the west arm, the inner region of the east
arm, the inner region of the west arm and the outer region
of the east arm. This profile crosses the inner and outer
regions of the west arm at the breaks in the arm. This
explains the relatively low level of the peaks when compared
with the peaks for the east arm. The profile in Figure 3-9
(c) passes through the west arm at approximately the
position of the "kink" in the arm. This profile gives a
qualitative picture of the general decrease in flux level as
the position along the arm is changed. A better
representation of the levels along the arm can be obtained
by plotting HI density as a function of azimuthal angle.
Figure 3-6 is a plot of this, in the plane of the galaxy,
for both the east and west arms. Noticeable is the decrease
in density levels at the positions of the breaks in the
arms. The profile in Figure 3-9 (d) passes through the
"kink" in the east arm and shows three distinct peaks. These
peaks correspond to the end of the west arm and two
crossings of the east arm. Figure 3-9 (e) shows the profile

106
which crosses the center of the galaxy at constant
declination. Very obvious is the lack of flux in the center
region of the galaxy. These profiles illustrate well the
very distinct and well-defined structural nature of the HI
distribution in NGC 1300.
The total HI mass can be obtained by integrating the
density distribution in Figure 3-1 in (x,y), or solid angle.
6 2
Integrating gives M /M =8.7x10 DMpc. Correcting to an
n O
adopted distance of 17.1Mpc de Vaucouleurs and Peters (1981)
Q
give a total HI mass is 2.54xlO^Mo. The value given by
Bottinelli et al. (1970) becomes 1.95x109mo, and that from
Reif et al. (1982) becomes 3.GOxlO^Mo. These determinations
were made using single dish profiles. Thus, apart from the
possibly low level gas in the center of the galaxy and the
interarm regions mentioned earlier, the interferometric
observations have not missed any significant HI emission.
Comparing the HI mass from the combined B/C and C/D array
dataset with the HI mass from the low resolution C/D array
dataset shows that no extra hydrogen was detected in the low
resolution dataset. The resolution limits for the arrays
used in this project are approximately 8” to 17' and, as no
structure in the maps is greater than about 7', no HI was
lost due to angular limits imposed by the array
configurations used in the observations.

Figure 3-9. Profiles Through HI Surface Density
Distribution.
A. Positions of the various profiles.
B. Profile at position 1.
C. Profile at position 2.
D. Profile at position 3.
E. Profile at position 4.

109
03 17 45 30 15
RIGHT ASCENSION
PEAK FLUX - 4.2413E+02 JY/'KM/S
LEVS - 4.2413E+01 * ( -1.00, 1.000, 2.000,
3.000, 4.000, 5.000. 6.000, 7.000. 8.000,
9.000. 10.00)
Figure 3-9 cont. (Part A).

2 ^
109
NGC1300 I POL NGC1300.MOMO.1
Figure 3-9 cont. (Part B).

2 ^
110
NGC 1300 I POL NGC 1300.MOMO. 1
CENTER AT RA 03 17 34.966
Figure 3-9 cont. (Part C).

2 :*
111
NGC 1300 I POL NGC1300.MOMO.1
CENTER AT RA 03 17 17.557
Figure 3-9 cont. (Part D).

s: *
NGC 1300
I POL
NGC1300.MOMO.1
RIGHT ASCENSION
CENTER AT DEC -19 35 41.00
Figure 3-9 cont
(Part E)

113
Continuum
Continuum emission was calculated by averaging several
line-free channels at both ends of the spectral range. The
resulting distribution is shown in Figure 3-10. The region
covered by this map is just the region surrounding the
galaxy and does not include most of the point sources in the
large field map, Figure 2-5. Continuum emission in the
region immediately surrounding NGC 1300 is confined to two
strong point sources and some weak extended emission. One of
the point sources coincides with the position of the nucleus
of the galaxy. This strong source and the weak emission
surrounding it continue the trend observed in the surface
photometry. The surface photometry indicates that as the
wavelength increases, the dominance of the central source
over its surroundings also increases (see Chapter 4 for
details). In an attempt to determine the extent of the low
level emission, specifically from the disk and the arms, the
central source was removed and the resultant image convolved
with a two beamwidth (FWHM), two-dimensional Gaussian
convolving function. This did not reveal any low level
emission from either the disk or the arms. The full
continuum emission is shown in Figure 3-10.
The low level continuum emission comes from the western
end of the bar and from the confused region at the eastern
end of the bar, between the bar and the extension of the
western arm. Some emission is also seen from the eastern arm

DEC
114
NGC 1300
NGC i 300 1575.
Figure 3-10. Continuum Emission. The contour levels
are plotted at intervals of the rms noise level. (*) repre¬
sent the positions of HII regions and (+) the positions of
fiducial stars. HII regions from Hodge (1969)’.

115
after the break. Also indicated in Figure 3-10 are the
positions of Hodge's (1969) HI I regions. There is a good
correlation between these positions and the continuum
emission. Continuum emission is also seen from a point
source 6.8' south-west of the galaxy center and some
extended emission 4' north-west of the center.
Kinematics of the Neutral Hydrogen
The temperature-weighted mean velocity at a point (x,y)
is given by equation 3-2. Before integrating, the spectra
are Hanning-smoothed in velocity space as indicated by
equation 3-3. The original sampling rate of the data,
20.62km/sec, is close to the filter bandwidth, 25.2km/sec.
Therefore, after the smoothing, the data are sampled at the
Nyquist rate. The smoothing also increased the signal-to-
noise ratio. Figure 3-11 is the resultant velocity field
plotted as a contour diagram. Figure 3-12 is the same
velocity field shown as a false color image, and Figure 3-13
shows the velocity field superimposed on an optical
photograph.
Figures 3-11 to 3-13 clearly indicate that reliable
velocities are difficult to obtain in regions of low atomic
gas density. The central region and the regions between the
spiral arms have no velocities indicated due to the lack of
gas. Irregularities can be seen in the velocity contours
where the optical arms cross the contours. These
irregularities are indicative of gas streaming motions

DEC
116
NGC 1300
VELOCITY
R fi 3 17
Figure 3-11. Velocity Contours. Velocity field
for NGC 1300. The contour interval is 20 km/sec and the
contours are labeled in km/sec. Fiducial star positions
(+) and the galaxy center (x) are narked.

Figure 3-12. False Color Representation of Velocities.
Blue represents low velocities and red represents high
velocities.


Figure 3-13. Velocity Field Superimposed on Optical
Object. The optical image of NGC 1300 is from the National
Geographic-Palom.ar Sky Survey.

DEC
120
NGC 1300
VELOCITY
R fl
3 17

121
associated with the spiral structure of the galaxy. The
northern half of the galaxy, where there is more interarm
gas than in the southern half, shows these irregularities
for both the western arm and the end of the eastern arm. In
the southern half these effects are emphasized by the lack
of gas in the interarm region and the fact that velocities
are only shown for the spiral arm regions. There does not
appear to be any offset in the velocity contours as they are
traced across the bar region. NGC 3992, which also shows a
"hole" in the center of the galaxy, displays an offset in
the velocity contours from one side of the bar to the other
(Gottesman et al., 1984). Although the velocity field
displays irregularities, the dominant component in the
velocity field is circular rotation.
To quantify the velocity field and to investigate
abnormalities, certain global properties of the system must
be defined. Defining two components for the velocity field
as V (R), the rotation velocity, and V (R,0), the
RO r N c
noncircular motions, the velocity at each point in the
galaxy, V (R,e), can be written
OBS
VOBS(R,9) = VROT(R)cos ® sin i + Vnc(R,0)+Vsys (3-6)
where Vgys is t^le systemic velocity, i is the inclination of
the galaxy, and R, 6 are the polar coordinates of the
position in the galaxy. The inclination is the angle between
the sky plane and the galaxy plane, and R, 9 are measured in
the galaxy plane, where the origin for 9 is the line of
nodes.

122
The noncircular effects, V (R,0) can be written
NC
(Mihalas and Binney, 1981 pg. 499)
VNC(R,e) = VR(R,6) sin 0 sin i+Vp(R,0)cos i (3-7)
where V (R, 6) is the radial velocity in the plane of the
R
galaxy and Vp(R,e) is the velocity perpendicular to the
plane. These noncircular effects can be seen as deviations,
in the velocity contours of Figure 3-11, from what would be
expected from pure circular rotation. However, it is
apparent that the overall dominant component in the velocity
field is circular rotation and therefore, for the purposes
of the immediate discussion, the noncircular effects will be
ignored. This leads to a solution for V , i and the
SYS
position angle of the line of nodes, residuals about equation 3-5 in a least squares fashion
(Warner, Wright and Baldwin, 1973). To minimize the effects
of radial streaming motions the data points used were
constrained to lie within ±15° of the major-axis. To reduce
the effects due to regions of low signal-to-noise ratio the
data were also constrained to lie between radii of 0.9' and
3.3'. The least squares procedure gave a position angle for
the line of nodes of =—85.5 ± 0.3d , a systemic velocity of
V=1575.0 ±0.5km/sec and an inclination angle of
i=50.2 ± 0.8°. The quoted errors are the standard deviations
and are estimates of internal uncertainties; they do not
imply that the actual values have been measured to this
accuracy. As a point of interest, the major-axis of the bar,
measured from the infrared image, is 4>=-79°.

123
The value for the systemic velocity is within the range
of previous determinations. Sandage and Tammann (1975) quote
V=1535 ± 9km/sec; Bottinelli et al. (1970) give
V=1573 ± 7km/sec and de Vaucouleurs, de Vaucouleurs and
Corwin (1976) give V=1502 ± 10km/sec. The inclination,
o
i=50.2 , agrees well with that from de Vaucouleurs, de
Vaucouleurs and Corwin (1976), i=49 °, but differs
significantly from that suggested by Burkhead and Burgess
(1973), who indicate that the galaxy is seen nearly face on.
The least squares procedure was run having the inclination
fixed and only solving for
LON
and Vgyg. The only
acceptable solutions were found when the inclination was
nearly 50°. All solutions with i=10-20° gave unacceptable
results for and Vgycn Thus, the value found originally,
o
i=50.2 , was adopted for the inclination of the galaxy.
Using these parameters an estimate for the rotation
curve can be derived. The scheme introduced by Warner,
Wright and Baldwin (1973) was utilized. This procedure
corrects the data for the inclination of the galaxy and
averages data in elliptical annuli, circular rings in the
galaxy plane. Each point is weighted by the cosine of its
azimuthal angle, 9 , to minimize the effects of systematic
radial noncircular motions. Thus, points near the minor-
axis will have lower weight than those near the major-axis.
The rotation curve was calculated using two different
methods:

124
1. All the data in each annulus were used (angle-
averaged method).
2. Only points within 15° of the major-axis, in the
plane of the sky, were used to calculate the rotation
curve (wedge method).
The rotation curves from these methods are shown in
Figures 3-14 and 3-15. The error bars represent plus or
minus one standard deviation and are due to a combination of
systematic noncircular motions and the sparse distribution
of data in that annulus.
The angle-averaged rotation curve, Figure 3-14, shows a
curve rising and reaching a maximum of V=185km/sec,
corrected for inclination, at around 2.5' and then dropping
slowly. No data are plotted for the inner 1.0' as there is
no reliable information in this region. This is the region
of the "hole" in the HI density distribution (see Figures
3-1 to 3-4). At radii greater than 2.8' the errors are very
large. However, in this region the value for the rotation
curve is determined by only a few data points. The error
bars for the rest of the curve are of the order of
10-15km/sec and are this large due to the very well defined
structure of the hydrogen distribution; each annulus crosses
both spiral arms and the interarm region. The interarm
region has a sparse data distribution and the errors will
consequently be larger than those for the spiral arm region
where the data are better distributed. The noncircular

VELOCITY ( km/sec )
250
H 1
1.0 2.0
RADIUS ( arcmin )
Figure 3-14. Angle-Averaged Rotation Curve,
error bars represent one standard deviation.

VELOCITY ( km/sec )
126
Figure 3-15. Wedge Rotation Curve. Values for the
east and west halves of the major-axis are shown. The
error bars represent one standard deviation.

127
effects which were ignored in calculating V , i and , al
u 1 u
so contribute to the error bars shown in the rotation curve.
As can be seen from Figure 3-11, these non-cicular effects
are non-zero and will make a large contribution to the error
bars in the rotation curve.
The rotation curve, calculated using the 30° wedge
about the major-axis is shown in Figure 3-15. The shape of
this curve is the same as the angle-averaged curve. The
curve is plotted for two halves of the major-axis. As the
data used for this curve are constrained to lie within 15°
of the major-axis, the errors are smaller than those in
Figure 3-14. This results from the fact that within 15° of
the major-axis HI emission is strong and not patchy. In this
case the errors are then mainly representative of systematic
noncircular motions. Once again, at radii greater than about
2.8', the errors become large due to the lack of reliable
information. From now on, "the rotation curve" will refer to
the wedge rotation curve shown in Figure 3-15. The most
significant difference between the angle-averaged rotation
curve( Figure 3-14) and the wedge rotation curve (Figure
3-15) is that the error bars are significantly larger for
the angle-averaged curve. In the region between r=1.9' and
r=2.5', the angle-averaged curve lies approximately 20km/sec
above that determined by using the +15° wedge.
The inner portion, r<1.2', of the rotation curve is a
fairly good approximation to solid-body rotation. This is

128
also the region occupied by the bar. Comparing this region
with the optical velocities of Peterson and Huntley (1980)
shows that the optical velocities and the HI velocities are
in good agreement with each other, with the optical
velocities rising just a little faster than the HI
velocities in the inner 30" of the galaxy, thereafter
corresponding well with the HI velocities. This is expected
as the optical velocity measurements have higher resolution,
3"-5", than do the HI measurements (resolution 20"). The
lower the resolution, the more the effects of beamsmearing
on the rotation curve. In the steeply-rising part of the
rotation curve the lower resolution HI measurements will
tend to underestimate the rotation curve (Burbidge and
Burbidge, 1975). Bosma (1978) suggests that the ratio R/B
should be greater than about 7 to avoid serious degradation
of the rotation curve. R is the Holmberg radius and B is the
halfpower beamwidth. The HI observations of NGC 1300 have
R/B=4.03'/0.33' or R/B=12.2. Thus the difference between the
optical and HI rotation curves should be small, as is seen
from Figure 3-16.
The optical velocities only extend to 1.6' and are
calculated from the emission lines of [Nil] and [SI I] and
from the stellar H and K Call absorption lines. Figure 3-16
shows a comparison of the rotation curves from HI, the
emission lines and the absorption lines for the inner 1.6'.
The HI rotation curve provides an estimate for the angular

VELOCITY ( km/sec )
129
Figure 3-16. Optical and HI Rotation Curves.
Comparison of rotation curves determined from optical
measurements and from 21cm radio measurements. Optical
measurements from Peterson and Huntley (1980).

130
velocity of the solid-body portion of the rotation curve. A
least squares analysis for the inner 1.3' gives
108 10km/sec/arcmin, or at a distance of 17.1Mpc,
22km/sec/kpc. This region is the region inhabited by the
bar. Outside this region the rotation curve rises less
quickly, being nearly flat, reaching a maximum at
approximately r=2.5'. In the above analysis of the 21cm
rotation curve it must be remembered that these values are
very dependent on only one or two data points. As can be
seen in Figures 3-4 and 3-12, the density and velocity maps,
the region covered by the optical velocities is the region
occupied by the bar and this region has almost no reliable
information at 21cm. Thus any analysis in the inner 1.3'
must be considered to be very crude and be used only as an
indication of general trends and not a definitive statement.
Casertano (1983) and Hunter, Ball and Gottesman (1984)
described the effects of truncating a disk on its associated
rotation curve. The rotation curve for a truncated disk
exhibits a sharp drop just beyond the truncation edge of the
disk. These truncation signatures may have been observed in
NGC 5907 (see Casertano, 1983), NGC 3992 (Gottesman et al.,
1984) and NGC 1073. As NGC 1300 has a well-defined hydrogen
distribution it would seem a likely candidate to display a
truncation signature in its rotation curve. However, Figure
3-17, which plots the rotation curve out to r=6.4', shows
that it is difficult to determine whether or not a
truncation signature exists.

VELOCITY ( km/sec
131
250
200
150
100
50
5C
3C
H 1 1 1 h-
1.0 2.0 3.0 4.0 5.0
RADIUS ( arcmin )
Figure 3-17. Rotation Curve to 6.4 arcmin.
averaged rotation curve for NGC 1300 out to r=6.4
bars represent one standard deviation.
jc
3C
-H—
6.0
Annulus-
Error

132
The lack of reliable data beyond about r=3.2' makes the
determination of the rotation curve very unreliable. The
apparent drop in the rotation curve is almost certainly only
due to the poor signal-to-noise ratio and not to any real
truncation signature. Comparing Figure 3-7, which is the
radial dependence of the deprojected, angle-averaged surface
density, with Figure 3-17, shows that the surface density is
extremely low and the signal-to-noise ratio is small. The
joined points in Figure 3-7 represent the upper and lower
limits for a value, and, as can be seen, beyond r=3.2' this
range is rather large. Thus, the conclusion is that the
rotation curve for NGC 1300 does not show any evidence for a
truncation signature at the sensitivity of this survey.
Mass Models
An estimate for the mass of NGC 1300 can be obtained by
fitting simple models to the rotation curve of Figure 3-15.
As more detailed models will be constructed in a later
section, these mass models will be utilized as the initial
input parameters for the hydrodynamical code. No attempt was
made to fit the perturbations evident in the rotation curve;
only the broad overall shape was modeled as the aim was to
get an estimate for the mass interior to the last reliably
measured point on the rotation curve and to get an estimate
for the type of disk and its parameters.

133
Various types of disks were used in attempting to model
the rotation curve. The first model considered was the
Generalized Mestel Disk, or GMD, of Hunter, Ball and
Gottesman (1984). The GMD is also a member of Toomre' s
(1963) family of infinitely flattened disks, specifically an
n=0 disk. The circular velocity in the GMD at r is given by
V (b,r) = C[l+b2/r2+b/r (l+b2/r2) 1//2]"1/2 (3-8)
o
and the disk mass interior to r by
MQ(b,r) = (C2r/G)[(l+b2/r2)1/2-b/r]. (3-9)
The length scale, b, and the amplitude, C, for the model
shown in Figure 3-18 are b=0.95' and C=210.Okm/sec. The
mass interior to the last measured point at r=3.2', 15.9kpc,
10
is therefore 7.8x10 Mo. However, as can be seen from Figure
3-18, for r>2.4' the model and the observations deviate
significantly. In the bar region, r<1.3', the GMD curve lies
above the observed HI curve but matches the optical
velocities reasonably well.
A better model would have a more centrally condensed
disk than the GMD. This type of disk has a rotation curve
which drops in the outer regions of the disk, unlike the
GMD. Figure 3-18 also shows the rotation curve for the n=l
disk of Toomre (1963). For this disk the circular velocity
at r is given by

134
Figure 3-18. Mass Models for NGC 1300. Rotation
curves for various mass models for NGC 1300 compared with
the observations. The radius of the bar and the radius at
25 mag/arcsec^ are shown.

135
(3-10)
(3-11)
The length scale, b, and the amplitude parameter, C, for the
model shown in Figure 3-18 are b=1.75' and
C=455.0(km/sec)arcmin. The maximum value for this rotation
curve occurs at r= y/2b" =2.47' and is given by
r U/4
max — c* (3-12)
^2V b
V^(b,r) = Cr[b(r2+b2)V2]"1/2
and the disk mass interior to r by
M1(b,r) = (C2r/G) [ 1-b (r2+b2) ~1//2]
This model is a good fit to the observations, especially in
the region of most interest and most reliable velocity data.
The disk mass for this model interior to r=3.2' is
4.9x1010Mo.
Higher order, n>l, Toomre disks decline too rapidly,
after reaching their maxima, to provide a good fit to the
observed rotation curve. An exponential disk was also
calculated in an attempt to match the observations. The form
of the exponential disk is (Freeman, 1970)
V2 = 7rGuQaR2
1 n(—)K^ (—) -1, (—)K (^)
° 2 ° 2 1?1?
(3-13)
where p is the surface density,
-1 ,
is the scale length and
Iq, 1^, K ^ are modified Bessel functions. Using the

136
scale length a ^=6.96kpc from Elmegreen and Elmegreen (1985)
gave the rotation curve shown in Figure 3-18. This curve
does not reach the velocities observed in the HI. However,
if a halo is added to this disk the rotation curve can be
made to fit the observations far more closely. This case
implies that the mass-to-luminosity ratio for the disk is
constant. However, the HI rotation curve can be fit well by
using an exponential disk with a different scale length.
This model does not have a halo. The rotation curve
resulting from this disk, with a“-^=10kpc, is shown in Figure
3-18. This curve and the n=l Toomre curve are very similar,
the main difference being that the exponential curve rises
faster than the Toomre curve in the inner 1.2'. In the
region near the ends of the bar, r=1.0' to 1.1' , the
exponential rotation law lies above the observed HI rotation
curve, whereas between r=2.2' and r=2.9', the exponential
lies below the observed HI curve. As this exponential
rotation law has a scale length greater than the scale
length for the luminosity distribution (Elmegreen and
Elmegreen, 1985), this implies that the mass-to-luminosity
ratio for this disk increases as the radius increases. The
total mass, out to r= °°, for this disk is 4x10 Umo. As
neither the exponential disk nor the n=l Toomre disk provide
significantly better fits to the HI rotation curve than the
other, an n=l Toomre disk is used initially in the
hydrodynamical modeling procedure.

137
The observed global profile of the neutral hydrogen in
NGC 1300 is shown in Figure 3-19. This spectrum has been
formed by integrating the Hanning-smoothed pixel spectra
over all pixels assumed to contain line signal. No
correction has been made for the effect of bandwidth
smoothing.
Table 3-2 presents a summary of the neutral hydrogen
observations.

FLUX DENSITY ( mJy )
138
Figure 3-19. KI Observed Global Profile. This
profile calculated from the interferometric observations
of NGC 1300.

139
TABLE 3.2
Summary of Neutral Hydrogen Observations for NGC 1300
Parameter
NGC 1300
Synthesized beam (FWHM) (arcsec)
20.05x19.53
Position angle of beam (°)
64.5
Channel seperation (km/sec)
20.6
Filter width (km/sec)
25.2
Channel rms noise (K)
1.26
Total HI map rms noise (1019cm”2)
5.00
Peak HI density (lO^cm-^
1.59
Observed systemic velocity (km/sec)
1575.2+0.5
Adopted distance (Mpc)a
17.1
Diameter of HI disk (arcminjp
6.40
Peak continuum brightness (K)
12.6
Position angle, line of nodes ( °)
-85.5 ±0.5
Inclination angle (°)
50.2±0.8
Observed width, Global profile (km/sec ¡p
345
Maximum rotation velocity (km/sec)
185
Radius of maximum velocity (arcmin)
2.47
9
Atomic hydrogen mass, M„T, (10 Mo)
rlJL
2.54
M^./L^ (solar units)
hi tí
0.11
a De Vaucouleurs and Peters (1981).
b Measured at an observed surface density, N =1.59x10^ cm
c Full width at 0.2 of peak.

CHAPTER IV
SURFACE PHOTOMETRY
Theoretical modeling of galaxies in recent years has
shown a tendency for the stellar disks to develop long-
lasting bar-like structures of global extent (see references
in Baumgart and Peterson, 1986). N-body experiments by
Miller and Smith (1979, 1980, 1981) and Hohl and Zang (1979)
suggest that prolate or triaxial bars are the natural form
to which a dynamical system may evolve. The conclusion is
that bar-like stellar structures are a preferred dynamical
form in the process of galaxy formation and evolution. In a
previous attempt to model NGC 1300, Peterson and Huntley
(1980) used a bar potential of the form given by Miller and
Smith (1979) as the non-axisymmetric perturbation. However,
Baumgart and Peterson (1986) show that the form of stellar
bars in barred spirals is not consistent with the
predictions of the three-dimensional N-body models of Miller
and Smith (1979). They conclude, in fact, that the
agreement is very poor. It would thus seem warranted that,
in attempting to model the response of the gaseous disk to
an imposed gravitational potential, some sort of "observed"
bar potential be used, rather than a "nice, convenient"
theoretical model which does not fit the observations very
140

141
well. With this objective set, surface photometry of NGC
1300 will be used to provide an "observed" bar potential to
use in the numerical modeling of the galaxy. As the modeling
procedure involves a search through a multi-parameter space,
any observational constraints that are available will help
to reduce the volume of the space that needs to be searched.
By providing the bar potential the number of possible
solutions is reduced and will hopefully lead to
astronomically plausible solutions as well as providing some
observational constraints for the non-axisymmetric mass
distribution.
The stellar population of the bar in a barred spiral
galaxy is expected to be well-mixed (Contopoulos, 1983). For
the modeling procedure used here the assumption can be made
that the imposed gravitational potential is due largely to
the stellar distribution and that the gas is responding to
this. Therefore for the "observed" bar potential some sort
of measure of the stellar distribution is needed. Near
infrared surface photometry is well-suited for this purpose.
Often the bar regions in barred spiral galaxies contain dust
lanes; NGC 1300 has two very prominent dust lanes in the bar
region (see Figure 1-1). Surface photometry is needed that
will penetrate these dust lanes and give the best possible
information on the unobscured brightness distribution of the
stellar population and contain as little contamination as
possible from the dust in the galaxy. The surface photometry

142
used for this purpose, as well as photometry in the blue
wavelength region, has been kindly provided by Drs. B.
Elmegreen and D. Elmegreen. Photometry at 2.2 um has been
provided by Drs C. Telesco and I. Gatley. For modeling the
bar, only the near infrared region will be used. However,
comparisons between colors and surface brightness
distributions will be analysed using all the wavelength
regions. Unfortunately, due to the lack of photoelectric
photometry, only relative intensity calibrations are
available. As the important quantities needed in the
procedure to calculate an "observed" bar potential are the
two-dimensional shape of the bar and the form of the
brightness distribution, having only relative intensities
will not hinder the determination of the "observed" bar.
Calculation ^f the Volume Mass Distribution
Surface photometry can only provide two-dimensional
information on the bar shape and the brightness
distribution. Some method is required to relate these two-
dimensional quantities to the three-dimensional quantities
needed in the modeling procedure. The modeling requires a
triaxial figure and a volume mass distribution. There is no
unique solution to this problem, which means that some
astronomically plausible assumptions have to be made so that
a three-dimensional figure can be calculated from the two-
dimensional information available. The assumptions used for
this conversion are

143
1. The mass-to-light ratio, M/L, within the bar is
constant.
2. The three-dimensional shape of the bar can be
described as a triaxial ellipsoid.
The assumption of constant M/L within the bar means
that the form of the mass distribution is the same as the
form for the surface brightness distribution. This
assumption also means that only having relative intensities
for the surface photometry will not preclude the extraction
of the form of the mass distribution from the surface
brightness distribution.
The assumption of a triaxial ellipsoid for the three-
dimensional shape of the bar is made for the following
reasons:
1. It is the most general form for a three-dimensional,
elongated object that is analytically tractable.
2. It is the form most often speculated to be the three-
dimensional shape of bars in barred spiral galaxies
and of elliptical galaxies as well.
Projection effects in triaxial figures have been
considered most recently by Stark (1977). He considered the
specific case in which the volume brightness distribution is
constant on similar concentric, nested ellipsoids. He shows
that irrespective of viewing angle the projection of these
surfaces will be similar concentric ellipses. The converse
is also true. Thus, in principle, a triaxial figure can be

144
calculated from a set of observed isophotes, if the
isophotes are assumed to be concentric ellipses. Ball (1984,
1986) applied this method to model the near infrared
isohotes of NGC 3359; Hunter et al. (1986) have also used
the technique to model the bar of NGC 3992.
The geometric parameters which describe the shape and
orientation of the triaxial figure are the axial ratio, 8 ,
of the isophotes and the three Euler angles, 0 , , and \p,
which relate the observer's coordinates to those in which
the equations of the ellipsoidal surfaces have the form
(tx)2 + (u/)2 + z2 = -a (4-1)
where is a parameter describing the volume brightness
distribution.
For a barred spiral galaxy where one axis is assumed to
be normal to the disk, the Euler angles become: 0 , the
complement of the inclination angle i; ^, the angle in the
sky between the major-axis of the isophotes of the bar and
the line of nodes of the disk; and , which is the angle in
the sky plane between the line of nodes and the projected
direction of the shorter of the two axes which lie in the
disk plane. The angle is an unknown and has a finite range
of values allowed by the observations (Ball, 1984).
The volume brightness distribution can be calculated
from the surface brightness distribution and, assuming
constant M/L within the bar, the form of the volume mass
density can be found. The relationship between volume

145
brightness distribution, Fv(av) , and surface brightness
distribution, F (ac), is given by (Stark, 1977)
S ¿5
F (a ) =
v v
1/2
aa_ ^ S
, 2 2-1/2 .
(ag -av ) aas (4-2)
v
where f is a constant for a given bar (Stark, 1977; Ball,
1984).
The function f., the surface brightness distribution,
S
is obtained by describing the observed surface brightness as
an analytical function. This function should be as good a
fit to the observed surface brightness distribution as
possible and must go to zero at infinity. For reasons of
convenience it is helpful if the type of function chosen for
F is one that allows equation 4-2 to be evaluated
analytically.
Thus, in summary, the quantities needed from the
surface photometry to describe the bar are
1. The functional form of the surface brightness
distribution, f (a0), gives , via equation 4-2, the
s s
volume brightness distribution, Fv(av) ¡ and, assuming
constant M/L within the bar, the form of the volume
mass density.
2. The axial ratio of the isophotes and their
orientation gives the axial ratio and semi-major axis
of the triaxial figure.

146
Surface Photometry of NGC 1300
Modeling the I Passband Features
The surface photometry used to model the bar for NGC
1300 is near infrared (I passband) having an effective
wavelength of 8250$ and a short wavelength cut-off of 7300$,
which thus excludes the Hydrogen alpha line emission. The
reduction procedures have been described previously by
Elmegreen and Elmegreen (1985). Figure 4-1 shows a gray
scale representation of the galaxy in this passband; Figure
4-2 is a contour plot of the I plate. The galaxy image in
this passband is clearly dominated by the bar, as expected
at this wavelength, although spiral arms can be traced
through almost 180° in azimuth. Clearly evident at the
center of the galaxy is a strong peak of emission, a nuclear
bulge component. The west arm shows a break at a position
angle of 0°. A similar but not as sharply delineated break
is evident in the east arm at position angle 170°. These
features correspond to the breaks evident in the optical
photograph.
The prominence of the bar in this passband and the lack
of evidence for major dust obscuration, although some will
be present, bodes well for the extraction of a triaxial
figure from this photometry for the hydrodynamical
calculations. Some evidence for the dust lanes, clearly
visible in the optical photograph (Figure 1-1), can be seen
near the ends of the bar. Here the isophotes are pinched

147
Figure 4-1. NGC 1300 Gray Scale I Passband

DEC
148
NGC 1300
N1300. IR
R fl 3 17
Figure 4-2. Contour Plot of I Plate. The contour
interval is 10% of arbitrary peak value. Fiducial star
positions are marked (+).

149
together. In following the isophotes from the center
outwards, the general trend is for an elliptical shape. The
dust lane region tends to pinch the isophotes together and
beyond this region they again broaden out. This
contamination of the isophotes will not be serious in the
attempt to extract a triaxial figure, as long as it is
recognized and compensated for in the modeling of the
brightness distribution. The relative lack of importance of
the dust obscuration at this wavelength can be estimated by
comparing profiles from the I passband with profiles from
other passbands, such as the blue. This will be done in a
later section.
The first step in modeling the bar as a triaxial figure
based on the observations is to remove some of these small
scale fluctuations in the isophotes. Some method is needed
to "average out" these fluctuations while leaving the
overall shape of the isophotes largely unaltered and not too
broadened. The data from Figure 4-2 were convolved with a
two-dimensional Gaussian function with a=0.045', or 2 pixels
(FWHM), and truncating the Gaussian at the 1% level. The
resulting image is shown in Figure 4-3. A good deal of the
small scale fluctuations have been smoothed-out but some are
still present. A convolution of the original data with a
two-dimensional Gaussian with a=0.09', or 4 pixels (FWHM),
showed a significant decrease in the small scale
fluctuations, but also showed a distinct broadening of the

150
isophotes. This convolution was therefore discarded and the
2 pixel convolution was used. Four components are clearly
present in this image:
1. A central bulge.
2. A broad elongated bar.
3. Spiral arms.
4. A low brightness disk component.
Using this passband to provide constraints for the
triaxial figure to be used in the hydrodynamical modeling
procedure requires that only the bar component be used.
Thus, estimates for the shapes and brightness contributions
to the overall brightness distribution of the bulge and disk
components must be made. The arms can, in actual fact, be
ignored as their contribution starts at the end of the bar
and does not affect the bar region itself. However, the
bulge and the disk effects must be allowed for and
corrections applied.
As an aid in isolating the various components, profiles
were constructed at various positions in the galaxy. The bar
major- and minor-axis profiles are plotted in Figure 4-4;
cross profiles at 20" intervals along the bar are also
shown. Some features of note in these profiles are the
central bulge and the rise at r=76" of the major-axis
brightness when compared with the other profiles. The latter
is the beginning of the spiral structure. The disk component
is seen at r=40" on the minor-axis and cross profiles. The

DEC
151
NGC 1300
CNVOLVEO
R R 3 17
Figure 4-3. Convolved I Passband Image NGC 1300.
Contour plot of the convolved image of NGC 1300. Contour
levels are arbitrary and fiducial star positions are
shown (+).

152
bulge has a steep rise and a noticeably flat plateau region
at the center. These profiles correspond to Freeman type 1
profiles, in that the intensity always lies above the
contribution from the disk (Freeman, 1970). This means that
I(r) > IQ exp[-ar] (4-3)
for all observable r.
Elmegreen and Elmegreen (1985) analyzed the disk
component of the galaxy as having an exponential form,
I(r) = Iq exp[-ar] (4-4)
where a--*- is an effective scale length and is a scaling
factor. The values quoted in their Table 2 are too large by
a factor of 2, thus their scale length for the I passband
for NGC 1300 is a ^=6.96kpc. At a distance of 17.1Mpc this
corresponds to a -1.399' for NGC 1300.
Estimates for the ellipticity, and hence the
inclination, and major-axis position angle were calculated
by using a few outer isophotes. These isophotes are far
enough from the bar and spiral arm regions so that the
assumption can be made that they are unaffected by these
components and only have contributions from the disk
component. The factor, I , was calculated using an iterative
o
procedure which calculates a model brightness distribution
for the disk. By comparing this model with the outer regions
of the observations a value for IQ can be found quickly.
This procedure yielded a good fit to the observed outer
isophotes using the following parameters:

INTENSITY
.figure 4-4. Bar Brightness Profiles. Major- and minor-axis
profiles for I band image of NGC 1300. Also plotted are cross-
profiles at intervals of r=20" along the bar.
153

154
1.
2.
3 .
4.
3 =1.546, (i=50u)
o
Axial Ratio
Position Angle
Length Scale
Scaling Factor
Thus, the form of the disk brightness distribution
4, = 101 .
i-1 =1.399'
1^=150, (arbitrary units).
i s
I(r) = 150 exp[-r/l.399] (4-5)
where r is in arcminutes.
Figure 4-5 shows this disk and the observed major-axis
profile. As this exponential form for the disk surface
brightness gave a good fit to the observations in all but
the very inner regions, no other functional form was tried.
In the inner region, where the exponential form deviates
most significantly from the observations, the exact form of
the components is unimportant, as the region of most
interest is in the outer bar region. The isophotes in the
central bulge region are not used in trying to extract a bar
figure from the observations. Using an exponential form for
the disk surface brightness rather than some other
functional form was a choice of convenience and because this
form gave a good fit to the observations. This does not
imply that the disk is actually an exponential disk. No
attempt was made to calculate a definitive disk type; the
objective of this component fitting procedure was just to
get an estimate of the bar figure.
The model disk brightness distribution was subtracted
from the smoothed image, leaving the bar, spiral arms and
bulge components. The spiral arms in this "disk-subtracted"

INTENSITY
Figure 4-5. Disk Surface
observed major-axis profile for
Brightness.
I band image
Exponential
of NGC 1300
disk and
155

156
image can be traced through almost 340° in azimuth. The next
step in isolating the bar contribution is to remove the
bulge component.
The removal of the bulge component does not have to be
exact. If the assumption is made that the bulge has a
limited radial size, and if only the outer isophotes of the
bar are used in the modeling procedure, then only a
reasonable estimate of the bulge need be removed. As can be
seen in Figure 4-5 the central portion of the brightness
distribution is rather steep with a broad plateau feature at
the center. This is partly due to the photographic plate
being saturated at the center (Elmegreen and Elmegreen,
1984). Various functional forms were tried in fitting these
inner isophotes. Gaussian functions of the correct width did
not have the correct plateau feature at the center;
cylindrical functions had the correct plateau feature but
not the required wings in the distribution. A functional
form represented by a cylinder, convolved with a two-
dimensional Gaussian function gave the best fit to both the
plateau feature and the wings of the distribution. The forms
for the cylinder and the convolving Gaussian are
1. Cylinder:
a) I(r)=I rr where I =900
° o o o
(arbitrary units), and ro=0.1125'.
2.
Gaussian:

157
2 2
-r /2a
a) f(r)=fe 7 where f Q=1 (arbitrary units), and
a=0.225' (FWHM).
The resultant bulge is shown in Figure 4-6. The bar
major-axis profile after subtraction of the disk and bulge
components is shown in Figure 4-7. A contour plot of the
resultant brightness distribution is shown in Figure 4-8.
In modeling the brightness distribution of the bar,
only isophotes away from the center are used. This is
because the true form of the bulge is not known and the
procedure used here is only approximate. Two sets of
parameters are needed to characterize the bar: a geometrical
set consisting of the axial ratio- and the position angle of
the major-axis of the isophotes; and a major-axis radial
brightness distribution.
The geometrical parameters were estimated by comparing
model concentric ellipses with the observed isophotes. The
parameters used for the geometrical set are
1. Axial ratio $=2.93
2. Position angle (j> =111°
Two functional forms for the brightness distribution in
the bar were used, an exponential of the form
I(r) = IQ exp[-a/r]
(4-6)
and a Gaussian of the form

INTENSITY
158
PIXELS
Figure 4-6. Bulge Component Model. Cylindrical
function convolved with a Gaussian function used to
model tne bulge in NGC 1300.

INTENSITY
Figure 4-7. Bulge Subtracted Disk Profile. Comparison
of model Gaussian and exponential bar major-axis profiles after
subtraction of the bulge.
159

160
Figure 4-8. Bulge Subtracted Contour Plot. Model
brightness distribution contours for NGC 1300. A Gaussian
distribution is shown for the bar model. Fiducial star
positions and the observed brightness distribution are
also marked.

161
(4-7)
In contrast to Baumgart and Peterson (1986), who find
that the radial distribution is best fit by an exponential
function, the observed profile is significantly better fit
by a Gaussian function than by an exponential. Figure 4-7
also compares the "best fit" Gaussian and the "best fit"
exponential with the bulge- and disk-corrected profile. Note
that at r~75" the rise in the observed major-axis profile is
due to the beginning of the spiral structure. Model
deviations from the observed isophotes occur for the
outermost levels near the ends of the major-axis. This is
due to the onset of spiral structure at the ends of the bar.
Some residual effects from the dust lanes are responsible
for the deviations near the ends of the major-axis. The
observed isophotes are significantly narrower than the model
isophotes. The overall fit is, however, good and a Gaussian
brightness distribution is used. This "Gaussian bar" is
shown in Figure 4-8.
The form of this Gaussian brightness distribution is
f(r) = fQ exp[-r2/2o2]
(4-8)
where f =450 (arbitrary units) and a=1.0' (FWHM).
As a final check on the quality of the model
components, the disk, bulge and bar brightness distributions
were added together and compared with the observations. The

162
isophotes are shown in Figure 4-9; the major-axis and minor-
axis profiles in Figure 4-10. The only significant departure
of the observations from the model occur at the ends of the
bar where the spiral structure begins. The model brightness
distribution does not have a spiral arm component, thus
discrepancies in the region of the spiral arms are to be
expected. This figure indicates that the overall model is a
good representation of the observed brightness distribution
and is adequate for the calculation of a triaxial ellipsoid
for the modeling procedure.
In summary the model components for the I passband are
1. Disk: Exponential
I(r) = Iq exp[-r/l.399]
2. Bulge: Gaussian convolved cylinder
a) Cylinder
I(r)=900 r < 0.1125' l(r)=0 r >
0.1125'
b) Gaussian function
f(r) = exp[-r2/2 (0.225)2]
3. Bar: Gaussian
f(r) = 450 exp[-r^/2]
@ = 2.93,


163
Figure 4-9. I Band Model Isophotes. Model
surface brightness distribution in I band for NGC 1300.
All components; disk, bar and bulge are added.

INTENSITY
60
40
20 0 20
RADIUS ( arcsec )
40
60
Figure 4-10. I Band Model Profiles. Major- and minor-
axis profiles for the resultant I band model for IJGC 1300.
The observed profiles are shown for comparison.

165
Comparisons Between Different Passbands
Surface photometry in the blue passband (\=435o'R) will
be affected significantly by dust obscuration in the bar
region. These dust lanes are very evident in the optical
photograph of the galaxy. By comparing blue photometry and
near infrared photometry some information on this dust
obscuration may be obtained. Figure 4-11 is a gray scale
representation of the blue image and Figure 4-12 is a
contour plot of the smoothed image. The image was smoothed
to reduce small scale fluctuations by convolving with a two-
dimensional Gaussian function with a =0.045', or 2 pixel
(FWHM), truncated at the 1% level. Although some
fluctuations are still noticeable in Figure 4-12, smoothing
with a broader function will degrade the resolution too
much. The main features can be identified in Figure 4-12.
The most noticeable features in the blue are the almost
circular, bright central bulge region, the arms and the flat
bar region. The arms can be traced for about 180° in azimuth
and show breaks where they are crossed by dust lanes. Figure
4-13 plots log-intensity as a function of radial distance
along the minor-axis for the northern and southern sections
separately for both the blue and infrared plates. The two
profiles agree well except at r~50" where the northern
profile is fainter than the southern one. This is due to the
break in the arms; the northern break being more sharply
defined, as can be seen in Figure 1-1. Thus the brightness

166
NGC 1300 BL 4350R
#e *
Figure 4 11. Gray Scale of Blue Passband.

DEC
167
NGC 1300
CNVOLVED
Figure 4-12. Contour Plot Blue Passband. Con¬
tour plot of tne convolved blue passband image of NGC
1300. Contour levels are arbitrary. Fiducial stars (+)
and the center of tne galaxy (x) are marked.

168
drops more significantly in the western arm than in the
eastern arm, as shown by these profiles (Figure 4-13). This
effect can be seen in both the blue and the near infrared
passbands.
These profiles also indicate that in the region between
the bar and the eastern arm the brightness drops below that
for the corresponding region in the northern section. The
effect is more noticeable in the blue than in the I
passband. Also hinted at in these profiles is the very steep
drop-off in luminosity at large radial distances from the
center. Blackman (1983) noticed a similar effect in NGC
7479. The data here do not go deep enough to warrant a
detailed analysis but certainly do not rule out the
possibility of a steep drop-off in luminosity.
The bulge is very nearly circular, having an apparent
axial ratio of 1.15. The rise from the bar region is steep,
rising quicker than in the near infrared passband. Figure
4-14 compares the major- and minor-axis profiles for the
blue and I passbands. Regions of enhanced brightness are
seen at the ends of the bar and the beginning of the spiral
arms, indicating vigorous star formation in these regions.
The luminosity distribution along the length of the bar is
fairly smooth, indicating a lack of star formation. The
regions of star formation at the ends of the bar and the
beginning of the spiral arms, r=80" on the major-axis, are
bluer than other regions. The region r=15" to 50" on the

INTENSITY
X
*
X
BLUE
• NORTH
x SOUTH
r*.
*
xx
X
X X X
Zj* xx
V^VxV, x
X •
x X
XC .
* X
**x
X
X
+
+
20
RADIUS
h-
40 60
( arcsec )
+ X*
X •
*•
X •
in
z
LÜ
x NORTH
• SOUTH
fib
\
:Yf.-
4»V
x •• ..
X'
•• •
X* x
* X
X x • •
X* X -
V
+
+
+
20 40 60
RADIUS ( arcsec )
Figure 4-13. Minor-axis Profiles Blue and I Passbands. Log-Intensity
as a function of radial distance for I and blue passbands. Two halves of the
minor-axis are shown for each passband.
169

170
major-axis clearly indicates the effects of the dust lanes
in that the shapes of the profiles are depressed when
compared with the I passband profiles. This justifies the
assumption that the I passband should give a better result
for the "observed" bar than the blue passband. Comparisons
between profiles perpendicular to the bar major-axis at
various radial positions along the bar (Figure 4-15) clearly
indicate the differing effects of the dust lanes in the
different wavelength regions. The profiles at positions
r=20" clearly show the blue profile depressed relative to
the I band profile, whereas at the other radial positions,
apart from small scale fluctuations, the blue and I profiles
are similar.
Photometry of limited spatial extent at 2.2um shows
effects similar to those seen in the blue and I passbands.
Figure 4-16 is a contour plot of the data, and Figure 4-17
is a false color image of the galaxy at 2.2um. The bright
central source is clearly visible as are the beginnings of
the spiral structure. Some pinching of the isophotes can be
seen near the ends of the bar region. The dust obscuration
is minimal, as the extinction due to dust at 2.2um is less
than 10% of the associated visible extinction, Ap,=0.
Although it is small, it has some effect on the isophotes as
can be seen in Figure 4-16. The two halves of the major-axis
profile are plotted in Figure 4-18 which plots log-flux as a
function of radial position from the center. The very bright
central source and the beginning of the arms are visible.

INTENSITY
Figure 4-14. Profile Comparison. Major- and minor-axis profiles
for I and blue passbands for NGC 1300.
171

Figure 4-15. Comparison of Blue and I Profiles.
Comparison of profiles perpendicular to bar major-axis
for blue and I passbands.
A. West arm.
B. East arm.
Positions indicated are arcseconds along the
major-axis east or west of the assumed center of the
galaxy.

INTENSITY
173
Figure 4-15 cont. (Part A).

INTENSITY
174
Figure 4-15 cont. (Part B) .

175
Figure 4-19 compares the average radial forms of the major-
axes for the three wavelength regions considered here. These
profiles are normalized to be approximately equal at the
center. The 2.2um profile has the highest peak-flux to
average bar-flux ratio of the three passbands. It is
interesting to note that the 21cm observations indicate a
bright continuum source at the center of the galaxy and
little signal in regions immediately surrounding it. It
thus, perhaps, suggests that the central source becomes more
dominant over its immediate surroundings as the wavelength
increases from the I passband to the 21cm observations. The
peak-flux to average bar-flux ratio increases as the
wavelength increases from 0.825um (I passband) to 2.2um to
21000um (radio). The ratio is approximately 3:15:20 for
0.825:2.2:2lOOum regions.
Triaxial Ellipsoid
The surface photometry describes the bar figure in
terms of the axial ratio of the isophotes, the two Euler
angles and the surface brightness distribution. Using values
of i=50.2°, ó =-79 ° <¿.^,=-85.5° and semi-major axis of
BAR ynON J
the bar a=77.66", these parameters are g =2.93, 0 =39.8°,
o
4^=6.5 and
2 2
FS (ag) = 450 exp[-a5 /2a ], a = 1.0' (FWHM)
(4-9)

176
Figure 4-16. Contour Plot 2.2um. Fiducial star
positions are marked (+).

Figure 4-17. False Color Plot 2.2um. Blue represents low
flux and yellow represents high flux. North is to the top and east
is to the left.


FLUX ( m Jy/ beam )
179
10,0
O EAST
8.0
X WEST
6.0
5.0
4.0
o
x
3.0
2.0
X
1.0
—I 1 1 1 I—
20 40 60 80 100
RADIUS ( arcsec )
Figure 4-18. Flux Profile 2.2um.
of the major-axis brightness profile for
of NGC 1300.
ARM
ARM
Two halves
2.2um image

INTENSITY
180
Figure 4-19. Comparison Between Different Wave¬
lengths. Radial forms of major-axis profiles for blue,
I and 2.2um images of NGC 1300.

181
The maximum value for the third Euler angle and the
parameters t and u, which describe the families of triaxial
ellipsoids, can be calculated from these parameters (Ball,
1984). If the semi-major axis is a and the other semi-axes
are b and c where c is perpendicular to the disk, then
(Ball, 1984) u=c/a, u/t=b/a, and
tan * v = cos 9 (sin2 + g2cos2 ^ (4-10)
(g-l) sin \p cos ip
Numerically $ =82.55°; the minimum value occurs when t
max
vanishes, giving All possible shapes of triaxial ellipsoids satisfying
the observations fall within this narrow range of . The
uncertainty in arises because, for an inclined triaxial
figure with three finite axes, the longest axis of the
ellipsoid need not point in the same direction as that of
its two-dimensional projection. As the figure becomes more
elongated the figure begins to resemble a rod of
infinitesimal thickness and the discrepancy between the
direction of its longest axis and that of its two-
dimensional projection diminishes (Ball, 1984). Following
the procedure outlined in Ball (1984) and Hunter et al.
(1986), the various figures for the triaxial ellipsoid can
be calculated. Table 4-1 shows the quantities of interest in
the range allowed by the observations. The ellipsoid is
prolate if b/c=l which corresponds to =81.56°. As b/c

182
increases the ellipsoid becomes more flattened in the disk
plane, b/c>l; as b/c decreases the flattening takes place
perpendicular to the disk plane, b/c correspond to the cases when one or the other of the shorter
semi-axes vanishes.
Thus, for NGC 1300 the prolate case corresponds to
a=77.66" , b/c = l. 00, a/c=2.94 and ((>=81.56°.
For values lower than 81.56° the figure is flattened
perpendicular to the disk plane. It is very unlikely that
the bar in a real galaxy is flattened perpendicular to the
disk plane; these values for will not be used here.
The volume brightness distribution can be calculated by
evaluating equation 4-2 (Stark, 1977; Ball, 1984)
1/2 r o
7T
d 2 1 -1/2
Fs(aq) (a -a ¿) / d aq (4-12)
das b s J S v b
a
v
Using
W = FSo exp[-as2/2o2]
and integrating gives (Appendix A)
exp[-av2/2o2]
(4-13)
Under the assumption of constant M/L within the bar
region, the volume density distribution is

183
TABLE 4.1
Bar Projection Parameters for NGC 1300
<{>
(O)
u2
t2
b/a
c/a
80.74
1.02xl0-4
5.27xl0-5
3.19x10"3
0.440
81.00
0.0343
0.2011
0.185
0.413 .
81.56
0.1156
1.0000
0.340
0.340
82.00
0.1860
2.7406
0.431
0.261
82.54
0.2847
327.87
0.534
0.029
a=l.2943'
9=39.8°
^=6.5°

184
P(r) = pQ exp[-r2/2o2] (4-14)
where o = 1.0' (FWHM).
The triaxial ellipsoid specified by this volume density
distribution and these geometrical parameters can now be
incorporated into the hydrodynamical models of the galaxy.
The photometric data should be quite valuable in reducing
the uncertainty associated with the non-uniqueness of the
models. The mass distribution of the axisymmetric component
has been constrained by the rotation curve from the HI
observations and the non-axisymmetric mass distribution has
been constrained by the near infrared surface photometry.

CHAPTER V
MODELING
The Beam Scheme
The hydrodynamical modeling of NGC 1300 and the other
galaxies considered in this project was carried out using a
two-dimensional, gas-dynamical scheme known as the "beam
scheme." This computational method was first introduced by
Sanders and Prendergast (1974) and has been used on numerous
occasions to model the two-dimensional gas flow in galaxian
disks (Huntley, 1977; Peterson and Huntley, 1980; Schempp,
1982; Huntley, Sanders and Roberts, 1978; Sanders and Tubbs,
1980; Ball, 1984, 1986; Hunter et al., 1986). The
hydrodynamical properties have been reviewed by Sanders and
Prendergast (1974) and various aspects of its applicability
to barred spiral galaxies have been discussed in the
references given above. Thus only a short overview of its
essential features will be given here.
The behaviour of the constituent gas in the galaxy is
represented by hydrodynamical equations. If the gas density
is given by p, the gas velocity vector by V, the pressure by
P and the kinetic energy density by E, then neglecting the
effects of magnetic fields, the equation of mass continuity
for a compressible fluid becomes
185

186
(P) + V* (PV) = O
(5-1)
the equation of motion
(pV) + V(pV2 + P)-F = o
(5-2)
and the energy density
ft (E) + V-[v(E + P)]-Q = o
(5-3)
Here Q explicitly represents dissipative terms, such as
viscosity and heat conduction;d F, the force, consists only
of gravitational and viscous terms. Omitting the viscous
terms from F means that F becomes solely gravitational and
is specified by Poisson's equation:
(5-4)
The essential characteristic of the "beam scheme" is
that the velocity distribution is broken into a number of
discrete beams with a velocity distribution F(u,v,w). The
velocity distribution is Maxwellian and for each
computational cell has the form
Fj(u,v,w) = Aj exp[(-l/2aj2)((u-uj)2-v2+w2)] (5-5)

187
where j represents the cell, Aj is proportional to the mass
density in cell j, and is the velocity dispersion.
As the two-dimensional form is similar to the one¬
dimensional form, the one-dimensional form will be used here
for illustrative purposes. In one dimension this consists
of a central beam and two side beams offset by Au from the
central beam. In each beam all matter moves at a single
velocity with the mass density in the beams being a^ for the
central beam and b. for the side beams. Sanders and
1
Prendergast (1974) show that a good choice is a.=4b._, giving
2 3 3'
(Auj) =3 o j
The mass density, p^, momentum density, , and energy
density, ej, for the three beams are
1. Central beam;
p .
= 4b .
1
1
p.
= 4b ü
1
1 j
E .
= 2b . ü.
1
3 1
> . a .
J J
2. Side beams;
pj = bj
P ■ - b . (u ± /3 a .)
D 3 j 3
(- 2
Uj +
v 2
^3 u. a• + 5/2a-2
J J J ,
(5-6)

188
where u. is the bulk velocity and a. is the velocity
1 1 1
dispersion.
The system evolves over a number of timesteps with each
beam transporting a proportion of its mass, momentum and
energy to a neighbouring cell. The fraction transported is
equal to the portion of the cell traversed in each time
step. The size of each time step, t, is computed by using
the Courant condition (Roache, 1976):
At < L/umax (5-7)
where L is the cell size and u is the maximum gas
max
velocity in any cell at the start of each time step.
At the conclusion of each time step the Maxwellian
velocity is re-established giving rise to an artificial
viscosity, Ti/ where
n = p .AujL. (5-8)
This viscosity has been discussed by Sanders and
Prendergast (1974), Huntley (1977) and Huntley, Sanders and
Roberts (1978) and its justification lies in the fact that a
real, physical viscosity must be present in the gas to avoid
gas streamlines crossing. Ball (1984) found that the details
of the viscosity are unimportant, which is fortunate as
there is little information available on the real viscosity
in the interstellar medium.
Having given a brief overview of the essential
characteristics of the beam scheme, the reasons for its use

189
in modeling the gas response for the galaxies considered
here will be discussed. The beam scheme has demonstrated its
effectiveness in modeling gas flows on a galactic scale
(Huntley, 1977; Sanders and Tubbs, 1980; Schempp, 1982;
Ball, 1984; Hunter et al., 1986) and the results agree with
those from other two-dimensional gas codes using the same
initial conditions (Sanders, 1977; Berman, Pollard and
Hockney, 1979). The numerical stability of the scheme is
excellent in all regions where the gas flow is not subsonic
(Ball, 1984). The artificial viscosity present in the scheme
ensures stability of the flow even in the presence of
shocks. Although the beam scheme indicates the presence of
shocks in the gas it does not accurately produce their
strengths or their positions. Van Albada et al. (1981) find
that the density maximum is severely underestimated and is
displaced downstream by a significant amount. In the smooth
region of the flow only the most general features are
represented. Despite these drawbacks the scheme which is
second order accurate in time and better than first order
accurate in space, has sufficient accuracy and spatial
resolution to model the VLA HI observations. The scheme,
while clearly resembling standard upwind, finite-difference
schemes, also exhibits properties similar to "smooth-
particle" codes (Roache, 1976). It thus represents a
compromise between the mathematical formality of treating
the galaxy as a continuous fluid and the physical complexity
of treating it as a collection of diffuse HI clouds.

190
Before describing the application of the beam scheme to
a particular galaxy (NGC 1300), some general properties of
its implementation must be noted. These properties describe
the initial conditions for the modeling and, once decided
upon, remain constant for a particular galaxy. They include
the choice of the grid size, the computational frame, the
sound speed and the initial start-up conditions.
The grid chosen is a two-dimensional Cartesian grid of
32x64 cells. A Cartesian grid is used, as both dimensions of
the cells are the same, which gives a numerical viscosity
which is nearly constant everywhere in the disk. A polar
grid for the computations could lead to confusion between
numerical artifacts and real structure. Numerical artifacts
could give rise to rings or possibly even spiral features on
a polar grid, whereas on a Cartesian grid these artifacts
are most unlikely to give forms that could be confused with
real structure. The grid size of 32x64 is used on the
assumption that the forces and gas responses are bisymmetric
and that the full 64x64 grid can be calculated using only a
32x64 computational grid. One of the longer boundaries
defines the meridian plane of the galaxy; any matter
crossing this boundary re-enters the grid at a point
symmetric, with respect to the galaxy center, with that
which it has just left. The other boundaries of the grid are
transparent and any matter crossing them is permanently lost
from the calculations. The gas disk is also constrained to

191
lie within a radius of 32 grid cells; again, any matter
having a radius greater than this is removed from
consideration. Thus, there is a gradual loss of gas during
the course of a calculation but the amount of gas lost,
typically, does not seriously affect the calculations until
four or five bar rotations have taken place. Tests showed
that if a quasi-static situation was going to develop
(steady-state apart from gas diffusion through the
boundaries), that it would develop after approximately 1 to
1.5 bar rotations. Thus the gas diffusion will not seriously
affect the calculations as long as the timescale is kept to
less than about 3 to 4 bar rotation periods.
The gas density is initially constant over the disk and
is maintained in a strictly isothermal state. The thermal or
turbulent velocity dispersion of the gas is chosen to be
17km/sec although the model calculations are not very
sensitive to changes of this value on the order of 10km/sec.
This result was shown in Huntley, Sanders and Roberts (1978)
and also confirmed by a series of tests during the modeling
of NGC 3992. Various models were calculated with velocity
dispersions ranging from 7km/sec to 27km/sec with very
little discernible difference between the models. Huntley
(1980) also found very little difference in the final models
when the velocity dispersion was changed by a factor of
four.

192
The gaseous disk initially rotates as a solid body with
angular frequency /2/2 that of the galaxian bar that will
eventually be established. The gas is in equilibrium
initially, but if at any timestep the velocity field is not
close to the equilibrium field for the forces then present,
severe disruption of the gas flow can result. This
necessitates the careful introduction of the perturbing
forces.
The perturbing forces are gradually introduced into the
system over 100 timesteps. Thus, for each timestep 1% of the
initial uniform-rotation force is turned-off and 1% of the
perturbing force is turned-on. This allows the gas to adjust
quasi-statically to the noncircular perturbing force of the
imposed galaxian bar. These first 100 timesteps generally
correspond to between 0.4 and 0.8 bar rotations which is
long enough so that no severe disruption of the gas flows
result. This should eliminate the problems found by Schwarz
(1985) in the beam scheme models of Schempp (1982). Schempp
used the following turn-on procedure. The gas is initially
in uniform circular motion and the bar field is turned-on
linearly over one-twentieth of a bar rotation, approximately
10 timesteps. Schwarz found that this very rapid,
essentially impulsive, turn-on of the bar force field
induces radial motions in the gas. These transient motions
have timescales which are long, compared with 0.5 bar
rotation periods. Thus some of these transients may still be

193
present after 0.5 bar rotation periods. Schempp, in his
models, turns on the noncircular force field over a period
of two bar rotations. However, as the beam scheme
continually, although gradually, loses mass through the grid
boundaries, two bar rotation periods was considered to be
excessively long for the turn-on period. The bar force was
thus turned-on in the first 100 timesteps of the
calculation. This generally meant between 0.4 and 0.8 bar
rotation periods. As the evolution of the model was
generally followed for about 3 to 3.5 bar rotations, the gas
has ample time to settle into a quasi-static configuration.
Numerical experiments were performed in which the
noncircular perturbing force was turned-on over 300
timesteps (1.2 to 2.4 bar rotations) and over 50 timesteps
(0.2 to 0.4 bar rotations); the response was compared with
models in which the perturbing force was turned-on over 100
timesteps. After 600 timesteps, 2.5 to 5 bar rotations,
there were essentially no differences between the two
situations, thus indicating that turning-on the noncircular
force field in the first 100 timesteps is slow enough so
that the gas can respond quasi-statically, and that all
transients have died away by the time the calculations are
stopped, but not too slow as to be computationally
excessive. The response from 400 to 600 timesteps can thus
be considered to be quasi-static, with the only secular
changes being the gradual decrease in mass, the gradual

194
increase in contrast between the highest and lowest
densities present and the gradual increase in the buildup of
matter at the center few pixels. This buildup is artificial,
a result of the code and has been discussed by Huntley
(1977) and Ball (1984); it does not seriously effect the
computations.
The choice of the computational frame is not
straightforward, as numerical effects alter the gas response
in various frames of reference (Huntley, 1980). In the
inertial frame the rotation speed of the bar can become
large enough so that it sweeps past more than one cell in
one timestep. The gas does not have a chance to respond
properly to the perturbation, which it sees as being
broadened or smeared out. This corresponds to effectively
increasing the viscosity in the grid. In a frame rotating
with the bar a "corotation zone" exists in which the
computed velocities are nearly zero. A non-physical ring of
gas forms at this zone as it is easier for the gas to enter
this region than it is to leave it. Huntley (1980) and Ball
(1984) have discussed these effects in more detail and
conclude that a frame intermediate between the inertial
frame and the rotating perturbation frame is the best choice
for the computational reference frame. However in choosing
this intermediate frame care must be taken to avoid having a
corotation zone in the computational frame. The intermediate
frame chosen is that recommended by Ball (1984). The frame
is chosen so that the estimated corotation zone occurs at

195
approximately five grid cells off the computational grid, at
r=37 grid cells. This ensures that all velocities on the
computational grid are high enough to avoid numerical
artifacts and to minimize the problems of added viscosity
and lower effective resolution in the outer parts of the
grid.
As mentioned earlier the beam scheme is a multi¬
parameter scheme; the task of searching through this multi¬
parameter space for an astronomically plausible solution
could be daunting, unless some observational constraints are
used to reduce the volume of this space. The constraints
used for this task have been discussed in detail in Chapters
2, 3 and 4, but they will be summarized here before the
discussion of the modeling results.
The axisymmetric mass distribution is initially
constrained by the rotation curve from the HI observations.
These observations resulted in the choice of the
axisymmetric mass distribution being a Toomre disk of order
n=l. This disk, out to a radius of r=3.2' , has a mass of
4.9x10^Mo. The total HI mass, at an assumed distance of
17.1Mpc, calculated from the observations is 2.54x10^Mo;
this gives the ratio M/M =0.052 and thus, as the gas is a
n i
small fraction of the total mass, the self gravity of the
gas will be ignored. No halo was added to the basic model
initially, although models with halos will also be
considered.

196
The initial non-axisymmetric mass distribution is
provided by the triaxial ellipsoid calculated from the near
infrared surface photometry. The shape of the ellipsoid,
whether it is prolate or flattened, and the central density
are free parameters. The form of the density distribution
and the length of the major-axis are fixed by the
photometry. The non-axisymmetric mass distribution is only
useful if the forces arising from it can be calculated.
Following the procedure of Hunter et al. (1986), the
ellipsoid is divided into 300 concentric homoeoids
(ellipsoidal shells). The potentials and hence, the forces,
for these homoeoids can be evaluated exactly without resort
to elliptic integrals or numerical integration. Thus the
triaxial ellipsoids given by the surface photometry can be
easily incorporated into the hydrodynamical modeling code.
Schempp (1982) in his conclusion states that the prolate
spheroids chosen for his models are completly arbitrary and
that the Miller and Smith (1979) bars are very restricted.
Also Baumgart and Peterson (1986) show that the Miller and
Smith (1979) bars are not good fits to the observations. In
light of these comments and the success in modeling NGC 3359
(Ball, 1984) and NGC 3992 (Hunter et al., 1986) using this
approach should provide good "observational" constraints for
the theory and should give more plausible results than
either an arbitrary bar figure or the purely theoretical
Miller and Smith bar.

197
The basic modeling philosophy is to start with a
gaseous disk and the triaxial ellipsoidal bar. The best
model using these components is calculated and gradually
various other components such as oval distortions and halos
are added. Each time a new component is added, the best
model is calculated, matching, as closely as possible, the
observed rotation curve, velocity field, and morphological
features. As the models are computed in the galaxy plane and
have greater resolution than do the observations, each
successful model is projected onto the sky plane and
convolved with a synthetic beam to give a resolution
matching that of the observations. For an elongated disk
galaxy, the shape of the angle-averaged rotation curve
depends considerably upon the true orientation of the galaxy
in space. By varying the location of the bar major-axis
relative to the position angle of the line of nodes, the
angle-averaged rotation curve can be radically altered.
Figure 5-1, taken from Hunter et al. (1986), shows the
change in the rotation curve for NGC 3992 when projected at
two different values of , where $ is the angle between the
bar major-axis and the line of nodes. This shows, very
vividly, that the models must be projected into the same
orientation as the observed galaxy in order for the results
to be meaningful. All the results displayed in the next
section are projected and convolved to the same orientation
and resolution as the observations and are thus directly
comparable with the observations in Chapter 3.

Figure 5-1. Dependence of Rotation Curve on Projection
Parameters. This diagram is from Hunter et al. (1986) and shows
tne curves for two values of is the angle between the
bar major-axis and the line of nodes. The velocity fields for
these two cases are also shown.
A.

B.
A
V
(km/t)
B
199

200
Hydrodynamical Modeling of NGC 1300
In this section the results of calculations for NGC
1300 using the beam scheme are presented. Three basic types
of models were constructed. The simplest form was an n=l
Toomre disk and a triaxial ellipsoidal bar. Adding oval
distortions of the disk density distribution to this simple
model increased the strengths of the gas response to the
perturbing potential. These models may also have a halo
component added. The halo, being axisymmetric, tends to
reduce the effects of the non-axisymmetric components, but
by differing amounts in the inner and outer regions. This is
due to the manner in which the matter is distributed in the
halo. Models which consisted of a disk component and oval
distortions of the disk were also calculated.
Triaxial Bar Models
Models using the n=l Toomre disk and the triaxial
ellipsoidal mass distribution (inferred from the surface
photometry in Chapter 4) were noticeably unsuccessful in
reproducing any of the features observed in the HI
observations.
Initially, the mass of the bar was 0.10 times the mass
of the underlying disk. This value was chosen as the mass-
to-luminosity ratio for the bar then approximates the mass-
to-luminosity ratio for the disk. The bar figure used was a
prolate figure with b/a=c/a=0.340. The pattern speed of the

201
perturbing potential, the bar, was then varied in a series
of models to find the best gas response. The results were
quite uniform. No spiral arm response was evident at all.
The density distribution can be characterized as a broad
ring of gas located outside the bar zone. Inside the bar
zone, the gas forms a bar-like feature with gas-depleted
regions on either side. This gaseous bar joins the ring thus
forming a figure-of-eight pattern. This type of gas
response was seen in all models with only a disk and a
triaxial ellipsoid. The only difference between models with
differing pattern speeds is the location and radial
thickness of the ring feature. As the pattern speed is
slowed, the ring feature becomes broader. The radial
distance to the center of the ring also increases, being
located at approximately the position of corotation. This is
expected as it is easier for the gas to fall into this
region than it is to move away from the corotation zone.
Figure 5-2 shows a typical example of the gas response for
models of this type. In this example, corotation occurs at
the end of the bar at 6.4kpc. The pattern speed
corresponding to this is 19.3km/sec/kpc.
Another departure from the observations occurs in the
velocity fields for these models. An example of a typical
result is presented in Figure 5-3 which is the velocity
field associated with the gas response in Figure 5-2. The
overall feature in this velocity field is circular rotation.
The departures from circular rotation are not very

202
NGC 1300
CNV0LVE0
h n 3 17
Figure 5-2. Gas Response for Disk and
Triaxial. Gas density for a model with a disk and
a bar. The contour interval is 0.10 times the peak
density. The bar is horizontal.

203
significant and do not match the kinematic effects seen in
the observations. The rotation curve for these models
reproduces the observed rotation curve well in the region
where reliable velocities can be calculated from the
observations. Figure 5-4 is the rotation curve for this
model. Once again it should be emphasized that the. models
were calculated in galactocentric coordinates and then
projected to the same inclination as the observed galaxy.
The model results were also convolved with a two-dimensional
Gaussian function to produce a final resolution comparable
with that obtained in the HI observations. Thus the modeling
results shown are directly comparable with the HI
observations, except that in the models the position angle
of the bar is -90° (horizontal) whereas in the observations
the position angle of the bar is -79°.
In an attempt to determine when spiral arms would begin
to form, the bar mass was raised gradually in a series of
models. The pattern speed was kept constant at
19.3km/sec/kpc, placing corotation at the end of the bar. No
spiral arm response was seen in the gas until the bar mass
was approximately 2.2 times the disk mass. With a bar mass
this high, the rotation curve, Figure 5-5, is very obviously
dominated by the bar in the inner regions and does not match
the observations at all. As this model is very unrealistic,
it is unlikely that a real galaxy would have a bar 2.2 times
as massive as the disk; it will not be considered any
further in this study.

204
CNVOLVED 0.0
Figure 5-3. Velocity Field for Disk and
Triaxial. The contours are labeled in units of
20 km/sec. The bar is horizontal.

205
Figure 5-4. Model Rotation Curve. Rotation
curve derived from the velocity field of Figure 5-3.
The projection parameters are the same as for the
observed galaxy. Each grid unit corresponds to
0.1 arcminute. The error bars represent one standard
deviation.

206
Figure 5-5. Supermassive Bar Rotation Curve.
The bar mass is 2.2 times the disk mass.

207
The reason that these models fail to reproduce the
observed galaxy is that the forces resulting from the bar
mass distribution have a limited radial range. At radial
distances greater than the length of the bar, the strengths
of the forces, both radial and azimuthal, decrease very
rapidly, until near the edges of the galaxy they have
essentially no effect on the gas. Thus, it is extremely
difficult for spiral arms to form in regions outside the
bar, as the gas sees the bar as essentially a point mass.
The only way to get spiral features to form in these models
is to use a supermassive bar, i.e. increase the strengths of
the forcing terms outside the bar region until they are
strong enough to evoke some response in the gas.
Oval Distortion Models
Following the lack of success using models consisting
of a disk component and a triaxial ellipsoidal mass
distribution (a bar), models were constructed using a disk
and oval distortions of the disk mass distribution. These
oval distortions are sometimes considered as "massless bars"
as they only involve a redistribution of the disk mass and
do not have any mass themselves. Appendix B contains a full
discussion and derivation of the forces for oval distortions
of an n=l Toomre disk.
Two forms of these perturbations were considered; the
£ = 1 and £ =2 cases. The forces, radial and azimuthal, for

208
these cases were calculated using equations B-28 to B-31
(Appendix B). The results using these distortions were quite
clear cut. Models using the %=1 distortions had spiral arms
which were very loosely wound and extended all the way to
the edge of the computational grid. This implies that the
forces arising from these distortions do not decay rapidly
enough as a function of radius. These distortions have
essentially all the gas residing in these loosely wound arms
and very little in the interarm regions. The arms have the S
shape characteristic of oval distortions and have a gaseous
bar. This gaseous bar is not observed in NGC 1300.
The parameter, 3, in equations B28 to B31, is a length
scale characterizing the radial dependence of these mass
distortions. A large 3 implies a large radial extent for the
mass distortions and, conversely, a small 3 means that the
mass distortions are more centrally concentrated. However,
even for small 3, these oval distortions affect essentially
the whole computational grid and do not give a gas
morphology which resembles the observations. The amplitude
of the perturbation, represented by e , was varied in
attempts to change the gas response. The only effect of
lowering was to lower the contrast between arm and
interarm regions until the arms essentially disappeared.
Changing e had very little effect on either the radial
extent of the arms or the amount of winding of the arms.
Thus, the strengths of the forces do not drop rapidly enough

209
and 1=1 perturbations were not considered any further in the
modeling procedures.
In the treatment of oval distortions in Huntley (1977)
and Appendix B, it is noted that as r->°°, the forces for the
£=1 perturbations are ar-^, whereas those for the £ =2
-4
perturbations are ar . Thus, the £=2 perturbations have a
lesser effect at large r than do the £ =1 perturbations and
should give arms more closely matched to the observed spiral
arms. Figure 5-6 is the gas response for a typical model
using a disk and an £ =2 oval distortion. The arms have a
better degree of winding than do the arms for £=1
distortions. A gaseous bar region is evident in this model;
the beginning of the arms slightly preceedes the bar
position. In the observations the central region is
completely devoid of gas. This model shows depletion only on
either side of a gaseous bar. The distortion used here is a
large amplitude distortion, but the arms do not have the
correct azimuthal extent.
The azimuthal extent of the arms is approximately 120°.
In the observations, out to the maximum modeling radius of
3.2' or 15.9kpc at the adopted distance of 17.1Mpc, the
azimuthal extent of the arms is apprximately 225 °. The
azimuthal extent of the arms for the £=2 distortions is
decidedly better than that for the £=1 distortions, but
still does not give an acceptable match to the observations.

210
The velocity field for this model (Figure 5-7) again
shows that the dominant component is circular rotation and
as such, fits the observations fairly well in its gross
properties. However, the noncircular effects seen in the
observations are not matched at all in this model. The model
suffers from the defect of having noncircular effects that
are much smaller than those in the observations.
Various combinations of , the pattern speed of the
perturbation, 3, the length scale of the mass redistribution
and e , the amplitude of the perturbation were tried. No
combination was found that gave an acceptable match to the
observations for either the gas response or the velocity
field. However, using 1=2 distortions resulted in models
which were more acceptable than those utilizing £=1
distortions.
Composite Models
The third type of models attempted were models using an
n=l Toomre disk, a triaxial bar figure, 1=2 oval distortions
and a halo component. Models were calculated without the
halo component, but the results are so similar to those with
the halo that no separate discussion of these will be given.
The difference between the models with halo components and
those without halo components is in the axisymmetric
component and the amplitude of the oval distortion needed to
generate the same spiral pattern in the two types of models.

211
MODEL *6R
Figure 5-6. Oval Distortion Model Gas
scale representation of the gas response for
disk and an £=2 oval distortion.
Response. Gray
a model with a

212
CNVOLVED 0.0
MAXIMUM CONTOUR i 5 S5
MINIMUM CONTOUR ISO
CINT = CO.COO
x i n r = o.ioo
Figure 5-7. Oval Distortion u-lode 1 Velocity
Field. Contours are labeled in units of 20 km/sec.
jection parameters are the same as for the observed
galaxy.
Pro-

213
The mass of the disk is higher in models without the halo
than in models with the halo. However, the match to the
rotation curve is as good in these models as it is in models
with a halo. The amplitude of the oval distortion, e , is
slightly greater in models with a halo than in models
without a halo. This indicates that the effects of adding a
halo are slightly different from those in models with a
higher disk mass. A slightly stronger oval distortion is
needed to overcome the effects of the added axisymmetric
halo than is needed to overcome the effects of the higher
disk mass. As the disk surface density drops-off quicker
than the halo core density this means that the oval
distortion has to be greater than that for the disk to
produce the same forces at large radii from the center.
However, apart from these slight differences, the two types
of models give very similar results. Only the best model
using a disk, a halo, a triaxial bar and an £=2 oval
distortion will be discussed in detail. This model
represents the best model possible using the modeling
philosophy outlined at the beginning of this chapter. Some
possible improvements and alternative approaches will be
discussed later in this chapter.
Figures 5-8 to 5-11 show the results of the
hydrodynamical modeling procedure for the best model for NGC
1300. Figure 5-8 is a gray scale representation of the gas
response and Figure 5-9 is a contour plot of this response.
The associated velocity field is shown in Figure 5-10 and

214
the angle-averaged rotation curve derived from these
velocities is shown in Figure 5-11. Several faults are
immediately obvious in these models.
The gas response shows some gas in the bar region (the
bar is horizontal in these diagrams), whereas in the
observations the bar region is essentially devoid of gas.
The spiral arms do not have the azimuthal extent seen in the
observations. The model arms have an azimuthal extent of
approximately 145° whereas the observed HI arms extend for
about 225°. However, the very low contrast extension of the
model arms, between 145° and 180° in azimuth, connects with
the beginning of the next arm, providing a resemblance of
the joining of the arms in the HI observations. The
amplitude along the arms in the model falls too rapidly to
successfully reproduce the observations. In the
observations, the amplitude of the arms remains
approximately constant apart from the breaks, through about.
180° in azimuth (see Figure 3-4). The spatial positioning of
the arms in the models does not coincide with the position
of the observed HI arms. The HI arms are more tightly wound,
having a pitch angle of approximately 5° in the inner
region, than are the model arms. The pitch angle of the
model arms is about 14°.
The most immediate difference between the observed
velocity field and the model velocity field in Figure 5-10
is that the model velocity field covers the complete grid,

215
MODEL »4fl
Figure 5-8. Composite Model Gray Scale. Gray scale
representation of the gas response for the composite model
consisting of a disk, a bar, an £=2 oval distortion and a
halo. The bar is horizontal.

.600 MINUTES OF RRC.
216
CNVOLVED 0.0
I I I TTTTTT I I I I I l~T I I I I I I I 'I I I I I I I rrlTTT I I I FT I I I I F I T~r I I I II í I II M I I I I 'I I
6.S00 MINUTES OF ARC.
MRXI MUM CONTOUR IS 8
MINIMUM CONTOUR IS 0
Cl NT = 0.015
XINT = 0.100
Figure 5-9. Composite Model Contour Plot.
Contour plot of the gas response in Figure 5-8.
Contours are plotted at approximately 10% of peak
density.

.600 MINUTES OF fifiC.
217
CNVOLVEO 0.0
MAXIMUM CONTOUR IS 35
MINIMUM CONTOUR ISO
CINT = 00.000
X I NT = 0.100
Figure 5-10. Composite Model Velocity
Field. Velocity field for the model in Figure 5-8.
Contour levels are numbered in units of 20 km/sec.

218
*r
;?*
T T T I l Í
í i f Í 1
I i f I “
iiili
r ¡ I ..
[lit
!
i
f i
â– 
I
t>
j
i
i f i
i
I i
Figure 5-11. Composite Model Rotation Curve.
Rotation curve derived from the velocities in Figure
5-10. Each grid unit is 0.1 arcminute. The error
bars represent one standard deviation and the pro¬
jection parameters are the same as for the observa¬
tions .

219
whereas the observed HI velocity field covers only the
spiral arm regions. Also evident in the model velocities is
the skewing of the velocity contours in a direction parallel
to the bar, in the center of the galaxy. However, this
region has no reliable velocity information in the HI
observations. Also shown on Figure 5-10 is the approximate
outline of the gas-depleted region in the HI observations.
Unfortunately, although optical velocities exist in this
region they are confined to a ring about the nucleus at
r=10" and at positions r=50". Thus, they do not provide
much additional information to elucidate the velocity field.
It is thus evident that most of the skewing of the model
velocity contours in this region occurs in the "hole" region
in the HI observations. Another noticeable discrepancy
between the observed and the model velocity fields is the
lack of strong noncircular effects in the model. The
observations show noncircular effects in all regions of the
galaxy, but the strongest noncircular effects in the model
occur in the center region. The overall pattern of circular
rotation in the galaxy is matched well by the velocities in
Figure 5-9, thus indicating that circular motion is dominant
in the galaxy, but that noncircular effects are strong.
The rotation curve for this model, Figure 5-11, matches
the observed HI rotation curve very well in the region of
reliable velocity information, r>1.0'. Again, the different
strengths of noncircular effects can be seen by comparing
the error bars in the model rotation curve with the error

220
bars in the observed HI rotation curve, Figure 3-15. The
error bars represent plus or minus one standard deviation
and, in the model, are due entirely to noncircular effects.
These effects are much more prominent in the observations
than in the model. Very large noncircular effects are
present, in the inner 1.0' of the model, but these correspond
to the region where the velocity contours are highly skewed.
This model is very successful in modeling the rotation
law of the galaxy thereby giving a good estimate for the
mass of the system. The procedure has demonstrated also
that the use of a triaxial figure based on the observations
can successfully reproduce some of the. observed features.
The model almost succeeds in clearing out the center region
of the galaxy, although some gas is seen in a bar-like
figure. The spiral arms have been modeled, although they do
not give an ideal match to the observations. However, in
spite of the lack of success in modeling all of the observed
features, this model gives valuable insight into the
dynamics and kinematics of NGC 1300.
This model has an n=l Toomre disk with
C=568.4(km/sec)arcmin and b=2.6162'. These parameters give
a disk mass, out to a radius of 3.2', of MQ=5.4x10"^Mo. The
halo component added has the form used by Hunter et al.
(1986) in modeling NGC 3992, with a core radius of
rc=4.9kpc. The mass of the halo is 1.004 times the disk
mass, giving M .42x10 ^^lo. The mass of the triaxial

221
ellipsoid is 0.094 times the disk mass, M B=5.1x10 Mo. This
implies that the mass-to-luminosity ratio for the bar is
approximately the same as the mass-to-luminosity ratio for
the disk, i.e. Mg/Lg^Mp/Lj-j. The bar figure is a prolate
figure with a radius of 1.293' (6.4kpc) and axial ratios for
the shorter axes b/a=c/a=0.340. The mass distribution is a
Gaussian distribution with a=0.5', 2.5kpc (FWHM). The total
system mass is thus MT=1.13x10"*"‘*'Mo. This gives a ratio
MHi/MT=0.022, and thus gives some justification for not
using self-gravity in these models.
The total perturbation consists of a prolate triaxial
ellipsoidal figure and an a =2 oval distortion of the disk
density distribution. The length scale for the oval
distortion, 3, is 2.9kpc. This parameter does not correspond
to anything physical in the galaxy and only characterizes
the radial dependence of the distortion. The amplitude of
the distortion, e , corresponds to a maximum perturbed
surface density of ~5% of the unperturbed density. This
maximum occurs at r=2kpc. At a radius of r=10kpc the
perturbed density is only 0.01% of the unperturbed density.
As there seems to be little observational evidence for an
asymmetrical disk, this value for e probably represents the
upper limit for the amplitude of the oval distortion. The
perturbation is rotated with a pattern speed of
19.3km/sec/kpc, thus placing corotation just outside the
bar. The bar radius is 6.4kpc and the corotation radius is
6.9kpc.

222
The values of these parameters represent the
combination in the model that gave the best overall match to
the observations. The pattern speed, halo mass distribution,
bar and oval distortion parameters were all varied in an
exhaustive search through parameter space to find the
optimal combination.
Varying the relative bar mass resulted in no
significant increase in the noncircular effects in the outer
regions of the galaxy. However, above a relative bar mass of
0.18Md, the effects became so strong in the central region
that the model no longer bore any resemblance to the
observed galaxy. Below a relative mass of 0.051^, the gas
depleted region began to lose its identity. The bar mass
chosen, MB=0.1MD, was thus selected to give M g/L g=M .
Models with flattened bars were constructed to
determine the effects of various triaxial figures. The bar
was flattened in the galaxy plane (bars flattened
perpendicular to the disk plane hardly seem plausible) such
that b/a>c/a. The major-axis of the bar was kept constant
for these experiments, but the density in the bar was
varied. This gives a total bar mass that was constant for
all models constructed. This allowed comparisons to be made
between the models. Agreeing with the results found by
Hunter et al. (1986), these experiments showed that
flattening the bar had little effect on the gas response as
long as the radial extent and relative bar mass were kept

223
constant. Some differences in the details of the velocity
fields are evident in the centers of the respective models,
but these differences are insignificant. As the results are
so similar to the results with a prolate bar, only prolate
bar models are discussed.
Various scale lengths and amplitudes for the oval
distortion were tried. The amplitude has an upper limit
which can be set by considering the surface photometry. An
oval distortion produces a dumbbell-shaped density
distribution. As no feature of this type is observed in the
surface photometry of NGC 1300, this indicates that the
perturbed surface density cannot be a significant fraction
of the unperturbed surface density. Using this surface
photometry constraint, the values for 8 and e can be set.
The strongest possible oval distortion is needed, both to
provide the spiral arms and to provide noncircular effects
in the velocity field.
The effects of changing the halo parameters are to
change the shape of the rotation curve and to change the
amplitudes of the perturbation terms for a given gas
response. The addition of a halo increased the strength of
the oval distortion needed to produce spiral arms; changing
its mass distribution by changing the core radius, altered
the shape of the rotation curve. A total halo mass of
approximately a disk mass interior to the disk radius was
chosen as being physically reasonable.

224
As the pattern speed varies, so does the amplitude of
the gas response. As the pattern speed is lowered from
19.3km/sec/kpc (corotation at the end of the bar) the gas
response decreases and the beginnings of the arms start to
preceed the bar. Figure 5-12 shows a gray scale
representation of this model with a pattern speed of
16.7km/sec/kpc, corotation at 1.5 times the bar radius. This
figure should be compared with Figure 5-8 for an
illustration of the effect of decreasing the pattern speed.
In both these diagrams, the bar is horizontal. Figure 5-12
clearly shows the gas preceeding the bar. This effect is
undesirable, as it is not seen in the HI observations. If
the pattern speed is increased beyond 19.3km/sec/kpc then
corotation would lie somwhere inside the end of the bar. In
other words, corotation must occur beyond the radius of the
bar; otherwise, it is difficult to understand how the bar
could be stable (Contopoulos, 1985). The experiments in
varying the pattern speed showed that the optimal value of
ftp is about 19.3km/sec/kpc, placing corotation just beyond
the end of the bar. This result is in agreement with the
conclusion from stellar dynamics.
From the numerous experiments investigating the effects
of changing various parameters, the following remarks may be
made about the hydrodynamical models of NGC 1300:
1. The gas response is most sensitive to changes in the
pattern speed, .

225
Figure 5-12. Slow Pattern Speed Model Gray Scale.
Gray scale representation of the gas response for the com¬
posite model with a slower pattern speed than that for the
model in Figure 5-8. The bar is horizontal.

226
2. Having fixed ftp, the models are not very sensitive to
the actual shape of the triaxial figure as long as
the radius and relative mass are kept constant. This
is in agreement with the conclusions of Sanders and
Tubbs (1980).
3. The gas response is not very sensitive to changes in
the disk and halo parameters, provided that they are
adjusted to produce a distribution of circular
velocities that approximate the observed HI rotation
curve. However, the actual axisymmetric component can
have profound effects on the gas response. Changing
the background potential, while still providing a
good match to the observed rotation curve for a given
perturbation can drastically alter the gas response
(Contopoulos et al., 1986).
These conclusions confirm those found by Ball (1984)
and Hunter et al. (1986).
The only previously-published dynamical model for NGC
1300 is that of Peterson and Huntley (1980). Their model
included the self-gravity of the gas and used a Miller and
Smith (1979) bar-figure as their bar perturbation. As with
the present models, the Peterson and Huntley (1980) model
suffers from shortcomings when compared with the
observations. The bar figure they used has no basis in
observational data. It is a "nice, convenient" theoretical
figure which mimics a bar. The models for NGC 1300

227
calculated in this study used a bar figure which is based on
observations, and thus more closely mimics the actual three-
dimensional figure in the galaxy.
The gas response in their models more nearly reproduces
the optical object than the HI observations. The model they
used has a central bulge component and a gas bar. The pitch
angle of the spiral arms is slightly less than in the
present models, a =12°, compared with ct=14° for the present
models. Both models, therefore, fail to reproduce the
position and extent of the arms correctly. The azimuthal
extent of the arms in Peterson and Huntley's model is about
155 ° whereas the extent in the present model is about 145°.
Corotation in the self-gravity model is at 8.5kpc or about
1.3 times the bar radius. The present models have a better
gas response when the corotation radius is at the end of the
bar, 6.9kpc, than when the radius is about 8kpc.
Roberts (1979) notes that dust lanes in the bar region
may be manifestations of shock fronts in the gas. In
recognition of the two straight dust lanes emerging from the
nucleus of NGC 1300 and their turning and following the
spiral arms, the best model for NGC 1300 was examined for
the presence of shock regions. Such evidence could consist
of abrupt changes in amplitude or direction of the velocity
vectors from one pixel to the next. Figures 5-13 to 5-15
show these velocity vectors. Figure 5-13 shows the total
velocity field. In all these diagrams the bar extent and

228
position is marked and is rotating in a clockwise direction.
The approximate position of one of the arms is also shown.
Figure 5-14 is a plot of the velocity vectors in the frame
of the perturbation; Figure 5-15 is a plot of the
noncircular velocities.
Various features are evident from these diagrams. Very
large perturbed velocities exist in the central regions of
this model. Gas is flowing into the very center of the
galaxy. Gas is flowing away from the "hole" on either side
of the bar. The magnitude of the velocities at these points
is large. This implies that the creation of the hole occurs
rapidly in the evolution of these models. There are abrupt
and large changes in direction and amplitude of the velocity
vectors in this region, possibly indicating the presence of
shock fronts. However, the gas density is so low in this
region that, if there are shock fronts, they are not evident
in the gas response. Also marked are the approximate
positions of the minor-axis Lagrangian points. Some
circulation is evident at these positions. Outflow occurs
near the end of the bar.
Shock fronts appear to exist on the leading edge of the
bar and in the region where the two arms join. These
positions are marked on Figures 5-13 and 5-14. The shocks on
the leading edge of the bar are evident only in the inner
half of the bar, and thus, although they are in
approximately the same positions as the observed dust lanes,

Figure 5-13. Velocity Field Vectors. Velocity
field vectors for the model in Figure 5-8. Each
arrow is proportional to the size of the velocity and
shows the direction of flow for each pixel. The bar
rotates clockwise. Maximum velocity is 223 km/sec.
The bar position and the approximate position of one
of the arms is shown. Shock regions (S) and Lagrangian
points (X) are shown.

230
Figure 5-14. Velocity Field in Perturbation
Frame. Maximum velocity is 190 km/sec. Symbols are
the same as for Figure 5-13.

231
Figure 5-15. Noncircular Velocities. The max¬
imum velocity is 179 km/sec. Symbols are the same as
for Figure 5-13.

232
they do not extend far enough along the bar. The change in
velocity across these regions is about 32km/sec giving a
Mach number of 1.8 (Mach number is the ratio of velocity
change in the shock to sound speed) . The shocks in the
region where the two arms meet is expected, as fast moving
gas meets slower moving gas. The change in velocity across
these regions is about 21km/sec giving a Mach number of 1.2.
Although the Mach number is not very large, the shock is
more evident in the abrupt change in direction of the
velocity vectors than in the change in amplitude.
Resonances, especially the Lindblad and the ± 4/1
resonances, have some important consequences in stellar
dynamics (Contopoulos, 1985). Consequently, the positions of
these resonances were calculated for the best model for NGC
1300. The positions of these resonances are
Inner Lindblad
Inner 4/1
Corotation 6.9±0.5kpc
Outer 4/1 11.2±0.5kpc
Outer Lindblad 14.4±0.5kpc
A good opportunity exists in NGC 1300 to supplement the
HI rotation curve with the optical rotation curve. The
optical values exist in the region where the most unreliable
HI data exists. The HI rotation curve in the inner 1.0' is
determined by only a few pixels. In this region the optical
rotation curve is well determined; it can be used to

233
calculate the positions of the inner resonances. However,
Figure 3-16 shows that the optical rotation curve lies only
slightly above the HI rotation curve and consequently, no
inner resonances are observed. Thus, although the model does
not match the rotation curve very well in the inner 1.0', it
does accurately indicate that no inner resonances exist.
NGC 1300 was examined for any peculiarities which may
be evident. The breaks in the arms could be manifestations
of some of these resonances. The position angles and radii,
in the plane of the galaxy, were calculated for these
breaks, as were the position angles and radii for the
"kinks" in the HI arms. For the east arm these parameters
are
Break
= 69.7±2°
R= 8.9+0.5kpc
Kink
=180.0±2°
R=12.3 ±0.5kpc
Break
=232.7±2°
R=16.2 +0.5kpc,
:st arm
/
Break
= 90.0±2°
R=ll.1+0.5kpc
Kink
4> =180.0±2°
R=12.8+0.5kpc
Break
=249.7 + 2°
R=21.8+0.5kpc
These measurements indicate that the peculiarities seen
in the observed gas distribution probably are not due to the
4/1 and Lindblad resonances.

234
Bulge Models
In the analysis of the infrared surface photometry the
subtraction of a bulge component was an important step.
However, none of the models discussed up to this point have
included a bulge component. Dr. R. H. Sanders pointed out
that adding a bulge component to the models should produce
an inner Lindblad resonance, helping the formation of shock
fronts. Consequently, a bulge was added to the model
containing a halo, a triaxial component, an oval distortion
and the Toomre disk. The bulge added closely resembled the
bulge fitted to the surface photometry. The mass of this
component was estimated from the light contribution of the
fitted bulge to the overall bar-bulge luminosity. As the
photographic plate is saturated in this region, only a lower
limit can be calculated. This lower limit shows that bulge
mass shoulb be greater than 10% of the bar mass. A series of
models was calculated using various bulge masses between
0.1M„-„n and 2.0M_. The mass distribution in the bulge is
a circular Gaussian distribution with a =0.225' (FWHM).
Models were also calculated in which the pattern speed was
varied. As with all previous models, the best gas response
occured when corotation was placed just beyond the end of
the bar. The model chosen as the best representation of NGC
1300 is shown in Figures 5-16 to 5-23. This model has the
same components as the composite model with the addition of
a bul ge. The bulge mass is 0.094 times the bar mass. Bulge

235
masses lower than 0.85M had essentially no effect,
BAR
whereas bulge masses greater than 1.1M caused large humps
BAR
in the rotation curve. Thus, the total system mass for this
model is 1.2xl0^iyio, giving M^/F^O . 021.
The gas response (Figure 5-16) shows a change in the
central region and the regions at the ends of the bar. The
central region now has a definite bulge component visible in
the gas response. In this respect the model now more nearly
resembles the optical morphology than the HI. The beginning
of the arms now leads the bar by approximately 12° in
azimuth. These regions now have slightly higher densities
than the model shown in Figure 5-9, although the azimuthal
extent and pitch angle of the arms has not changed (Figure
5-17). The velocity field shown in Figure 5-18 shows
essentially no change in the outer regions of the model. It
still shows a lot of twisting of the contours in the central
region. However, as can be seen from Figure 5-18, this
twisting is confined to the region where no reliable
information is available from the HI. The optical velocities
from Peterson and Huntley (1980) help only at the very
center and at a radius of about 1.0'. The region of no HI
velocity information is indicated on this diagram. Figure
5-19 shows the outer regions of this velocity field compared
with the observed velocities. As is common with all the
models calculated, the model velocity field does not have
the required deviations from circular rotation.

.600 MIHUIE5 OF flKC.
CnvOlvEO
0.0
S.GOO minutes of arc.
max I“UM CONTOUR 15 3
MIN!mum CONTOUR Is 0
C;NT = 0.015
XINT = 0.100
Figure 5-16. Gas Response for Bulge Model.
Contours for the gas response for the composite
model containing a bulge. Contour interval is
0.1 times peak density. The bar is horizontal.

Figure 5-17. Density Compared with
Observations. Position of model arms compared
with the 20% level of the observed HI distribu¬
tion. The position and size of the bar is
marked.

238
CNVOIVED 0.0
MAXIMUM CONTOUR 15 36
MINIMUM CONTOUR IS 0
CINT = 00.000
XINT = 0.100
Figure 5-18. Bulge Model Velocity Field.
Velocity field for the model shown in Figure 5-16.
The approximate outline of the "hole" region in
the observations is drawn. Contours are labeled
in units of 20 km/sec.

Figure 5-19. Velocity Compared with
Observations. Observed velocity contours
(_) compared with model velocity contours
(—). Contours are labeled in units of
20 km/sec.

240
The rotation curve from this model fits the observed
rotation curve very well, even in the inner 1.0’ where the
optical velocities define the rotation curve. Figure 5-20
shows the model rotation curve compared with the
observational rotation curve. Apart from a hump at r=1.2'
the model rotation curve is a good match to the
observations. The radial extent of the bar and bulge are
indicated on this figure. The error bars are representative
of the errors in the various positions along the observed
rotation curve.
The addition of the bulge has substantially increased
the shock fronts. These shock fronts are indicated in
Figures 5-21 to 5-23 which are the velocity field vectors,
the velocity vectors in the perturbation frame and the non
circular velocities respectively. The bar and arm positions
are also indicated. Bar rotation is clockwise. The
positions of these shock fronts are on the trailing edge of
the bar. These fronts extend all the way along the bar and
show some indication of turning along the arms. The Mach
number across these fronts is approximately 7. The position
of these shocks is not accurately given by the beam scheme.
The velocity vectors in the perturbation frame (Figure
5-22) show circulation around the minor-axis Lagrangian
points very clearly. Figure 5-23 shows the noncircular
velocities. The largest noncircular motions occur in the bar
and bulge region.

VELOCITY ( km/sec )
241
Figure 5-20. Comparison of Rotation Curves. Observed
rotation curve compared with tne rotation curve for the
composite model with a bulge. Representative error bars
are shown for the observations. Error bars represent one
standard deviation.

242
Figure 5-21. Velocity Vectors for Bulge
Model. Velocity field vectors for the composite
model with a bulge. The bar rotates clockwise.
Shock regions are shown (—) as well as the approxi¬
mate position of the bar and arm. The maximum
velocity of 292 km/sec. is shown in the bottom right
corner.

243
Frame. leíocf ly vecTolT“ in. ’«turbación
the perturbation. Symbols are^he^1"9 fâ„¢e of
Fi miro ; hi , are tne same as for
Figure 5-21. Maximum velocity is 315 km/sec.

244
Figure 5-23. Noncircular Velocities. Velocity
vectors for composite model with a bulge. Symbols are
the same as for Figure 5-21. Maximum velocity is
272 km/sec.

245
The difficulties with the present modeling philosophy
may be reduced by considering other techniques. The
inclusion of self-gravity in the models may reduce the
spatial discrepancy between the model arms and the observed
HI arms by making the model arms more-tightly wound than
they are without self-gravity. However, the model of
Peterson and Huntley (1980) does not have the arms wound
tightly enough, and self-gravity is included in their model.
As the inclusion of self-gravity requires a self-consistent
bar and disk combination, after considering the results of
Peterson and Huntley (1980), no models with self-gravity
were calculated. It is also unlikely that the inclusion of
self-gravity will solve all the problems of the present
models but is certainly worth investigating.
An alternative approach is to use a spiral potential
outside the bar. In a series of models Contopoulos et al.
(1986) have shown that it is possible to generate arms
outside the bar region with a spiral potential. But what is
the origin of the spiral potential? Is it provided by the
stellar component or through some other mechanism? The near
infrared surface photometry indicates that there is some
spiral structure evident in the red light distribution.
This probably indicates that the older stellar component may
provide a spiral potential for the perturbation outside the
bar region. The inclusion of a spiral perturbation which
mimics the near infrared photometry could solve the problem

246
with the positioning and strengths of the model arms.
However, no models using a spiral perturbation have been
calculated, but should be investigated.

CHAPTER VI
RESULTS FROM OTHER GALAXIES
The observations and analyses of the barred spiral
galaxy NGC 1300 have been described in detail in Chapters
1-4. The hydrodynamical modeling results will be compared
with the results from three other barred spiral galaxies,
NGC 1073, NGC 3359 and NGC 3992. The analyses of these
galaxies have been published elsewhere and only a summary of
the main features, both observational and theoretical, will
be given here. Full details for each galaxy can be found in
the references given in each section.
NGC 3359
This galaxy has been studied extensively by Ball (1984,
1986).
Observational Results
The neutral hydrogen distribution in NGC 3359 was
mapped at the VLA during 1983 using both the C and D arrays
(Ball, 1984, 1986). The beam synthesized in these
observations was 18.04"xl7.64" (FWHM). This angular
resolution is somewhat better than previous observations of
HI in barred spirals. The observed channel maps were
247

248
corrected for continuum emission, CLEANed using the Clark
variation of the Hogbom algorithm and integrated using the
"window" technique of Bosma (1978), to give the neutral
hydrogen distribution and its associated temperature-
weighted velocity field (Figures 6-1 and 6-2).
The most striking feature of the gas distribution
(Figure 6-1) is its clumpy nature. The initial impression is
that NGC 3359 is not an example of a grand design spiral,
but the overall, global distribution does indeed follow a
grand design spiral pattern traced by a broad ridge of high
surface density. These observations are in accordance with
Elmegreen and Elmegreen (1985) who classify it as a grand
design spiral whose spiral structure is nevertheless patchy.
Emphasizing the grand design nature of the spiral structure
is the location of Hodge's (1969) HI I regions. These regions
are strongly correlated in position with the broad ridge of
surface density which traces the spiral structure (Ball,
1984, 1986). This broad ridge has a surface density >
21 — 2
1.6x10 era upon which many irregular gas complexes are
found.
Away from the arms, the clumpy structure of the HI
persists, but the background level of the surface brightness
is appreciably lower. Toward the nucleus the HI distribution
may be characterized as forming an irregular, slightly-
elongated ring with a radius of approximately 1.0'. This
could be the HI arms becoming blended by beamsmearing at

249
gmTTTTTpTJTTTTTT TI II111 gT I'M.11111IIII1111111 l'|l III11 III I M ' ggJT 11 i 111111111II11^11IIIII11111111M â–  TTTC
E “ » 9 * “ ' 1 ' n
I o ■ k .•a » 0 9 a
Figure 6-1. HI Distribution NGC 3359.
Observed gas density for NGC 3359 from Ball (1984).
North is to the top and east is to the left.

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251
small radii. However, this region, interior to the ring,
coincides rather closely with the region that would be swept
out by the bar rotating about its center. The angle-
averaged, deprojected surface density of HI also shows this
region to be depleted relative to the rest of the galaxy.
This depletion in HI is observed to a greater or lesser
extent in all the barred galaxies in this project. Sensitive
observations in the CO line would be required to determine
whether or not the total gas surface density (HI and H^) is
depleted in this region.
The temperature-weighted, mean radial velocity field
(Figure 6-2) shows perturbations in the galactic rotation
field associated with the spiral structure. The demarcation
of the spiral structure is even more prominent in the
velocity field than in the density distribution. The effects
•appear as well-defined, continuous distortions in the
velocity contours at positions which coincide with the HI
and optical arms. Some skewing of the velocity contours
occurs in the region dominated by the bar. The contours are
skewed away from the direction perpendicular to the
kinematic major-axis; this is indicative of gas flow along
the bar (Kalnajs, 1978). "Thus, the underlying dynamics of
NGC 3359 are evidently dominated by a broad, bisymmetric,
grand design spiral pattern, which strongly perturbs the
rotational velocities of the gaseous disk" (Ball, 1986).

252
The angle-averaged rotation curve derived from these
results is presented in Figure 6-3. Several features are
evident. First, there is no truncation signature apparent in
the rotation curve. Second, the curve, in the inner 1.0',
rises steadily, then at the end of the bar flattens
abruptly, remaining approximately constant at 130km/sec,
r=1.2' to 2.5'. The curve then begins to rise again,
reaching its maximum of 153km/sec at r=3.5', then flattens
and enters into a long, gradual decline.
Table 6-1 summarizes the observed, integrated
properties of the galaxy.
Hydrodynamical Models
The results of the hydrodynamical modeling procedure
are determined by the masses and mass distributions of the
axisymmetric and non-axisymmetric components, the disk and
bar respectively, and the angular velocity at which the non-
axisymmetric component stirs the gaseous disk. The
axisymmetric component was determined largely by the
rotation curve. An n=0 Toomre disk was found to provide a
good representation for the axisymmetric component as
determined by the angle-averaged rotation curve. Two
differing approaches were used to determine the non-
axisymmetric component. A triaxial ellipsoidal figure,
calculated using Stark's (1977) method, and an oval
distortion were used.

253
T
I I i i i
2.0 4.0 6.0
RADIUS (ARC MINUTES)
Figure 6-3. Rotation Curve NGC 3359.
rotation curve for NGC 3359 from Ball (1984)
bars represent one standard deviation.
Observed
Error

254
TABLE 6.1
Summary of Integrated Properties of NGC 3359
Parameter
NGC 3359
Synthesized beam (FWHM) (arcsec)
18.04x17.64
Synthesized beam (FWHM) (kpc)
0.96x0.94
Total HI map rms noise (lO^cm-^
13.0
Peak HI density (lO^^cm-^)
3.51
Observed systemic velocity (km/sec)
1009.0
Adopted distance (Mpc)
11.0
Diameter of HI disk (arcmin)
8.20
Position angle, line of nodes (°)
-8.0
Inclination angle (°)
51.0
Observed width, Global profile (km/sec)
326
Maximum rotation velocity (km/sec)
153
Radius of maximum velocity (kpc)
11.20
Mass within hydrogen disk, M, (lO^Mo)
12.0
9
Atomic hydrogen mass, M. ^ (10 Mo)
HX
5.00
mk/m
0.042
M/LB (solar units)
11.1
M. j/Lg (solar units)
0.46

255
The results using these parameters were quite clear-
cut. Models using the triaxial ellipsoid failed to produce
results which were similar to those observed. No combination
of pattern speed and bar mass yielded a "good model." The
oval distortion", however, worked very well in matching the
locations and amplitudes of the velocity distortions in the
galaxy. A hybrid model, consisting of an oval distortion and
a triaxial ellipsoid, was found to be the best compromise in
fitting the density, velocity and luminosity distributions
of NGC 3359. The bar has a mass of approximately 3.9% of the
disk mass, giving M^/L^-0.óM^/L^; thus it does not
contribute significantly to the non-axisymmetric forces. The
pattern speed of the bar-oval distortion combination lies
somewhere between 108.5km/sec/arcmin and 95.Okm/sec/arcmin
or, 34.Okm/sec/kpc to 29.8km/sec/kpc. This places corotation
at between 1.05' and 1.2', or between 1.0 and 1.2 times the
radius of the bar. The mass of the disk for this model is
5.9x10^ Mo; the bar mass is 2.3x10^ Mo, giving a total
galaxy mass within 3.75' or 12kpc of 6.13x10^ Mo. No halo
was added to these models.
NGC 3992
NGC 3992 has been studied observationally by Gottesman
et al. (1984) and theoretically by Hunter et al. (1986).

256
Observational Results
This galaxy was observed between 1980 and 1983 at the
VLA using both the C and D arrays. The beam synthesized in
these observations was 26.I"x20.0" (FWHM). These
observations were converted to a series of channel maps,
corrected for continuum emission, CLEANed and integrated
using Bosma's (1981) method to give maps of the neutral
hydrogen density distribution and the temperature-weighted,
mean radial velocity field (Figures 6-4 and 6-5).
The spiral structure is only weakly visible in the HI
distribution, although when only densities greater than 0.5
of the pe ak gas density are considered, the correlation
with the observed spiral structure is more apparent (Figure
1 of Hunter et al. , 1986). The contrast between this gas
structure and the general background level of the gas is
low, indicating that the structure is not strongly defined
at the resolution of this survey. Inside the optical ring,
or roughly the region dominated by the bar, the HI is
deficient. This "hole" can be approximated by an ellipse
with a semi-major axis of 0.95'. After referring to -*-^30
observations (Gottesman et al., 1984) conclude that
"...while it is possible that the H^ density is somewhat
larger than that of the HI, the total gas content in the
center of NGC 3992 appears to be less than in the disk." The
depletion of gas in the central region is vividly
illustrated by the angle-averaged, deprojected surface

257
Figure 6-4. HI Distribution NGC 3992. Observed gas
distribution for NGC 3992 from Gottesman et al. (1984).
The beam is indicated in tne bottom left. North is to the
top and east is to the left.

258
/
/
i
Figure 6-5. Velocity Field NGC 3992. Contours are
labeled in km/sec. The extent of the gas depleted region
is shown.

259
density (Figure 4 of Gottesman et al., 1984). This gas
depletion in the central region of NGC 3992 is more
pronounced than in NGC 3359.
The temperature-weighted, mean radial velocity field is
shown in Figure 6-5. Reliable velocities are not shown in
the central 1.0', the hole, due to the low density of the
atomic gas in this region. Weak irregularities in the
velocity contours are associated with the optical spiral
structure. These irregularities are not as strong as those
observed in NGC 3359; the velocity field as a whole is
dominated by circular rotat ion. However, there is a
discontinuity in the contours as the line of sight crosses
the bar. This is explained as gas flowing around strong bars
and skewing the velocity contours, but as the gas density is
so low in these observations, this interpretation is
uncertain.
The angle-averaged rotation curve derived from the
velocity field is shown in Figure 6-6. The curve inside
r=1.0' is uncertain due to the gas-depleted "hole," but
between r=1.0' and r=3.5', the curve rises slowly, reaching
its maximum value of V=278km/sec at r=3.0'. At r=3.8' there
is a very noticeable drop in the rotation curve which then
flattens out again to V=250km/sec. This sharp drop, seen in
both halves of the galaxy has been interpreted as resulting
from the truncation of the disk of the galaxy (Gottesman et
al., 1984; Hunter et al., 1984).

260
RADIUS (Arcmin)
Figure 6-6. Rotation Curve NGC 3992. Observed
rotation curve for NGC 3992 from Gottesman et al.
(1984). Two halves of the major-axis are shown.
Error bars represent one standard deviation.

261
Table 6-2 summarizes the observed, integrated
properties of the galaxy, NGC 3992.
Hydrodynamical Models
The dynamical components considered by Hunter et al.
(1986) in modeling NGC 3992 were
1. An axisymmetric Toomre disk of index n=0, truncated
as indicated by the observations.
2. A spherical halo constrained by the observed
kinematics and truncation of the disk.
3. A triaxial stellar bar constrained by near infrared
photometry.
4. An oval distortion of the axisymmetric disk.
Combinations of these parameters yielded models which
displayed the main features in the observations but also had
significant deviations from the observations. Spiral arms,
the kinematic offset and the central hole were all partially
reproduced. However, the arms are not in the correct
position and are more tightly wound in the observations than
in the models.
The results from the modeling show that a halo
containing roughly one disk mass, interior to the disk
radius, must surround the galaxy. A stellar bar and an oval
distortion must coexist in order to excite the observed gas
response. Neither component by itself satisfactorily
reproduces the observations and, although the combination of

262
TABLE 6.2
Summary of Integrated Properties of NGC 3992
Parameter
NGC 3992
Synthesized beam (FWHM) (arcsec)
26.10x20.00
Synthesized beam (FWHM) (kpc)
1.80x1.38
19 -2
Total HI map rms noise (10 cm )
4.80
Peak HI density (lO^cm ^
1.71
Observed systemic velocity (km/sec)
1045.8
Adopted distance (Mpc)
14.2
Diameter of HI disk (arcmin)
8.40
Position angle, line of nodes (°)
-111.5
Inclination angle (°)
53.4
Observed width, Global profile (km/sec)
598
Maximum rotation velocity (km/sec)
273
Radius of maximum velocity (kpc)
12.80
Mass within hydrogen disk, M, (lO^Mo)
22.8
g
Atomic hydrogen mass, M^, (10 Mo)
3.80
mHI/m
0.017
M/L (solar units)
B
9.50
M/L (solar units)
HI B
0.16

263
triaxial bar and oval distortion only partially reproduces
the observations, the combination is better than either
component individually. The stellar bar must have a mass of
between 18% and 30% of the mass of the truncated disk. Bars
less massive than 18% of the disk mass do not exert forces
strong enough to sweep out the hole, nor provide the
observed velocity contour discontinuities, nor generate the
required contrast and extent of the spiral arms. Bars more
massive than 30% of the disk mass are ruled out
observationally as no central maximum at r=1.0' is seen in
the rotation curve. However, a bar of this mass implies
that the mass-to-luminosity ratio for the bar varies between
4 and 7 times that for the disk. Models were completely
unsuccesful when the mass of the bar was such as to make
Mg/Lg- M^L^ . The pattern speed of the non-axisymmetric
components is 51.7km/sec/kpc, placing corotation at just
beyond the end of the bar at r=4.3kpc or 1.02 times the bar
radius. The disk mass for this model is 9.75xlO1-0 Mo, the
halo mass is 9.14xlO^Mo and the triaxial bar mass is
2. 5xlO^Mo, giving a total system mass, out to r=14.9kpc
(r=3. 6 ' ), of 2.14xl011Mo.
NGC 1073
This barred spiral galaxy has been observed and modeled
by England, Gottesman and Hunter (1986, private
communication) .

264
Observational Results
NGC 1073 was observed in 1983 and 1984 using the VLA C
and D arrays. The final resolution achieved was 20.3"xl9.7"
(FWHM). In contrast with the other galaxies in this survey,
the velocity bandwidth used for NGC 1073 is 12.63km/sec
(FWHM); the channel separation is 10.35km/sec. As with.all
the galaxies in this project, the channel maps were
corrected for continuum emission, CLEANed and integrated to
produce maps of the neutral hydrogen distribution and the
associated temperature-weighted, mean radial velocity field
(Figures 6-7 and 6-8).
In contrast with the optical image, the neutral
hydrogen distribution shows little evidence for spiral
structure. If only densities greater than 0.5 of the peak
observed gas density are considered, a correlation exists
between the bright optical regions and these regions of high
HI density. Though the majority of these bright optical
patches occur near the arms, no clear spiral pattern
emerges. At a gas density level of 0.4 of the peak observed
gas density the observed gas forms a broad ring, extending
from approximately the inside of the optical spiral arms to
well outside the arms (r=1.0' to r=2.0’). A gas bar, aligned
with the optical bar, becomes evident at a gas density level
of 0.3 of the peak observed density (peak observed density
21 2
is 1.77x10 atoms/cm j . On either side of the bar the gas
level is below about 0.15 of the peak density. This gas in

DEC
DENSITY
NGC 1073
Figure 6-7. HI Distribution NGC 1073. Observed
gas density for NGC 1073. North is to the top and east
is to the left.

DEC
266
NGC 1073
VELOCITY
i 1 r
I 1 L
20 5 50
R fl 2 41
Figure 6-8. Velocity Field NGC 1073.
are labeled in km/sec.
16
Contours

267
the bar region for NGC 1073 is the exception for the
galaxies studied for this project. No other barred galaxy
used here shows evidence for any gas along the bar. In fact
all the other galaxies show gas depletion in a large region
surrounding the bar. The general background gas density in
the disk is approximately 0.25 to 0.30 of the peak observed
gas density.
The temperature-weighted, mean radial velocity field
(Figure 6-8) shows that the dominant component in the
rotation field is, once again, circular motion. The bar
major-axis coincides very closely with the kinematic minor-
axis, and the velocity contours are very nearly parallel to
the bar. Some irregularities in the velocity contours
(departures from circular motion) are evident where the
velocity contours cross the peak of the gas ring.
Figure 6-9 shows the angle-averaged rotation curve
derived from the velocity field shown in Figure 6-8. The
curve rises steeply in the inner region, then flattens out,
reaching its maximum of 96km/sec at r=1.8'. The rising part
of the curve is approximately the region occupied by the
bar. At r=2.5 ' , the rotation curve drops off, exhibiting the
features of a truncation signature. The angle-averaged,
deprojected surface density indicates that the signal-to-
noise ratio in this region is good and that the apparent
truncation signature is not solely a result of low hydrogen
surface brightness. This apparent truncation signature is

VELOCITY ( km/sec )
RADIUS ( arcmin )
Figure 6-9. Rotation Curve NGC 1073.
Representative error bars shown are plus or
minus one standard deviation.

269
o
evident in the rotation curves calculated using a ± 15 wedge
around the major-axis for both halves of the galaxy.
Table 6-3 summarizes the observed, integrated
properties of NGC 1073.
Hydrodynamical Models
An n=0 Toomre disk is used to provide the axisymmetric
component for the models of NGC 1073. The axisymmetric
component is determined from the observed rotation curve.
The non-axisymmetric component consists of a triaxial
ellipsoidal bar and an oval distortion. The triaxial
ellipsoidal figure is calculated using near infrared surface
photometry as a constraint. As little evidence for spiral
arms exists in the HI, the oval distortion is needed only
for providing perturbations in the radial velocity field. A
disk and the triaxial figure are sufficient to reproduce the
broad ring and the gas bar, but do not provide sufficient
perturbations in the velocity contours. The bar has a mass
of 7% of the disk mass. A mass larger than this gives a
large central peak in the rotation curve; this peak is not
observed. This bar mass gives /L= 1.5M
The oval distortion is very weak and its sole function
is to provide perturbations in the radial velocity field.
The maximum perturbed surface density (at r=0.89') is 3.6%
of the unperturbed density. If the distortion is increased,
the ring is broken into spiral arms, which are not observed

270
TABLE 6.3
Summary of Integrated Properties of NGC 1073
Parameter
NGC 1073
Synthesized beam (FWHM) (arcsec)
20.30x19.70
Synthesized beam (FWHM) (kpc)
1.33x1.30
Total HI map rms noise (lO^^cm-^)
5.30
Peak HI density (10^\:m-^)
1.77
Observed systemic velocity (km/sec)
1208.9
Adopted distance (Mpc)
13.6
Diameter of HI disk (arcmin)
6.60
Position angle, line of nodes ( °)
-15.4
Inclination angle ( °)
18.5
Observed width, Global profile (km/sec)
107
Maximum rotation velocity (km/sec)
96
Radius of maximum velocity (kpc)
7.10
Mass within hydrogen disk, M, (lO^Mo)
3.00
9
Atomic hydrogen mass, , (10 Mo)
2.80
mh/m
0.093
M/L (solar units)
B
3.22
M /L (solar units)
HI B
0.30

271
in the HI. The oval distortion also perturbes the gas bar,
giving it the characteristic dumbbell shape of oval
distortions. This shape may be observed in the HI gas
distribution but is at the limit of the resolution and
signal-to-noise of the observations, so the evidence is not
conclusive. These non-axisymmetric components, the bar and
oval distortion, have a pattern speed lying between
28.5km/sec/kpc and 19.3km/sec/kpc, placing corotation at
between 1 and 1.2 times the bar radius (bar radius is
2.8kpc). The disk mass for this model is 3. OxlCT^Mo, the
triaxial mass is 2.1x10 ^Mo giving a total mass for the
system of 3.21x10 ^i^Mo. No halo component is used in modeling
NGC 1073.

CHAPTER VII
PROPERTIES OF BARRED SPIRAL GALAXIES
Observational Comparisons
The neutral hydrogen observations of the four barred
spiral galaxies (NGC 1073, NGC 1300, NGC 3359 and NGC 3992)
show differences in the morphologies of the galaxies. NGC
1073 shows a complete ring with some high density clumps at
positions corresponding to some features in the optical
object. NGC 1300, on the other hand, shows almost perfect
correlation of the HI features with the optical features.
NGC 1300 has arms in the HI, and very little gas in the
interarm regions; however, NGC 1073 shows little correlation
between the the HI and the optical. NGC 3359 and NGC 3992
lie somewhere between these extremes. NGC 3359 has
reasonable correlation between the HI and the optical arms
when only the upper levels of the gas are considered. NGC
3992 shows the same effect, but the correlation is not
globally as good as in NGC 3359. This is mainly due to
resolution effects broadening the HI and causing the arms to
be smeared together. However, both NGC 3359 and NGC 3992
have these arm features, in the HI, superimposed on a large
broad disk feature. The contrast between the HI arms and the
background gas is low for NGC 3992, but slightly higher for
272

273
NGC 3359. Neither galaxy has a contrast greater than 1.5:1.
Thus, although NGC 1300, NGC 3359 and NGC 3992 all may be
classified as grand design spirals in the HI, only NGC 1300
is obviously a grand design system in the HI.
All four galaxies show a depletion of gas in the
central region. NGC 1300 and NGC 3992 have a complete "hole"
in the gas. Any gas in these regions is below the
sensitivity limit of this survey. NGC 1073 has a depleted
central region, but uncharacteristically, has a gas bar. The
bar gas density is enhanced when compared with the
surrounding region, but is still lower than that in the rest
of the galaxy. NGC 3359 has the least depleted region of the
survey objects. These depleted regions all correspond very
closely to the region occupied by the bar of the galaxy,
which strongly suggests some interaction between the bar and
the gas as being the cause of the gas depletion. The extent
of the neutral HI gas is larger than the optical object for
all the observed galaxies.
The velocity fields for these four galaxies all show
that the dominant component is circular rotation.
Superimposed upon this general rotation are deviations from
circular motion. NGC 1300 shows the largest amplitude
irregularities in its velocities, while NGC 1073 has the
smallest amplitude irregularities. However NGC 1300 only has
reliable velocities in the arm regions; the gas density is
too low in the center and interarm regions to give reliable

274
velocity information. NGC 1073, on the other hand, has
reliable velocity information over the whole region of the
observations. NGC 3359 and NGC 3992 lie between the extremes
of NGC 1073 and NGC 1300. NGC 3992 does not display many
(nor very large) irregularities in the velocity contours,
whereas NGC 3359 shows moderately large deviations. In all
galaxies these deviations occur at the positions of the
spiral arms. NGC 3992 shows a discontinuity in the velocity
contours as the line of sight crosses the bar region. This
may be due to the gas flowing around a strong bar and
skewing the velocity contours, but as there are no reliable
velocity data in the bar region, this interpretation is
uncertain. NGC 3359 shows skewing of the velocity contours
in the bar region but NGC 1073 and NGC 1300 show little
evidence for this effect.
Two of the survey galaxies, NGC 3992 and NGC 1073, have
evidence for truncation of their disks. The rotation curves
exhibit features which have been interpreted by Hunter, Ball
and Gottesman (1984) and Gottesman et al. (1984) as being
the signatures characterizing a truncation of the disk. The
other galaxies in the survey do not exhibit these features.
Their rotation curves continue to rise or remain
approximately flat; whereas the curves for NGC 1073 and NGC
3992 have the abrupt drops at their truncation radii.
Near infrared surface photometry of all four galaxies
shows an object dominated by the bar. In NGC 1073, NGC 3359

275
and NGC 3992 there is very little evidence for spiral arm
structure. NGC 1073 has some low surface brightness evidence
for the broken ring feature observed in the optical images.
NGC 3359 and NGC 3992 have stumpy protrusions at the end of
the bar. These features correspond to the beginning of the
spiral arms, but do not extend for more than about 30 in
azimuth from the ends of the bar. In contrast to these
galaxies NGC 1300 shows significant spiral structure in the
near infrared. The spiral arms can be traced through almost
180 in azimuth from the ends of the bar. This indicates
that the arms in NGC 1300 have a significantly larger
portion of red stars than do the arms in the other galaxies
in this survey.
Dynamical Properties
The hydrodynamical models calculated for the four
barred spiral galaxies considered in this survey have
several features in common. The pattern speed for the
perturbation is quite fast, placing corotation just outside
the end of the bar for all the galaxies. The response of the
gas to the imposed perturbation decreases as the pattern
speed is lowered. A faster pattern speed would place
corotation within the ends of the bar; it would be difficult
to imagine how the bar could remain stable (Contopoulos,
1985). The most successful models for the survey galaxies
had corotation just outside the bar, the conclusion is that

276
corotation in barred spiral galaxies occurs just outside the
end of the bar. It cannot be inside the bar or too far from
the end of the bar. Other studies of gas motions in barred
spiral galaxies (Teuben et al., 1986; Sanders and Tubbs,
1980; Schwarz, 1985) have also indicated that corotation is
just outside the end of the bar.
This conclusion is reinforced by models for other
barred spiral galaxies using stellar and gas dynamics.
Teuben and Sanders (1985) used numerical integrations of
two-dimensional stellar orbits to study the dynamics of
barred spiral galaxies. Their results show that bars can
only be constructed from the principal basic parallel family
of periodic orbits (x^ in the notation of Contopoulos,
1983), as all other families have orbit density
distributions which are not conducive for the formation of
bars. Periodic orbits have been studied by Contopoulos
(1970, 1975) and others. These studies have indicated that
the simple periodic orbits are ovals which may be elongated
either parallel or perpendicular to the bar. Near a
resonance both families are present, but far from a
resonance only one family is dominant. The three principal
resonances in a galaxy with a bar distortion are the inner
and outer Lindblad resonances and corotation. Between the
inner Lindblad resonances and corotation, the parallel
family is dominant. Thus, as the inner Lindblad resonances
do not exist, the bar must exist from the center to just

277
inside corotation. Evidence for the non-existence of the
inner Lindblad resonances comes from an examination of the
gas density contours in the center of the models. Little
evidence is seen for a gas response perpendicular to the
imposed perturbation, which would indicate the presence of
the inner resonances as the dominant stellar orbits in this
case are the ones perpendicular to the imposed perturbation.
Teuben et al. (1986) in their study of NGC 1365, and Sanders
and Tubbs (1980) in their study of NGC 5383 support the
conclusion that the inner Lindblad resonances are deep
within the bar.
Both stellar orbit theory (Teuben and Sanders, 1985)
and the present study indicate that the bars must tumble in
the same sense as galactic rotation implying trailing spiral
arms.
The presence of dust lanes in these galaxies is a most
conspicuous characteristic of the gas in the region of the
bar. Two of the survey galaxy models, NGC 3992 and NGC 1300,
were examined for evidence of shocks. As expected evidence
for shock regions can be seen in the bar region. The
positions of the shock regions in NGC 1300 approximately
correspond to the positions of dust lanes seen in the
optical image of the galaxy. The shock fronts in the models
for NGC 3992 also correspond to the approximate position of
the dust patches seen in the optical image. Other gas
dynamical calculations have revealed the same phenomenon

278
(Sanders and Tubbs, 1980; Schwarz, 1985 amongst others).
Unfortunately, due to resolution and viscous effects
discussed in van Albada and Roberts (1981) and van Albada et
al. (1981) only the general position of shocks can be
estimated from the models. However, it seems that shock
regions should exist in the bar region in barred spiral
galaxies, and will most likely be evident in the galaxy as a
dust lane. Shock regions may also occur at the end of the
bar. At these points, there is gas outflow as seen in the
velocity vectors for NGC 3992 and NGC 1300. It is this
outflow which results in the shocks in the region where the
bar meets the arms. In NGC 1300, in particular, this region
has a concentration of HII regions. These HI I, star forming
regions are the result of these shocks. At the Lagrangian
points perpendicular to the bar on the minor-axis, there is
stable circulation. Evidence for these points can be seen in
the models for NGC 1300 and NGC 3992.
Spiral arms are difficult to produce using triaxial
ellipsoids as the only perturbation. The bar figures used in
the models for the present survey are unsuccessful in
producing spiral arms in the models. This could imply that
these bars are generally weak, as their effects are not far-
reaching. The lack of a spiral response is due to the lack
of a tangential force component in the outer reaches of the
disk. Strong bars (bars whose forces have significant
effects far from their ends) can begin to produce a spiral

279
response. The supermassive bar model for NGC 1300 began to
show a stubby spiral response at the ends of the bar. The
only procedure successful in producing significant spiral
response was the addition of some other perturbing
component. Oval distortions of the underlying disk were used
in this study to provide this extra potential, but other
studies have used spiral perturbations (Roberts, Huntley and
van Albada, 1979) to provide the extra forcing terms. The
addition of these extra forcing terms is very successful in
producing a spiral arm response in the gas. Although the bar
is incapable of producing spiral arms by itself, it can
produce very strong effects in the center of the galaxy.
Good examples are the effects in the center of the models
for NGC 1300. Thus it seems that even moderate bars can
drive large noncircular gas motions, typically 50-150km/sec.
Linear theory predicts that the arms cannot exist
beyond the outer Lindblad resonance. However, the models
calculated for NGC 1300, NGC 3359 and NGC 3992 all show
spiral arms extending beyond the outer Lindblad resonance.
This arises from the fact that, as the bar is a strong
deviation from axial symmetry, the linear theory is no
longer applicable. The use of non-linear theory allows the
arms to extend beyond the outer Lindblad resonance, as is
evident from the models calculated here. Other computations
of the gas response in barred spiral galaxies have shown
also that the arms can extend beyond the outer Lindblad

280
resonance (Sanders and Tubbs, 1980; Schwarz, 1985 and
others).
Contopoulos (1985) noted that the 4/1 resonances play
an important role in stellar dynamics. Two of the galaxies
in this study which were examined for effects of these
resonances, NGC 1300 and NGC 3992, showed no noticeable
effects in the gas response. Thus, it appears that although
these resonances may be important in stellar dynamics, their
effects may not be as important in gas dynamics.
The existence of halo components surrounding barred
spiral galaxies has not been resolved. The models for NGC
1300 and NGC 3992 incorporated a halo component, but the
models for NGC 1073 and NGC 3359 did not. The models with
halo components did not give significantly better matches to
the observations than those without a halo. In the models
with halo components, the halo was about as massive as the
disk, possibly indicating that, if halos do exist, they do
not have masses within the disk radius many times larger
than the disk mass.
What about the central "hole" in the gas observed in a
number of barred spiral galaxies? The models show a build-up
of some gas due to the loss of angular momentum of the gas
as a result of interactions with the bar. Some of the gas
build-up in the center is due to numerical viscosity
effects. However, observationally it appears that there may
be a total gas deficiency in the central regions. Further

observations of different gas components and further
numerical simulations are required to elucidate this
dilemma.

CHAPTER VIII
SUMMARY
The conclusions for this dissertation fall into three
categories. The observational results for NGC 1300, the
hydrodynamical modeling results for NGC 1300 and the
dynamical properties of barred spiral galaxies.
Neutral Hydrogen Results for NGC 1300
The 21cm observations of NGC 1300 reveal the galaxy to
be an excellent example of a grand design spiral system. The
HI gas is confined almost exclusively to the spiral arms,
with very little interarm gas. These HI arms correlate very
well with the positions of the optical arms. In common with
a number of other barred spiral galaxies, NGC 1300 shows a
large gas-poor region in its center. This is the region
occupied by the optical bar. The HI arms can be traced
through about 310° in azimuth. The HI gas has a well-defined
extent, with a major-axis diameter of 6.4' at a level of
21 9
1.59x10 atoms/cm^. The mass of gas observed at the VLA was
2.54xlO^Mo.
The velocity field shows reliable data only in the
regions that have detectable HI gas. Thus the central
portion and interarm regions do not have any velocity
282

283
information. The dominant component of the velocity field is
circular rotation. Analysis of this velocity field yielded
a systemic velocity of 1575.Okm/sec, a position angle for
the line of nodes of -85.5° and an inclination of 50.2° with
respect to the plane of the sky.
The rotation curve derived from this velocity field
rises, reaching a maximum of 185km/sec at a radial distance
of 2.5', then drops slowly out to a distance of about 3.2'.
The effects of the noncircular component in the velocity
field is evident in the rotation curve. The observational
parameters are summarized in Table 8-1.
Hydrodynamical Results
The hydrodynamical models for NGC 1300 were partially
successful in reproducing the observed features. The models
consisted of an n=l type Toomre disk, a halo component, a
triaxial ellipsoidal bar figure, an a=2 oval distortion of
the disk density distribution and a central bulge.
This model produced spiral arms which did not have the
correct pitch angle (the pitch angle was too large). The
arms did not have the observed azimuthal extent. However,
the circular component of the velocity field and the
rotation curve were well-matched by this model. The
noncircular velocity amplitudes in the model were not as
large as those in the observations. The central gas-depleted
region was partially reproduced by the model. It is unlikely

284
TABLE 8.1
Summary of Results for NGC 1300
Parameter
NGC 1300
Synthesized beam (FWHM) (arcsec)
20.05x19.53
Position angle of beam (°)
64.5
Channel seperation (km/sec)
20.6
Channel rms noise (K)
1.26
Total HI map rms noise (10 19cm “ 2)
5.00
Peak HI density (10 21cm~2)
1.59
Observed systemic velocity (km/sec)
1575.2±0.5
Adopted distance (Mpc)a
17.1
Diameter of HI disk (arcmin)b
6.40
Peak continuum brightness (K)
12.6
Position angle, line of nodes ( °)
-85.5 ±0.5
Inclination angle (°)
50.2 ±0.8
Observed width, Global profile (km/sec) c
345
Maximum rotation velocity (km/sec)
185
Radius of maximum velocity (arcmin)
2.47
Mass within hydrogen disk, M, (lO^^o)
1.20
Atomic hydrogen mass, M , (lO^VIo)
HI
2.54
M /M
HT
0.021
M/L (solar units)
B
5.02
M _/L (solar units)
HI B
0.11
a De Vaucouleurs and Peters (1981).
b Measured at an observed surface density, Nh=l.59xlo20cm-2.
c Full width at 0.2 of peak.

285
however, that the inclusion of the self-gravity of the gas
will reduce these problems.
Models using just a bar and the background disk were
totally unsuccessful in reproducing the observed features.
Only a combination of all parameters yielded good results.
The component parameters for the best model were, a disk
(Md=5.4x10^Mo) , a triaxial bar (M^=0.094M ), a halo
(M =1.004M ) , an 1=2 oval distortion and a central bulge
ri D
(M =0.094M ). Corotation was placed just outside the end
dULi D
of the bar, r =6.9kpc. The pattern speed corresponding to
CR
this is ft =19.3km/sec/kpc. Ranges for these parameters were
found by inspecting partially successful models. This
indicated that for this disk and halo combination
0.05Md resonances occurred at r=11.2kpc (outer 4/1) and r=14.5kpc
(outer Lindblad). The inner Lindblad and inner 4/1
resonances do not exist.
Dynamical Properties
The dynamical conclusions resulting from the comparison
of models for NGC 1073, NGC 1300, NGC 3359 and NGC 3992 are
1. The bar figure must tumble in the same sense as
galactic rotation and is a rapidly rotating figure.
Corotation must occur just beyond the end of the bar.
2. The inner Lindblad resonances must either not exist
or be very close to the center of the galaxy.

286
3. Bars only are not sufficient to generate the observed
spiral arms. Another component, an oval distortion or
a spiral perturbation must be added to produce spiral
arms.
4. The arms can extend beyond the outer Lindblad
resonance. Linear theory restricts the arms to lying
inside the outer Lindblad resonance.
5. Shocks are observed along the bar in approximately
the same positions as the observed dust lanes. Shock
regions are evident at the ends of the bar. These
may be observed as HII regions.
Although these models have some shortcomings (they only
partially reproduce the observations), they provide an
important stepping stone in the construction of self-
consistent models for barred spiral galaxies, and should
.thus be considered as only one of the first steps in the
development of a general theory.
Future analyses of barred spiral galaxies should
include observations of as many gas components as possible
(molecular observations could be very significant All
observed components should be taken into account when
modeling these systems. If spiral features are seen in the
older stellar population, these should be included in the
models.

APPENDIX A
DERIVATION OF VOLUME BRIGHTNESS DISTRIBUTION
In utilizing the infrared surface photometry and the
method of Stark (1977) in the hydrodynamical modeling code,
a procedure is needed to extract the volume brightness
distribution from the surface brightness distribution.
Two functional forms for the surface brightness are
considered and the corresponding volume brightness distribu¬
tions described. The two forms are Gaussian and Exponential.
Stark (1977) has shown that the volume brightness distribu¬
tion, F (a ), and the surface brightness distribution,
F (a ), are related by,
s s
1/2
T7 ( a \ —
<°o
i
>
3
>
H
G
d F (a )
la s s
- s —
, 2 2-1/2
(as "av }
a
v
(A-l)
where f is a constant for a given bar geometry.
Gaussian Surface Brightness Distribution
If the surface brightness distribution is Gaussian,
F (a ) = F exp(-a 2/2a2), (A-2)
s s so s
then the volume brightness distribution can be derived by
substituting equation (A-2) into equation (A-l) and inte¬
grating .
287

288
Thus,
F (a ) =
v v
-f
1/2
É F exp(-a 2/2a2)
. 2 2 -1/2
(as 'av } das
= -f
V
1/2
-F_a„ , 2 /0 2, , 2 2,-1/2 ,
so s exp(-a /2a )(a -a ) da
« S S V s
¿ a2
v
= F f
so
1/2
TT0
, 2 2W 2 2\ "1/2
a exp(-a /2a )(a -a„ )
s s s V
(A-3)
a
v
Changing variables, letting w = ag , gives,
F„(a) = F--f
1/2
'a>
V '“V'
so
0 2
2a 7i
exp (-w/2a2) (w-a ) d//2 dw. (A-4)
v
v
The integral can be evaluted by using equation 3.382.2
of Gradshteyn and Ryzhik (1980) to give,
F (a ) = F f
vv v' so
1/2
, 2
2 a TT
2
2a
1/2
exp(-a 2/2a2)r(1/2)
v
.1/2
Fso£ ' . (2a2) exp(-av2/2a2)
0 2
2a TT
2
F f
so
o 2
2a tt
1/2
exp(-av2/2a2).
(A-5)

289
Thus,
W =
F 2flV2
so
9 2
2 a tt
exp (-a^2/2a2),
(A-6)
and a Gaussian surface brightness distribution leads to a
Gaussian volume brightness distribution.
Exponential Surface Brightness Distribution
If the surface brightness distribution, Fs(as), in
equation (A-l) has the form,
F (a ) = F exp (-aa ), (A-7)
s s so 53
then, the volume brightness distribution, Fv(av), is,
Fv(av}
= -fV2
^as
F exp(-aa )
so 5
, 2 2,-1/2 .
(a -a ) da
' s v s
v
= -f
1/2
’ co
F exp(-aa )(-a)
so s
. 2 2,-1/2 .
(a -a ) da
s v s
a
v
= aF f
so
i/2 r
exp(-aa ) (a 2-a 2) da . (A-8)
s S v s
Using formula 3.387.6 of Gradshteyn and Ryzhik (1980) the
integral in equation (A-8) can be evaluated, giving,
1/2
F (a ) = aF f
v v so K (aa ),
(A-9)

290
where KQ(x) is a modified Bessel Function of the second
kind of order zero.
Thus, for a Gaussian surface brightness distribution,
the volume brightness distribution is also Gaussian,
Fy(av) = exp(-a,72/2a2) ,
(A-10)
o c ' v
and, for an exponential surface brightness distribution,
the volume brightness distribution has the form,
F (a ) = F K (aa ). (A-ll)
V V o o V

APPENDIX B
OVAL DISTORTIONS FOR n=l TYPE TOOMRE DISKS
The unperturbed stellar density distribution for the
n=l Toomre disk is of the form, Toomre (196 3) ,
a(r) = C,1 (a2+r2)-3/2, (B-l)
2ttG
where G is the gravitational constant, and and a are
constants.
Perturbations were added to the stellar density
distribution of equation (B-l), resulting in oval dis¬
tortions of this density distribution. The resultant density
distribution has the form,
, , C 2 (a2+r2)~3/2[l+e(B,r)cos 2e], (B-2)
a(r,6) = 1
2irG
where e(B,r) is the amplitude of the perturbation.
A functional form for e(B,r) can be obtained from
Huntley (1977) and Hunter (1986, private communication).
The form for e(£,r) is,
e(6,r)
£leV(a2+r2)3/2
(B2 + r2) i' + 3/2
y = 2U-1)
£ = 1,2. . . .
The resulting density distribution is,
(B-3)
291

292
2rrG
1+e firr (a +r )
V.2,,2.^2. 3/2
cos 20
(B-4)
8 is a length scale for the distortion, and
l is the order of the distortion.
Only distortions of order £=1 and 2 are considered
here.
The potential for this density distribution becomes,
Hunter (1986, private communication),
(B-5)
0+4>' (r,0,Z=O) ,
where is the unperturbed axisymmetric potential
The form of the perturbed potential ' (r, 0 ,Z = 0) ,
for the m=2 (dipole) distortion is, Hunter (1986, private
communication),
00
(B— 6)
'(r,0,o) = 2rG Z (kr) u J2(ku)a(u,0) dudk
m=o
o o
The perturbed density distribution, a'(r,0), given
by equation (A-4), is,
(B-7)
2ttG (8 +r )
£+3/2
Substituting equation (B-7) into equation (B-6)
gives,

293
'(r,0,o) = 2ttG
J2 (kr) dk
Cl^ e-j_BTr^ cos 26
—0 7 ¿+3/2 r J0(kr)dr,
ó2ttG (B2+r2r 2
or simplifying,
2
'(r,0,o) = cos 20
J2(kr)dk
o
,00
r^j^ (kr)(B^+r^) ^ dr.
Let the inner integral be Q^, i.e.,
Q1 =
r J2 (kr)
0 (B 2+r2) ^ + 3//2
dr ..
This can be evaluated using equations 6.565-4 of
Gradshteyn and Ryzhik (1980), hereafter designated GR,
giving,
0 - 8l/2-i k¿+3/2 (ke)
Ü1 “ B * K (1/2-2.) V ;
2¡1 + 3/2 r(1+5/2)
where K(i/2-£) ^B) is a mo<3ified Bessel function,
Equation (B-9) becomes,
1 _ Cn e, cos 20
hr,0,0) “ 1 1
2*+3/2 r(t+5/2)
e(y+l/2-e) x
J2(kr)kt+3/2 K(1/2_i)(k0)dk.
(B-8)
(B-9)
(B-10)
(B-ll)
(B-12)
6

294
Evaluating the integral, Q2, using equation GR
6.576-3, where
Q2 =
J0(kr)b£+3/2K , (ke)dk,
2
(B-13)
gives
2
Q2 = r r(5/2)r(£+1) F(5/2,£+l;3;-r2/B2); (B-14)
?-(¿+l/2) o S.+ 3/2-n
Z B (3)
F(m,n;o;p) is Gauss' Hypergeometric function.
Thus,
(¡>'(1,0,0) = C1 £x cos 26 r2BY 4 2£ F (5/2) F (&+1)
? r r
1(i+5/2)1(3)
x F(5/2,£+l;3,-r2/B2). (B-15)
Two forms of the oval distortion are considered here;
the Z = 1 and the £ = 2 forms. As Z increases, both the
amplitude and radial extent of the perturbation decreases.
Z = 1 Perturbations
The perturbed potential, <¡>' (r, 0 ,o) , is, from
equation (B-15) with Z = 1,
2 2 “6
*1 ^ r" pi o'! — c, e, cos 20r B
4 ¿_;LJr'0'0' 1 1
F(5/2,2;3;-r2/B2) = Ci e1 cos 20
10
F(2,5/2;3;-r2/B2) .
r(5/2)F(2)
r(7/2)r(3)
(B-16)

295
From Huntley (1977), using equations 15.2.18 and 15.1.13
from Abramowitz and Stegun (1964), hereafter AS, the hyper-
? 2
geometric function, F(2,5/2;3;-r /0 ) can be evaluated,
F(2,4/2;3;-r2/82 =
46'
<'3+2 (B +r^)
2+t-2 \ 1/2
3 (02+r2) 3//2
[B+ (B2+r2)1/2]2
(B-17)
Hence, the perturbed potential, for the £ = 1 per¬
turbation, is,
2. -- “2 rB+2(B2+r2)1/2 ^
4' £ = 1(r,0,o) =
2C-|_ ecos 20 r
15(B2+r2)3/2
[B+(62+r2)1/2]2
. (B-18)
£ = 2 Perturbations
The perturbed potential, for the ¡1 = 2 perturbation,
♦\.2(r'9'0) = Cl2ei COS 26 f! ri5/2)r(3)
1,6 F (9/2) F (3}
F(5/2,3;3;-r2/B2) = 2C1 C1 COS 29 £_
35 By
(B-19)
Using AS 15.1.8 to evaluate the hypergeometric function
F(5/2,3;3;-r2/B2).
gives
F (5/2,3; 3;-r2/B2) = (l+r2/B2) .
(B-20)
Therefore, the perturbed potential, for the £ = 2
perturbation, is,

296
4>1 £=2 (ri0f°)
2
2C^ e^ cos 20
r2[e6(l+r2/e2)
2 /o 2. 5/2 -i-l
]
35
or
6 (32+r2)5/2
2
1
(B-21)
35
The perturbed potentials for the n=l Toomre disk differ
from those for the n=0 Toomre disks by constant factors. These
factors are, for the i = 1 case,
K1 = ' (B-22)
53
and, for the SL = 2 case,
K_ = 2 (B-23)
2 7 *
Thus,
n=l
1=1
(r, 9 ,o) 2 ' (r, 9 ,o)
= f n=0
53 a=i
(B-24)
and,
4>' (r, 0 ,o)
(B-25)
The radial and tangential forces corresponding to
these perturbed potentials are
F' (r, 0 ) 34> _ ' (r,9)
P = ¡L
R
%
(B-26)
3

297
and,
F' (r, 9) _ 1 3^' (r,0)i (B-27)
T ~ r
l 30
Thus, the forces can be calculated easily from the
n=0 disk forms, giving,
F' (r,6) 2C, e. cos 20 r
R = 1 1
¡¿ = 1 2
is e
-36 (2B2-r2) (62+r2)1/2-r2(B2+4r2)+664^
x
(32+r2)5//2 (6+(62+r2) 1//2) 3
(B-28)
F' (r,0)
T
1=1
-4C^ sin 20 r
15(B2+r2)3/2 6'
6+2(B2+r2)1/'2
[6+ (82+r2)1/2]2
(B-29)
and,
F'
R
i=2
= 2C^ e-j^ cos 20 1
35 B
2r62-3r3
(B2+r2)7/2
(B-30)
F' 2
T = -4C^ £g s^-n ^0 r
i=2 35 6(62+r2,5/2 â– 
The total forces are,
F (r,6) = F° (r,0) + F ' (r,0) ,
R R F
and,
FT(r,0) = Ft'(r,0),
(B-31)
(B-32)
(B-33)

298
where,
o -C 2r
F°(r,0) = 1
R
(B-34)
a(a2+r2)3/2
is the axisymmetric force for the n=l Toomre disk.
The forces from the i,= l perturbations effect essentially
the whole computational grid, whereas the forces from the
1=2 perturbations have a lesser effect at large r. As r+ °°
the forces for the £=1 perturbations are a. r-^ and the forces
for the 1=2 perturbations are a r-^.

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BIOGRAPHICAL SKETCH
Born on the 17th of December, 1954, in Pretoria, South
Africa, Martin Nicholas England attended Springs Boys High
School, Springs, South Africa. With his parents, Michael and
Maureen England, and his younger brothers, Neil and Paul, he
emigrated to New Zealand in 1973.
He received a B. Sc. and a B. Sc. (Hons.) in physics
from Victoria University of Wellington, Wellington, New
Zealand, and a M. Sc. in astronomy from the University of
Canterbury, Christchurch, New Zealand.
Graduate study for the Ph. D. in astronomy was carried
out at the University of Florida, Gainesville, Florida. The
Ph. D. degree was received in December 1986.
He married Sheila Murphy in 1982 and they have two
children, Kathryn and Maureen.
305

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
•Stephen T. Gottesman, Chairman
Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
é
* LL
James H. Hunter
Cochairman
Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Thomas D. Carr
Professor of Astronomy
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
/
Haywood C. Smith Jr.
Associate Professor of Astronomy

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Gary G. Ihas A
Professor of Physics
This dissertation was submitted to the Graduate Faculty of
the Department of Astronomy in the College of Liberal Arts
and Sciences and to the Graduate School and was accepted as
partial fulfillment of the requirements for the degree of
Doctor of Philosophy.
December 1986
Dean, Graduate School

UNIVERSITY OF FLORIDA




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