Properties and observations of dwarf irregular galaxies

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Properties and observations of dwarf irregular galaxies
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xv, 186 leaves : ill. ; 29 cm.
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Simpson, Caroline Elizabeth, 1961-
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Dwarf galaxies   ( lcsh )
Astronomy thesis, Ph. D
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Thesis:
Thesis (Ph. D.)--University of Florida, 1995.
Bibliography:
Includes bibliographical references (leaves 180-185).
Statement of Responsibility:
by Caroline Elizabeth Simpson.
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Typescript.
General Note:
Vita.

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University of Florida
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Full Text









PROPERTIES AND OBSERVATIONS OF DWARF IRREGULAR GALAXIES









By

CAROLINE ELIZABETH SIMPSON


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

UNIVERSITY OF FLORIDA

1995


















To my parents
Richard and Emily Simpson,
and my sister
Elizabeth Simpson.














ACKNOWLEDGMENTS


The chairman of my Ph.D. committee, Dr. Stephen Gottesman, must be commended


for all of his tutelage and patience during my time as his student.


from him.


I have learned much


would also like to thank the other members of my committee for their


help and advice, especially Dr. Haywood Smith and Dr. Humberto Campins.


Financial


support for much of this work was provided by the Florida Space Grant Consortium, and

travel money for the observations was provided by a Sigma Xi Small Research Grant.

I would also like to acknowledge the support I've received from my former super-


visors and coworkers at Space


Telescope Science Institute.


Drs. Conrad Sturch, Barry


Lasker, Brian McLean, and my dear friend Vicki Laidler all played very important roles

in my decision to pursue a graduate degree.


There


have


been


many


graduate


students


at the


University


of Florida


have made my time here enjoyable as well as productive:


Billy Cooke, Dan Durda,


Sumita Jayaraman,


Dave


Kaufmann,


Morrison,


Jaydeep


Mukherjee,


Ricky


Smart, among others.


Liz Moore and Elaine Mahon provided not only friendship, but


also advice on making and reducing my


VLA observations.


Special thanks go to my


officemate and coworker Seppo Laine.

I would like to thank my ex-roommate and very good friend Jamey Bell as well.


Without his good humor and support, life would have been much duller!


I would also








Finally, I would like to thank my family

the drive, and my sister for the confidence.


my mother for the dream, my father for


Without their love and encouragement, none


of this would have been possible.


















TABLE OF CONTENTS


ACKNOWLEDGMENTS


S S S S S . S S S S S I iii


LIST OF TABLES


LIST OF FIGURES


ABSTRACT


S S I I 9 5 5 S S S S S S S S S S I S S S S S I S S S


.... .... vii


viii


CHAPTERS


INTRODUCTION


a a S f S 1


Star Formation in Dwarf Irregular Galaxies


Project Descriptions .
HI Survey .
LSBD-BCD Study


2 DWARF GALAXIES.


Type Descriptions


Dwarf Elliptical Galaxies
Dwarf Irregular Galaxies


* S S S S S S
* S S S S S S


* 9 S ft
* a a a a


a f a 5


. 7

. 8
. 8


S I 5 I a a a a S S S S I a 5 9


Blue Compact Dwarf Galaxies


. 1


Stochastic Self-Propagating Star Formation


System Evolution


3 OBSERVATIONS


. . . 5 I .. 5 10


I S I S S I S 5 1


22


21-Centimeter Line Emission


Aperture Synthesis


Theory


Imaging


S 32
SS S 32


Calibration


Imaging


A Y I Ci Tf'K Tl t flf n rrrr '2


nr m~ r~~l










Observations


S C S S S S 9 5 5 5 5 S S S S S S S S S S S S S S S S S S S S S S S 5 '.8


Data Reduction


Analysis


* S S S S S S S S
* 9 5 S S 9 5 9 S


* 9 S 9 9 5

* 9 S S S 5 5-


Noise.


Detection Criteria


Survey Results
Void Field .


Cluster Field
Interaction Fiel


S S 9 5 9 a S


* S S S S S S S
* S 5 9 5 5 5 5


* S S 68
SS S 9 73


Discussion.


5 5 S S S S S S S S S S S S S 9 9 5 5 5 9 8


BLUE COMPACT AND LOW SURFACE BRIGHTNESS DWARF


Discussion.


9 5 S S S 5 4 S 9 5 5 5 5 5 5 5 5 S S S S F S S85


Introduction .


The Data


Sample Description.
Observations .
Data Reduction .


* S a S S 85

SS 9 87
SS S S S 87


* C S S S
* S S S S 9


a a S S S S


.102


S S S 9 9 5 9 5 9 5 5 5 9 5 5 9 5 5 5 a S S . 113


6 CONCLUSIONS

Summary .


Future Work


APPENDICES


A COMPANION TO DDO


B VOLUME CALCULATION.


S5 9 9 a a S 5 172

. . . . . . 17


REFERENCES.


BIOGRAPHICAL SKETCH


* 5
* S 5


PROJECT


Analysis
HI Distribution and Kinematics. .
Observed Parameters and Correlations


163


169


180
















LIST OF TABLES


Physical Properties of target galaxies.


Derived Properties of detected galaxies.


SS I S I I .419


S. a . 82


Physical properties of BCD galaxy sample, taken from the RC3.


Physical properties of LSBD galaxy sample, taken from the RC3.


Observational parameters for entire galaxy sample.


Derived parameters for BCD galaxy sample.


. 118


. 119


. . 120


S* S . 121


Derived parameters for LSBD galaxy sample.


Correlation parameters for BCD galaxy sample.


. .
. a .* .


122


a a a a a a 1


Correlation parameters for LSBD galaxy sample.


I I S S S S I S S 12et















LIST OF FIGURES


Star formation rate (SFR) as a function of time over a 2.6 billion year


period for model galaxies having radii between 0.4 and 6 kpc.


The SFR


is the fraction of cells undergoing star formation per 10 million year


time step.


Taken from Figure 1 in Gerola et al.,


1980. .


Radial frequency function determined by


Tyson and Scalo (1988).


. 40


Gaussian fit (solid line) to the noise in a channel with no signal


emission.


. C 5 6


Peak signal-to-noise per channel for the low redshift data set for the


Void field observations.


C S S C C C C C S S S S S S S S S 5 62


Peak signal-to-noise per channel for the low redshift data set for the


Void field observations; including the data for UGC 10805.


Flux spectrum of the blanked data cube for UGC 10805.


Integrated HI column density map of UGC 10805. Cont'
0.24 (2or), 0.5, 1, 2, 3, and 4 x 1020 atoms cm-2


S S S S 5 63


64


our levels are
* 64


Peak signal-to-noise per channel for the high redshift data set for the


Void field observations.


. S C S C S C . . . . 6 6


Flux spectrum of blanked cube for possible detection in the high
redshift Void field. . . . . . . .


. . 67


Peak signal-to-noise per channel for the low redshift data set for the


Cluster field observations.


S C S C S S S C S C S C S S S S 69


15








4.12:


Integrated HI column density map of UGC 2014.
0.79 (2cr), 1, 3, 5, and 8 x 1020 atoms cm-2. .


Contour levels are
S* . 7 1


4.13:


Peak signal-to-noise per channel for the high redshift data set for the


Cluster field observations.


4.14:


~. S* ... .. ..72


Peak signal-to-noise per channel for the low redshift data set for the


Interaction field observations, excluding M81dB and UGC 5455.


4.15:


S *S 74w


Flux spectrum of blanked cube for possible detection in the Interaction


field.


4.16:


C S S S S S S S S S P S S S S S C S S S S S 5 7 5


Peak signal-to-noise per channel for the low redshift data set for the
Interaction field observations; including the data for M81dB and UGC


5455.


S C S S S C C S S S U S S C S C C S S S S S S S C S S S C S C S 5 /7 6


4.17:


Flux spectrum of the blanked data cube for M81dB.


Vertical error bars


indicate +1la variation.


76


4.18:


Integrated HI column density map of M81dB.


(2cr), 3, 5, and 9


4.19:

4.20:


x 1020 atoms cm-2


Contour levels are 1.2


S S S S S S S S S S S S 7F7


Flux spectrum of the blanked data cube for UGC 5455.

Integrated HI column density map of UGC 5455. Cont
(20r), 5,9,and 11 x 1020atomscm-2......... .


S C S S S C S C


our levels are 2.5
S. .. a79*


4.21:


Peak signal-to-noise per channel for the high redshift data set for the


Interaction field observations.


5 5 5 5 5 S C S S S C C S S C C 80


Color-Color plot of galaxy sample. Blue is to the lower left..

Integrated HI intensity (0th moment) map of A 1116+51. Con
are 1.4 (2cr), 2, 2.5, 3, 3.5 x 1020 atom cm-2.. . .

Integrated velocity field (1st moment) map of Al 116+51. .

Optical greyscale image with HI contours for A1116+51.. .


. .. .88


tour levels
125

. 125

. 126








Integrated velocity field (1st moment) map of Haro 33. . . 127

Optical greyscale image with HI contours for Haro 33. . . 128


Global velocity profile for Haro 33.


128


Integrated HI intensity (0th moment) map of Haro 4. Contour levels are


1.8 (2ar), 2.5, 5, 7.5


x 1020 atom cm-2


129


5.11:

5.12:

5.13:

5.14:



5.15:

5.16:

5.17:

5.18:



5.19:

5.20:

5.21:

5.22:


Integrated velocity field (1st moment) map of Haro 4.

Optical greyscale image with HI contours for Haro 4..


Global velocity profile for Haro 4.


. . . . . 130


Integrated HI intensity (0th moment) map of Haro 27. Contour levels
are 2.2(2a),5,7.5,9.0 x 1020 atom cm-2. . . . . .131

Integrated velocity field (1st moment) map of Haro 27.. . . 131

Optical greyscale image with HI contours for Haro 27. . . 132


Global velocity profile for Haro 27.


Integrated HI intensity (0th moment) map of Haro 36. Contour levels
are4.5(2ar),5, 10, 15,20 x 1020atom cmn-2 ..... . . .133

Integrated velocity field (1st moment) map of Haro 36. . . 133

Optical greyscale image with HI contours for Haro 36. . . 134


Global velocity profile for Haro 36.


Integrated HI intensity (0th moment) map of Mrk 328.


Contour levels


are 1.1 (2cr), 1.5,


2.5, 3, 3.5


x 1020 atom cn-2


* S S S S S S S S 5 135


- -


5.10:


129


132


..................... 134








Integrated HI intensity (0th moment) map of Mrk 51.
are 2.1 (2cr), 5, 7.5, 8.5 x 1020 atom cm-2. . .


Integrated velocity field (1st moment) map of Mrk 51.

Optical greyscale image with HI contours for Mrk 51.

Global velocity profile for Mrk 51 . . .

Integrated HI intensity (0th moment) map of Mrk 67.


are 1.3 (20r), 2, 3,


5.31:

5.32:

5.33:

5.34:


x 1020 atom cm-2


Contour levels
.. 137


S. 138


... . 38


Contour levels


S . 139


Integrated velocity field (1st moment) map of Mrk 67.

Optical greyscale image with HI contours for Mrk 67.

Global velocity profile for Mrk 67.. . . .

Integrated HI intensity (0th moment) map of DDO 43.


139

* a S 140


S S a aa S a S 141A


Contour levels


are 3.3 (2cr), 5, 7


9,11


x 1020 atom cm-2


S* T141


5.35:

5.36:

5.37:

5.38:


Integrated velocity field (1st moment) map of DDO 43.

Optical greyscale image with HI contours for DDO 43. .


Global velocity profile for DDO 43.


Integrated HI intensity (0th moment) map of DDO 169.
are2.2(2a),5,7.5,10 x 1020atomcm-2. . ..


* a a a a a a a a 141

S. a 142


142


Contour levels
. . 143


5.39:


Integrated velocity field (1st moment) map of DDO


5.40:

5.41:

5.42:


Optical greyscale image with HI contours for DDO 169.


S *S ** a 1441


Global velocity profile for DDO 169.


Integrated HI intensity (0th moment) map of DDO 52.


Contour levels


5.26:


5.27:

5.28:

5.29:

5.30:


143


144









5.45:

5.46:


Global velocity profile forDDO


. * . 5 14 6


Integrated HI intensity (0th moment) map of NGC 4163.


Contour levels


are 3.1 (2or),


10, 12.5


x 1020 atom cm-2


S S S S S S S *1el7


5.47:

5.48:

5.49:

5.50:


Integrated velocity field (1st moment) map of NGC 4163.

Optical greyscale image with HI contours for NGC 4163.


Global velocity profile for NGC 4163..


* S S S S 147

* S S S 148


S S S S S S S S 5 S S S 5 148


Integrated HI intensity (0th moment) map of DDO 131


are 2.4 (2cr), 3,


x 1020 atom cm-2


Contour levels


S S S S C .. 149


5.51:


Integrated velocity field (1st moment) map of DDO


131.


149


5.52:

5.53:

5.54:


Optical greyscale image with HI contours for DDO 131.


Global velocity profile for DDO 131.


S S 6 5 5 5 5 150


S S S S S S S S S 150


Integrated HI intensity (0th moment) map of DDO 242.


Contour levels


are 1.9 (2ar), 3,


x 1020 atom cn-2


S S 5 151


5.55:

5.56:


Integrated velocity field (1st moment) map of DDO 242.

Optical greyscale image with HI contours for DDO 242.


* S S 151

S. . 152


Global velocity profile for DDO 242.


5.58:


Integrated HI intensity (0th moment) map of DDO 88.


Contour levels


are 2.0 (2cr), 3,


x 1020 atom cm-2


5.59:

5.60:

5.61:


Integrated velocity field (1st moment) map of DDO 88.

Optical greyscale image with HI contours for DDO 88..


Global velocity profile for DDO 88.


* S S S A153

. . . 154


. . . . . 154


152


................153








5.64:

5.65:

5.66:

5.67:


Optical greyscale image with HI contours for DDO 56..


Global velocity profile for DDO 56.

Velocity width Avso vs. axial ratio (b


. . a 156


C C . a 15 6

/a). p * 15 7


Corrected velocity width (Av50/sin i) vs. axial ratio (b/a).


U U15'7


5.68:


5.69:


HI concentration (ijT))


HI mass M(2)HI


vs. color (U


vs. HI radius R(2)HI.


S . ..158


. a C U U C C U C U P U U U 5 158


5.70:

5.71:


Average dispersion velocity (tra)vs. color (U


Holmberg diameter R26.5 vs. .color (U


U C U S U U U U U 15 9


. . U U 159


5.72:

5.73:

5.74:

5.75:


Optical surface brightness aL


HI radius R(2)m 1

HI mass-to-light (

HI mass-to-light (


vs. color (U V).


S U U C S C U S S S S 1~itJ


vs. absolute magnitude Mu (log


vs. HI surface density p(

vs. HI mass to total mass


,fl. -


U U S S 5 5 161


Total mass (MT) vs. luminosity (LU). .


. U C S C S C C U S S U U C 162


Integrated HI intensity map of DDO 169 Companion..


C CU SU C U C 17z1


Velocity field map of DDO 169

Global velocity profile of DDO


SCompanion.

169 Companit


n. C U S S C C C l75


Integrated HI intensity map of both DDO 169 and its companion.. 175

Optical image with HI contours of both DDO 169 and its companion. 176

Combined global velocity profiles of DDO 169 and its companion. .. 176














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.


PROPERTIES AND OBSERVATIONS OF DWARF IRREGULAR GALAXIES

By

CAROLINE ELIZABETH SIMPSON


August, 1995


Chairman:


Stephen


Gottesman


Major Department:


Astronomy


Dwarf irregular galaxies, which are small, low mass, asymmetrically shaped systems,

are of interest both because of their large numbers and their usefulness as laboratories

in which to study large-scale star formation. It is believed that these galaxies form stars

through a process known as Stochastic Self-Propagating Star Formation (SSPSF) in which

star formation occurs in episodic bursts involving most or all of the galaxy, with the time


between starbursts increasing for smaller galaxies.


The long quiescent intervals between


star-forming episodes ensures that such galaxies spend much of their lives in an optically


faint state.


In this work, the results of (1) a survey to detect low mass dwarf irregular


galaxies, and (2) a study of the atomic hydrogen in eight blue compact dwarfs and eight

low surface brightness dwarfs are presented.








which was sensitive to HI masses as low as


x 10


M, detected only four systems:


the three catalogued target galaxies and another previously catalogued galaxy.


This is in


sharp contrast to the large number of systems predicted by the steeply rising luminosity

function, and rules out the existence of a large number of low mass galaxies.

The second part of this work examined the HI distributions and kinematics of a sample


of 16 dwarf galaxies in varying stages of star-formation. This project investigated the

effects of star-formation on the properties of low mass systems. The results of this study


indicate that the state of the HI reservoirs in small galaxies is related to the evolutionary


stage of the systems with respect to their star-formation histories.


Less active galaxies


are found to have more diffuse HI distributions, and the ring-like structure associated


with some of the systems indicates that the HI has been disrupted.


This is in accordance


with the SSPSF scenario that predicts an expansion and contraction of the HI in response

to the energy produced from a star-formation episode.













CHAPTER


INTRODUCTION



Star Formation in Dwarf Irregular Galaxies


Dwarf irregular galaxies are small, low-mass, asymmetrically shaped galaxies.


to their small sizes and masses, these systems are excellent laboratories for examining


star formation and evolution in galaxies as local, rather than global, phenomena.


Much


work on star formation on a global scale has been done by studying spiral galaxies.

These larger, more massive systems have substantial rotation velocities and also undergo


differential


rotation.


It has


been


shown


that only


higher rotation


velocities


support


spiral density wave shocks (Strom,


1980),


which act as triggers for star formation.


interstellar matter moves through the wave,


gas and dust is compressed,


causing the


collapse of protostellar clouds and initiating a burst of star formation.


The differential


rotation in spiral galaxies may also spread out regions of star formation, so that the stars

are no longer located in the area in which they formed.

In contrast to spiral galaxies, dwarf irregular galaxies (dlrrs) rotate slowly and as

rigid bodies (Gallagher and Hunter, 1984, and references therein), and so are not subject

to either the spiral density wave shocks or the shearing forces that tend to spread out


star-forming regions in larger late-type (spiral) galaxies.


The rigid-body nature of the








Since


dwarf


irregular


galaxies


not have


rotation


velocities


necessary


support the gas compression present in larger, spiral galaxies, they must form stars via a

mechanism other than density wave compression. It is believed that dlrrs form stars in a

process known as stochastic self-propagating star formation (SSPSF) (Searle and Sargent,


1972; Gerola et al.,


1980).


In this scenario, a galaxy undergoes occasional episodes of


very active star formation, interspersed with long quiescent periods of inactivity while


the star-formation region "recovers" from the burst.


The star-formation bursts occur in


"cells"


the size of the cell is independent of the host galaxy (Hunter,


1982), but larger


galaxies will have more cells, thus more star-forming regions.


fewer cells,


Smaller galaxies,


will therefore on average have fewer bursts over a given time, and longer


quiescent intervals (Gerola et al.,


1980).


In order for star formation to occur, there must be a reservoir of atomic hydrogen


(HI) gas present.


According to Skillman (1987) and Gallagher and Hunter (1984), the


formation of O and B stars will occur only when the surface density of the HI is above a

critical minimum column density (number of atoms per unit area), thought to be between


0.5 and


atoms cm-2


As the stars created during a burst evolve, energy is


released into the interstellar medium (ISM), primarily from supernova explosions in the


form of supernova winds.


This kinetic energy can then cause an expansion in the ISM


surrounding the burst as the gas is heated and dispersed,


producing a


"bubble" in the


ISM as the gas is both ionized and pushed outwards (Puche et al., 1992, and references


therein).

mass (i.e.


For very low mass systems, such as those we are investigating, the galaxy's

the potential well of the system) may be insufficient to gravitationally bind






3

star-formation burst once the gas has recollected in the galaxy (e.g. Davies and Phillipps,


1988; Puche and Westpfahl,


1994).


The amount and location of HI gas in a galaxy are


clues to its past, and possible future, star formation, and therefore to its evolution.


Project Descriptions


In this study,


we investigate the large and small scale properties of dwarf irregular


galaxies, focussing on the relationship between their HI morphologies and star-formation


history.


We have completed two observational projects using the National Radio Astron-


omy Observatory's


(NRAO) Very Large Array (VLA) Radio Telescope in New Mexico.


The first study is an investigation of the more global properties of dwarf irregular galaxies


as a class:


we have conducted a search at 21-cm for these gas-rich systems to examine


both their overall numbers and their distribution throughout space. The second study

investigates the more local process of star formation within these systems, and how star


formation can affect the properties and evolution of dwarf galaxies.

HI Survey


The first project involves determining the number and spatial distribution of dwarf


galaxies


It has been suggested that a great many of these low-mass systems exist but


have not been detected at optical


wavelengths due to their intrinsic faintness (Tyson


and Scalo,


1988).


Only systems undergoing fairly vigorous star formation are easily


visible in the optical since it is the luminous, young O and B-type stars that are detected.


According to SSPSF,


low-mass galaxies will undergo episodes of star formation very


rarely,


and since the lifetime of the burst (~


yr) is short compared to the interval






4

between bursts predicted for these systems (~ 109 yr) (Gerola et al., 1980), there should

be many quiescent (and therefore optically hard to detect) dirrs for each highly visible


"active"


To determine whether this is indeed the case, we have performed a survey


for these quiescent dIrrs.


Although these objects are faint optically, atomic hydrogen


emits at a wavelength of 21-cm, and these galaxies should contain enough HI to make

them detectable at this wavelength.

In addition to examining the number density of dIrrs, we have also investigated their

spatial distribution. According to the theory of biased galaxy formation (Dekel and Silk,


1986),


lower-mass galaxies should be distributed more uniformly through space than


high-mass systems.


Therefore, dIrrs should be located not only in clusters but also in


galactic "voids"; regions where no galaxies are currently observed.


We have surveyed


three different extragalactic environments in an effort not only to find such galaxies, but

also to see whether they are indeed ubiquitous, or if their distribution is as inhomogeneous

as that observed for larger, brighter, more massive galaxies.

It has been speculated that dwarf galaxies may be repositories for large amounts of


dark matter.


Theoretical work by Dekel and Silk (1986) requires dwarf formation within


massive envelopes to account for their observed properties.

the mass-to-light ratio (M/L) of dwarf galaxies range from 2


Observational estimates of

- 10 (Gallagher and Hunter,


1984),


with a median value of 5 as reported by Roberts and Haynes (1994).


However,


a study of binary dwarf systems by Lake and Schommer (1984) results in MIL ratio


estimates of 20 5000, indicating a large amount of dark or low-luminosity matter.


indeed, dwarf galaxies are reservoirs for dark matter, their spatial density and distribution








the number of galaxies increases as galaxy size decreases), there may be enough of


these small systems to provide the mass necessary to close the Universe.


LSBD-BCD Study


Our survey results, and the suggestion that starburst winds can deplete low mass


galaxies of their


us to initiate a project


to investigate more closely


mechanism and evolution of star formation in dwarf galaxies.


The bursting nature of the


star formation that occurs in dwarf galaxies supports a possible connection between blue-

compact dwarfs (BCDs) and low surface brightness dwarfs (LSBDs). LSBD galaxies are

rich in HI, optically faint, and undergoing little star formation. BCDs, on the other hand,

are distinguished by a small compact region of high surface brightness; they have large

amounts of ionized hydrogen (HII) and are undergoing significant star formation. It has


been suggested by several authors (Wirth and Gallagher,


1983 and references therein;


Davies and Phillipps, 1988) that LSBDs, upon undergoing a burst of star formation, will

evolve into BCDs and then back into LSBDs, when the star formation slows or stops as

the HI column density falls below the critical threshold necessary to support it.

We have examined the location and kinematics of HI in a variety of dwarf galaxies


to investigate this "evolutionary"


sequence.


We have observed 16 very low mass dwarf


galaxies believed to be in varying stages of


a star-formation episode to examine the


relationship between their HI distributions and their properties.


Eight of the galaxies


are BCDs, and eight are LSBDs;


therefore we are


looking at galaxies that are in (or


have recently completed) a burst of star formation (the BCDs), and galaxies that are






6

end of the spectrum primarily, it is believed that bluer galaxies are currently undergoing

vigorous star formation, while redder objects are more "quiet." By choosing objects with

different color indices within each sample, we are examining galaxies in different stages


of star-formation activity. If the properties of dwarf galaxies do indeed evolve as their

HI reservoirs contract and expand, we should observe different HI morphologies not


only between the two types of dwarf galaxy, but also between those of different color


indices.


By mapping the location and motion of the HI gas in each of these systems,


we are investigating (1) how star-formation episodes affect a galaxy's


properties and


characteristics; (2) whether the proposed expansion and contraction of the HI gas does

indeed occur; and (3) how it affects the star formation and evolution of dwarf galaxies.


In the following study, we present the results from these two projects:


an HI survey


to detect optically faint dIrrs, and an HI study of a sample of BCDs and LSBDs. A more


detailed discussion of the galaxy types, SSPSF

systems is presented in Chapter 2; and a gen

provided in Chapter 3. The HI survey project,


and the properties and evolution of these


Leral discussion of the HI observations is


including background, observations, data


reduction and results, is described in Chapter 4, and Chapter 5 reports in the same way


on the BCD-LSBD project.


Conclusions and a discussion of the implications from both


these projects are presented in Chapter 6.













CHAPTER


DWARF GALAXIES


According


to Roberts


Haynes


(1994),


there


are three


fundamental


types of


galaxies: elliptical,


"classical" spiral, and dwarf.


Dwarf galaxies are usually considered to


be those galaxies with absolute blue magnitudes (MB) fainter than approximately -18 or


As a class, these systems possess smaller sizes, lower masses, lower luminosities,


bluer (B-


V) and (U


-B) color indices,


lower surface brightnesses, lower (total mass)


surface densities but higher HI surface densities, and higher ratios of HI to total mass

than either elliptical or spiral galaxies (Roberts and Haynes, 1994; Gallagher and Hunter,

1984).


The large number of dwarf


galaxies in the Local Group and other nearby galaxy


clusters indicate that these small faint systems are probably the most common type of


galaxy (Davies and Phillipps,


1988).


Estimates of the luminosity function (the number


galaxies per magnitude per cubic


megaparsec)


for dwarfs both in clusters and in


field indicate that it is rising exponentially


(Binggeli


et al


1988


and references


therein).


Determination of the actual number of dwarf galaxies is difficult due to the


severe selection effects imposed by their faint magnitudes (e.g.


Tyson and Scalo,


1988).


It has been shown that low surface brightness objects are hard to detect optically, and

the tight correlation between faint magnitude and low surface brightness ensures that


dwarfs tend to he overlooked in optical surveys (Bin2eeli et al..


1988: Tyson and Scalo,








1988).


Further discussion of the number and space density of dwarf irregular galaxies


is presented in Chapter 4.


Type Descriptions


There


are three


basic


types


dwarf


galaxy:


dwarf


ellipticals


or spheroidals


(dE/dSph), dwarf irregulars (dIrr; these include LSBDs), and blue compact dwarfs (BCD)


(Tammann, 1994).


Dwarf ellipticals are very low surface brightness systems, containing


mostly metal-poor Population II stars and little or no HI gas.


Dwarf irregulars are also


low-to-intermediate surface brightness systems, but contain Population I stars and possess


considerable amounts of HI gas.


Blue compact dwarfs, on the other hand, have small


areas of high surface brightness and emission lines that indicate the presence of massive


(O and B-type) stars.


The bright emission regions are therefore identified as HII regions


and so these systems are currently undergoing significant star formation.

These three dwarf galaxy types are discussed in further detail below. Although they


are not the focus of the present study,


a brief


description of dEs is included, as it is


postulated that these systems may be part of an evolutionary chain linking all


dwarf


galaxy types (see discussion of system evolution, below).

Dwarf Elliptical Galaxies


The distinction, if any


between dE and dSph is not clear (see


Binggeli


1994 and


Kormendy


1994 for a recent overview of the controversy), and we will refer here to


all such systems as dEs for simplicity.


These galaxies possess fairly smooth, elliptical


isophotes, and are spheroidal in shape (Davies and Phillipps, 1988; Bothun et al.,


1986).






9

indicating that for some of these systems there have been at least two separate episodes


of star formation (Davies and Phillipps,


988; Held and Mould,


1994; Da Costa,


1994;


Smecker-Hane et al


., 1994).


Their metallicities range from 1/3 to


times the metallicity


of the sun (


and they contain very little or no HI (Davies and Phillipps, 1988


Hodge


1971).



Dwarf Irregular Galaxies


These


systems


exhibit


irregular,


chaotic


structure


optically.


general


surface


brightness


systems,


Population


II and Population


stars,


latter indicating current star formation activity.


Their fractional HI masses are fairly


(about


on average


according


to Roberts


Haynes,


1994),


their


metallicities


from


approximately


(Davies


Phillipps,


1988;


Bothun et al


., 1986).


They rotate slowly,


with average circular rotational velocities of


around 50


70 km


Observed rotation


curves


indicate


that these systems often


exhibit solid-body rotation over at least the optical part


of the


galaxy,


with little or


no differential


rotation


(Gallagher


Hunter,


1984;


Hunter


Gallagher,


1986).


This


is in


sharp contrast


to the


larger,


more


luminous


spiral


galaxies,


which


have


circular velocities of


> 200 km


and exhibit differential rotation over an extensive


(Gallagher


Hunter,


1984).


general,


dIrrs


are thought


to be


essentially


pure disk systems (Gallagher and Hunter,


1984;


Fisher and Tully,


1981).


However,


for the smallest, least-luminous dwarf irregulars, the rotation velocity can be equal to


or less


the random


(turbulent)


gas motions (~ 10 km s'


resulting


in a fairly








Blue Compact Dwarf Galaxies


Blue compact dwarf


galaxies, also known as HII galaxies, are identified by their


compact sizes, uv-excesses, and strong emission line spectra, which show strong, narrow,

high-excitation lines superposed on a nearly featureless continuum (Kunth, 1989; Thuan


and Martin,


1981).


Although these systems possess low total luminosities, they contain


small regions of high surface brightness from which the emission lines originate.


Their


spectra strongly resemble those of giant HII regions, and it has been shown that they


are undergoing episodes of intense star formation (e.g.


Sargent and Searle,


1970; Arp


and O'Connell, 1975; French, 1980).


Phillipps,


They can contain large fractions of HI (Davies and


1988) and often have large HI extents with respect to their optical diameters


(Gordon and Gottesman, 1981).


They are metal-poor, with metallicities ranging from 1/3


to 1/40


although most BCDs have metallicities of about 1/10


(Thuan, 1986). II


Zw 18, with a measured abundance of 1/40


;, is currently one of the lowest metallicity


galaxies known.


Stochastic Self-Propagating Star Formation


970, Sargent and Searle published a study of two blue compact dwarf galaxies,


I Zw


18 and II Zw


which they


concluded from the observed spectral energy


distributions and color indices that either (a) their current star formation rates (SFRs)

were much higher than the average rate in the past, or (b) that these galaxies preferentially


formed high mass stars.


They stated that the former would indicate these systems were


young (just beginning to form stars),


while the latter implied their initial mass functions








greatly exceeds that in the past.


If instead the IMF were such that primarily high mass


stars were formed at a steady rate over the lifetime of the galaxy, most of the gas would


have been converted into elements heavier than helium.


and raise the metallicity of the galaxy.


This would both exhaust the HI


The large amounts of HI and low metallicities of


both of these systems precluded this possibility


Having


established the high current SFRs for these galaxies,


they then proposed


two possible explanations: that the systems are young (as mentioned in the first paper),

or alternatively that the star formation had proceeded in extreme bursts separated by


long periods of inactivity.


These two options were examined by Searle et al.


(1973),


who used theoretical evolutionary tracks of individual stars to model the UBV colors of


model galaxies consisting of aggregations of open clusters.


They found that the colors


and properties of normal (i.e. non-dwarf) galaxies were consistent with a constant SFR


over 1010 years.


This was not true for the bluest galaxies,


which are dwarf systems.


they too had a constant SFR, then they would have to be young in order to produce


the very blue colors observed for these systems.


colors of a population of


However,


galaxies of different ages (108 to


when they then modelled

1010 years), the predicted


colors did not match the observed colors, and so they


determined that essentially all


galaxies are of the same approximate age.


Therefore,


very blue galaxies such as I Zw


and II Zw


40 are not young,


and so


must be forming stars currently


at a much


greater rate


the past.


The results from this work led them to propose a method of global star formation in


which galaxies undergo periodic "flashes"


or bursts of vigorous star formation, followed








This


idea,


which


became


known


as stochastic


self-propagating


star formation


(SSPSF),


was expanded and refined by several authors,


including Mueller and Arnett


(1976),


who used it to explain the chaotic structure in late-type spirals; Gerola and Seiden


(1978) and Seiden and Gerola (1979),


(1979),


who applied it to spiral galaxies; and Seiden et


who invoked it to account for the morphological differences between early


(elliptical) and late-type (spiral) galaxies.


Gerola et al.


(1980) discussed SSPSF for dwarf


galaxies and found that whereas for larger systems the SFR will be essentially continuous,

in dwarf galaxies the global star formation will occur in discrete short-lived bursts.

Mueller and Arnett (1976) formulated a simple model for what they called "self-


propagating star formation"


(SPSF) and applied it to spiral galaxies.


Essentially, they


divide


a (2-dimensional)


galaxy


into star-forming


boxes;


star formation


in one box


will propagate to neighboring boxes (presumably via expanding gas shells


massive stars).


produced by


After undergoing an episode of star formation, a box is unable to form


more stars until after a certain amount of time (known as the regeneration time) has


passed.


To keep the global star formation from dying out, they also found it necessary


to include spontaneous star formation:


the chance that a box


will form stars without


triggering from a neighboring box.


A spontaneous level at about 1% of the overall star


formation was found to produce the most


"typical"


spirals.


From their models,


determined a regeneration time of about


108 years.


In 1978, Gerola and Seiden expanded Mueller and Arnett's


model by introducing a


finite probability of having a star-forming cell trigger a neighboring cell.


This means that


star formation will propagate stochastically, and so they called the process "stochastic








probability Ps, of inducing star formation in the next time step in a neighboring cell. After

experiencing an episode of star formation, the probability that it will undergo another


episode is reduced for a refractory period

for the cell to replenish its supply of gas.


Tr, which may be thought of as the time required

This probability is not zero but varies over time.


The time step used is essentially the time required for some physical process, such as a

supernova shock wave, to propagate from one cell to the next, thus (possibly) triggering

star formation; it depends on the cell size (i.e. the size of the galaxy and the number of


rings) and the propagation velocity of the physical process.


In addition to the stimulated


probability Pst, a probability for spontaneous star formation, Psp, is also included.

In a paper published in 1980, Gerola et al. applied SSPSF explicitly to dwarf galaxies.


modelling


SSPSF


galaxies


different


sizes,


showed


whereas


formation in larger systems is basically continuous over long times,


smaller galaxies


undergo


a discontinuous,


bursting


mode


star formation.


reason


twofold:


(1) the amplitude of the fluctuation in the SFR increases as the size of the


galaxy


decreases,


so that smaller systems are


more


likely to experience


fluctuations


large enough to completely halt star formation propagation;


and (2) as star formation


propagates to neighboring regions, the rate of propagation in a small system can outpace


the regeneration of the cells, so that all cells


will have undergone star formation too


recently to be triggered again.


These are both consequences of the number of cells per galaxy.


As the cell size


for star formation is chosen to be constant, larger galaxies have more cells, so that at

any given time, more cells are both available for star formation and are actually in star








brief periods of time (< 108 years),


and such an event can have dramatic consequences


on the system as a whole (e.g.


Searle et al.


,1973).


The star formation can then switch


off, as mentioned above, and the galaxy will remain in a quiescent state until the cells


have a chance to regenerate.


Thus under SSPSF


, small systems will have short intense


episodes of star formation, separated by long inactive periods.


For the models used in their 1980 paper, Gerola et al.


found that the star formation


mode switched from continuous to bursting for galaxies with radii


< 10 cells.


As they


chose galactic radii from 0.4 to 6 kiloparsecs (kpc) and a cell size of 200 parsecs (pc), this


translates to galactic radii


< 2 kpc. Both this and the increase in fluctuation amplitude are


illustrated in Figure


taken from Gerola et al.


(1980).


Observations of star formation


regions in both irregular and spiral galaxies supports the use of a constant cell size. Hunter


(1982) finds an average size of 100 pc for al


star forming regions, and an average of


180 pc for the three largest HII regions in a galaxy.


Gerola et al.


used this bursting mode of SSPSF to explain the large dispersion of


properties observed for dwarf irregular galaxies.


Small galaxies will experience very


large changes in their SFRs over time, which leads to a wide distribution in their physical


characteristics.


For the small galaxies in their model, Gerola et al. found very large ranges


in values of the average SFR, the (B-


V) and (U


-B) colors, HI mass to blue luminosity


(MHII/LB), and especially total LB, which varied by as much as 5 magnitudes over the


million time period used.


These changes come about as a natural consequence of SSPSF.


A refinement to this bursting mode of star formation was proposed by Tosi et al.


1991 and 1992.


By comparing synthetic color-magnitude diagrams and stellar luminosity










et al.


(1994),


this can be viewed as a transition between the continuous SF seen in larger


irregulars and the bursting SF predicted for low mass dIrrs in the SSPSF model.


R=0.4 kpc


k i .


A A ft


1500


sacwo


500 IN


O.12


twoacoac


IiWO 00S


0 0 00 1C O


C 00


tic as


0 50 100 1500


d#Ooa


500 100


1600200


ur ts 2o


years)


Figure


Star formation rate (SFR) as a function of time over a 2.6 billion year period for


model galaxies having radii between 0.4 and 6 kpc.


The SFR is the fraction of cells undergoing


star formation per 10 million year time step.


Taken from Figure 1 in Gerola et al.,


1980.


System Evolution


relationship,


between


the three types of


dwarf


galaxies


not well-


understood at the present time, and indeed is one of the motivations for this investigation.

One school of thought maintains that these three categories represent different stages in


moo


1aoce








dEs (Davies and Phillipps,


1988; Bothun et al.,


1986).


A second theory claims that the


three types are too dissimilar in their properties to ever evolve from one into another, and

so we are not seeing the sequential evolution of one galaxy class but parallel evolution


of at least two and perhaps three separate classes (e


Binggeli,


1994; Bothun et al.,


1986


Davies and Phillipps,


1988 and references therein).


Lin and Faber (1983) found that the Local Group dEs had luminosity profiles that

could be fit by an exponential, like those for disk systems, and unlike normal (giant)


elliptical galaxies,


which follow an R1/4 law.


This led them to propose that dEs were


more closely related to dIrrs than ellipticals and that these Local Group dEs may be the

remnants of dlrrs that had lost their gas, perhaps through ram-pressure sweeping or tidal


stripping.


Support for this structural relationship between dEs and dIrrs was offered by


Kormendy (1985),


whose photometric study showed that the core parameter relations


(core radius rc and central surface brightness jo vs.


absolute magnitude M and velocity


dispersion a


, and vs. each other) for dEs and dIrrs are essentially the same.


In addition


to this, it was determined by Skillman et al.


(1989) that there is a correlation between


oxygen abundance (O/H) and absolute magnitude for dirrs, and that this correlation is

also followed by dEs, consistent with the idea that dEs could be gas-stripped versions


of dIrrs.


Sandage and Binggeli (1984),


in a study of Virgo Cluster dwarf galaxies, also


found that dEs have exponential luminosity profiles and that at low surface brightnesses

it becomes difficult to distinguish a dE from a dirr.


Binggeli


(1986) examines this stripping hypothesis


some detail.


As evidence


for it, he quotes the following:


(1) the morphology-density relation found in the


Virgo








and faint) dIrrs will photometrically resemble dEs if allowed to "fade"


years.


over a few billion


Arguments against this hypothesis include (1) the disparate flattening distributions


between dIrrs and dEs (as demonstrated by the different distributions of


with the dEs being rounder than dIrrs,


ellipticities),


and BCDs being in between (Davies and Phillips,


988 and references therein), (2) that the brighter dEs have higher surface brightnesses


than the irregulars (class Sd/Sm) they should be formed from (also Bothun et al.,


1986),


and (3) the existence of dEs with small bright nuclei (presumably stellar) which are not

seen in the class of dlrrs.

Some of these objections can be overcome by invoking different formation mecha-


nisms for bright and faint dEs:


few of the faint dEs are nucleated, and since rotation


velocities and dispersions decrease with magnitude (i.e. size),


extreme dIrrs will not be


very flattened (Kormendy


1985).


Hence,


as concluded by Binggeli (1986),


only the


fainter dEs may be candidates for formation from dIrrs via stripping.


variation on the gas-loss hypothesis,


Dekel and Silk (1986) investigated the


possibility that internal mechanisms such as supernova winds could remove mass from


these systems.


They postulated that dEs lose most or all of their gas as a result of an initial


starburst and the subsequent supernovae; and that perhaps the dIrrs are systems which

managed to retain some gas (they invoke the presence of dark halos) during this episode.

They also mention the possibilities of the dEs passing through a dlrr stage first, undergoing

a starburst, and then becoming dEs as they lose their gas; and that perhaps, for the systems

with larger potential wells, the initial expansion of the gas after the burst could be followed


by infall, thus recollecting in the galaxy and (re)forming a dIrr.


They determined that








In work reported on by


Athanassoula (1994), simulations of galaxy formation suc-


cessfully reproduce dEs with and without nuclei; the difference depends on the mass of


the initial gas cloud.


More massive clouds are more likely to produce nucleated dEs,


in accord with the observations that it is primarily the more luminous (i.e. larger) dEs


that are nucleated.


The simulations show three scenarios for dE formation and evolution


following initial collapse; which case occurs depends only on the mass of the progenitor

cloud. Massive clouds become centrally concentrated in both gas and stars (i.e. become

nucleated) and then undergo a starburst which uses up most of the gas, leaving a stellar

remnant that then undergoes very slow star formation. Intermediate-mass gas clouds fol-

low the same path, but form non-nucleated systems and lose essentially all of their gas;

and low-mass gas clouds undergo a re-expansion upon starbursting and can be completely

disrupted. It should also be noted that these models do not require dark matter halos.


Another caveat for formation of dEs from dlrrs was pointed out by


Thuan (1985).


From


infrared


observations of


samples of


Virgo Cluster and


surface


brightness (LSB) dIrrs and BCDs, he found "mutually exclusive"


metallicity ranges:


for the dEs, and


1/30 -


for the LSB dIrrs and the BCDs.


He further


stated that the difference in the metallicities between the dEs and dIrrs/BCDs precluded

the formation of dEs from dirrs via mass loss unless there was some period of metal-

enrichment that occurred either before or during the episode of mass loss.

Bothun et al. (1986) also explored the connection between dEs, dIrrs, and BCDs.


Based on 21


cm, infrared photometry, and CCD multicolor surface photometry,


found that dIrrs tend to have bluer colors, lower surface brightnesses, and larger scale








or the dEs.


They concluded that letting the dIrrs fade could not produce dEs with the


observed properties (especially since the dIrrs already have fainter surface brightnesses


than the dEs)


but that the BCDs could.


Therefore, they proposed that the progenitors


of dEs could be BCDs instead of dIrrs; and that dIrrs and dEs evolve in a parallel,


sequential fashion, separated by a difference in surface mass density.

On the other hand, there is quite a bit of evidence that BCDs are dIrrs that are currently

bursting, and it is thought that once the burst is over, these systems will appear as lower


surface brightness dIrrs.


Gordon and Gottesman (1981) showed that the characteristic


relations for colors, luminosities, HI masses, and MHI/L ratios for BCDs follow those


for normal late-type (Sd, Sdm) systems,


the faint end.


with the BCDs extending the relationships at


Thuan (1985) showed that dIrrs and BCDs have similar underlying older


stellar populations and HI contents and offered this as evidence that BCDs are dIrrs in


a bursting stage.


Tosi (1994) reviewed work that used the SSPSF scenario to construct


detailed chemical evolution models


of BCDs.


The results show that for BCDs, the star


formation episodes are short (, 106 yr) and separated by long (~-


109 yr) intervals.


In order


to reproduce the observations that BCDs are more underabundant in oxygen (0) than in

some other elements, such as helium (He) and nitrogen (N), they invoked differential

galactic winds, which preferentially remove elements from massive stars (such as O) via


the explosions of those massive stars.


Models with no gas loss result in galaxies that


are too metal-rich, and "simple" supernova winds remove all metals equally; therefore

differential winds are required to produce BCDs with the appropriate abundances.

However, Staveley-Smith et al. (1992) conclude that some LSBD galaxies (those with






20

contain approximately the same HI mass, as found by Thuan (1985), but the LSB galaxies


have lower velocity widths.


In order to create a BCD from a bursting LSB dwarf, they


found that the burst would have to occur preferentially in the high Mm galaxies; that the

kinetic energy produced by the supernovae from the burst be transferred very efficiently

to the HI gas; and that therefore to retain the gas after the burst, a large dark halo (or

some method of increasing the potential well) must be present.

Davies and Phillipps (1988) proposed a sequential evolution involving all three types


of dwarf (see also Puche and Westpfahl,


1994; and Westpfahl and Puche,


1994).


Their


model begins with a very low metallicity dIrr with a large reservoir of HI. Star formation


proceeds bimodally


with low mass stars forming essentially continuously over the entire


body of the system and high mass stars forming in occasional condensed bursts. During


a burst, the galaxy appears as a BCD.

may eventually begin infalling again,

reached the critical surface density (E


Skillman, 1987


The gas is expelled/expanded by the SF burst, but

which can trigger another burst once the gas has

crit) thought to be necessary for star formation (e.g.


Kennicut, 1989; further discussion of this will be presented in Chapter 5).


This cycle can repeat, with the galaxy appearing alternately as an LSB dwarf and a BCD,


until the gas becomes too depleted to support more bursts.


as a dE.


The galaxy will then end up


This sequence explains why dEs are more metal-rich than either dirrs or BCDs,


and they state that since each succeeding burst becomes more centrally concentrated, the

stellar population created in the later bursts will be occurring only in the nucleus and so

the resultant dE can appear both nucleated and less flattened than the progenitor dIrr.

To conclude, there are indications both for and against the proposition that all three








stripping or supernova winds, or whether BCDs represent an intermediate step in this


process is not clear.


It may be that dEs, dIrrs and BCDs are separate types of systems;


or that BCDs are related to either dEs or dIrrs, but not both.


This


is the focus of the work that comprises the LSBD-BCD part of this study.


We have observed the HI distribution in eight LSBD and eight BCD galaxies.


If the


proposed evolutionary scheme of


-+ BCD -* dIrr/dE is correct,


we should


see more compact and centralized HI distributions in the (bursting) BCDs than in the


(quiescent) LSBDs.


This work is presented in Chapter













CHAPTER


OBSERVATIONS


The observations of the 21-cm line emission of atomic hydrogen for both the projects

that comprise this study were made using the Very Large Array (VLA) Radio Telescope.

The VLA, a 27-element interferometer that uses the principle of earth-rotation aperture


synthesis, is run by the National Radio Astronomy Observatory,


which is operated by


Associated


Universities,


under cooperative agreement with the National


Science


Foundation.


The nature of 21-cm line emission, a discussion of earth-rotation aperture


synthesis, and a general description of the calibration and imaging techniques used to

reduce the observations are presented in this chapter.


21-Centimeter Line Emission


The ground state of atomic hydrogen consists of two hyperfine energy levels deter-

mined by the orientation of the magnetic dipole moments (or spins) of the electron and


the proton that make up the H atom.

they are antiparallel in the lower state.


In the higher energy state, the spins are parallel;

The difference in energy between these two levels


is extremely small:


x 10-6 eV


, which corresponds to a temperature difference (AT)


of only 0.07 K. A transition between these two states, referred to as a spin-flip transi-

tion, will result in the absorption or emission of a photon with a frequency of 1420.405

Megahertz (MHz), or a wavelength of 21.105 cm.








mean half-life,


of the excited state is


~ 1.11


years (Rohlfs,


1990,


p. 225:

years.


The rate for collisional excitation or deexcitation is, however, only about 400


This means that HI atoms will undergo decay transitions by radiating a photon at


21-cm only once every 1.11


x 10' years; but they will undergo collisional excitation ro


deexcitation once every 400 years. Since the collisional rates are so much higher than the

radiative decay rate, collisions can establish approximate thermodynamical equilibrium


(TDE) populations for the two energy states (Mihalas and Binney, 1981, pp.


484 485).


Expressing this in terms of the collisional probability coefficients C12 and C21, and


the radiative decay probability coefficient A21,


we get


nC12 = n2(C21 + A21) = n22 1 + 1


As noted above, A21


(3-1)


1, and so equation (3-1) reduces to


(3-2)


demonstrating that the populations are in approximate equilibrium (England, 1986).

The upper energy level is threefold degenerate since the total spin h can be oriented

in three different ways, so that in TDE there will be three H atoms in the upper level for


every one in the lower level.


This can be shown by the Boltzmann formula:


exp T- ,


where n2 and nl


(3-3)


are the number of atoms in the upper and lower energy states, and gz


and gl, representing the degeneracy of each level, are 3 and


1 respectively.


The value


of exp (


_-) will be close to


1 since Ts in an HI cloud is 100 K, and so


Mn f


__


_


nl Clz na C21,








radiative decay.


In spite of the infrequency of the radiative decay transition, the large


column densities of HI present in galaxies make this "rare"


transition detectable, and it


is this radiative decay that produces the 21-cm emission observed by radio telescopes.

Emission from a radially moving source (such as a receding galaxy) will be shifted


to longer wavelengths due


to the


Doppler


effect,


higher


recessional


velocities


corresponding to longer wavelengths (lower frequencies).


In addition to this frequency


shift, the width of the emission line will be broadened by any bulk motions (such as

turbulence and/or rotation) inherent in the emitting gas, so that the emission from a source

with radial motion will be spread across a continuous range of frequencies corresponding


to the radial


velocities of the emitting gas atoms.


This is the essence of spectral line


observations: by examining the amount of gas associated with each observed frequency,

we can determine the (radial) velocity associated with it and hence examine the kinematics


of the


We can calculate the column density Nm of atoms per square centimeter in the lower

state along the line of sight for a source by integrating the spin temperature over all

frequencies (in units of Hertz):


N111


x1014


TS'rV


(3-5)


where


Ty is the optical depth.


We can recast this equation in terms of the observed


brightness temperature TB by using the transfer equation:


- e-v)


(3-6)






25

for the column density associated with a position (a,6):
+o00


NHI(a, 6)


= 1.8226


x101


TB( w, 6) dv,


(3-7)


with NHJ in atoms cm-2


v in km


, and TB in Kelvin.


If the material is not optically


thin, the calculated column density will be underestimated (England,


an optical depth 7,


1986, p. 22).


= 1, equation (3-6) becomes


- e


= Ts(1


- 0.36


= 0.63212 Ts.


(3-8)


Substituting this into equation (3-5), we


see that NHI(rv


_ 0.63212 NHII(rv


The corresponding mass of the HI can be found by integrating this equation over the

solid angle subtended by the galaxy and expressing the brightness temperature in terms


of the observed flux


S(v) (see equation (3


MHI


)) and the distance to the galaxy D:


S(v) dv.


(3-9)


For D in megaparsec


(Mpc), S in Janskys (10-26W


m-2 Hz-1), and v in km


, MH


will be in units of solar masses (1 M


x 1033


gm).


The velocity field of the gas can be determined by calculating the intensity-weighted


mean velocity of the gas associated with each position (a,6).

first moment of equation (3-7) with respect to velocity:


This is done by taking the






26

The velocity dispersion associated with the gas is then found from the second moment:


v'P2(Na, ,


TB (c, 6) (v (v))


-00


(3-11)


TB (a, 6) dv


-00


Aperture Synthesis Theory


As the observations for this work were done using the VLA, an earth-rotation aperture

synthesis radio interferometer, an overview of aperture synthesis and interferometry are


provided in the section below. Good overviews and further references can be found

in England (1986), Florkowski (1980), and Christiansen and Hbgbom (1985), and more


thorough discussions in Hjellming and Basart (1982) and Fomalont and Wright (1974).

For very detailed information about aperture synthesis with an emphasis on the VLA in


particular, the collection of lectures from the


Third NRAO Synthesis Imaging Summer


School is recommended (1989, Synthesis Imaging in Radio Astronomy, eds.


F.R. Schwab, and A.H. Bridle (ASP Conference Series Vol. 6:


The resolving power of a telescope is ideally


R.A. Perley,


PASP)).


determined by the diffraction limit


where A is the wavelength being observed, and D is the aperture diameter


telescope.


optical


wavelength


observations,


where


A is


of the


order


a few


thousand


angstroms


angstrom


= 10- 10


meters),


limit


actually


instead


scintillation


earth'


atmosphere


arcseconds)


rather than


diffraction


same


not true


for radio


astronomy,


where


wavelengths


observed range from roughly


mm to


20 m.


In order to achieve the same


sort of






27

telescope aperture using an array of smaller, discrete antennas has been developed. For

thorough discussions of this, good references include Christiansen and H6gbom (1985)


and Fomalont and Wright (1974).


The following brief description follows


those given


these


authors.


The principle of aperture synthesis can be demonstrated by considering a conventional


(filled-aperture) telescope as being divided into


N elements.


Each of these elements


measures the emission from a source, and the signals from all of these elements are then


brought together and summed at the antenna focus.


In terms of measured voltages, this


sum can be expressed as


-z


AVi(t).


(3-12)


Since the measured power is proportional to the time-averaged voltages,


A17~)


(3-13)


can be


seen


sum


products


individual


voltages


(Al and


Vk) from all


possible pairs of


elements.


Thus a filled-aperture telescope


can be synthesized by only two antennas, placed at all possible positions i and k.


practice, not all positions of i and k need to measured, since combinations of (i, k) that


correspond to the same spacing and orientation are redundant.


between the two antennas along the direction of the earth'


Aligning the baseline


rotation allows the aperture


to be "filled" over time, as the apparent orientation of the two antennas with respect to

the source being observed (i.e. their projected baseline as "seen" by the source) changes


due to the earth's


rotation.


This is known as earth-rotation aperture synthesis.


C~(ac:


a V~ > > ,








the pointing direction) for all sources in the antennas' beams.


The intensity distribution


of a radio source can be thought of as the superposition of many components of an

electromagnetic field wave, where these components are of different sizes, locations, and


orientations.


The correlation of the electromagnetic field at two different locations can be


described by the spatial coherence function, and the visibility function is a combination

of this and the normalized reception pattern of the interferometer elements (the primary

beam) (Clark, 1989). It can be shown (e.g. Clark, 1989; Fomalont and Wright, 1974) that

these components and the brightness distribution are Fourier transforms of one another,

and so by measuring enough of these various components (the visibility function) and

applying a Fourier transform, it is possible to recover the intensity distribution of the


source being observed.


A pair of antennas, acting as an interferometer, samples these


different Fourier components as the projected baseline between them (as seen by the


source),


changes in length and orientation as the earth rotates.


More non-redundant


baselines mean more components that can be measured and more complete recovery


of the intensity distribution.


VLA,


with 27 antennas arranged in a


Y-shape, is a


multiple-interferometer instrument consisting of 351


pairs of antennas (the number of


pairs is equal to


N(N-1)
2


, where N is the total number of antennas), and so is able to


measure, at any instant, 351 Fourier components (Hjellming and Basart,


1982).


The signal from a two-element interferometer can be written as


Vob,(u, v)


Iobs(x,y)e


-2ri(uz+vy) dx dy


(3-14)


+00 +oo


where


Vobs is the observed complex visibility function, lobs is the observed brightness








single Fourier component of the observed brightness distribution (England,


Since


986, p. 25).


Vobs and lobs are Fourier transforms of one another, a small extent in the (x,


plane corresponds to a large extent in the (u,


v) plane according to the Similarity Theorem


(Bracewell, 1965,


101).


Thus short baselines will measure large-scale structures, and


long baselines will measure small ones (i.e.


have high resolutions).


As the visibility function and the brightness distribution are related by a Fourier

transform, equation (3-14) can be inverted to obtain lobs:

+oo00 +00oo


lobs (, y)


Vobs(u, v)


e[+2ri(ux+vy)] du dv


(3-15)


-00 -00

It should be noted here that lobs, the observed distribution, is actually the convolution

of the true brightness distribution and the synthesized beam (synthesized antenna power

pattern):


Iobs(X, y)


= Itrue(X,


y) B(x,y)


(3-16)


where B(x, y) is the synthesized beam and the denotes convolution.

For spectral line observations such as are done to observe the 21-cm emission from

hydrogen (H), the observed frequency range (the bandwidth) is divided into a number of


independent, contiguous narrow-frequency range channels.


a delay,


This is done by introducing


into the signal path which destroys the coherence of the signal except for


a specified range centered on a given central frequency, vj.


The frequency range being


observed can then be changed by changing the delay (England, 1986).


Adding the delay


is equivalent to multiplying the visibility function by a complex exponential:


4),;,


Yr* T'TL h~ r -


^-


- -


/n








the bandwidth now becomes:


Vobs(U, v, ) =


Iobs(z, y, v)F(v)e


-i[2rvr+2rv(uz+vy)] dx dy dv


(3-18)


where F(v) is the frequency bandpass function (Hjellming and Basart,


1986).


Since the delay is introduced into the signal from first one antenna and then the


other, the resultant lags are both positive and negative.

the imaginary part of the complex visibility function.

the real part of equation (3-18) with respect to r, and


and then v,


This symmetry allows us to ignore

Taking the Fourier transform of


integrating with respect to first r


we finally


Re{ Vob,(u, v, 7)}ei2*vrdr =


Iobs(x, y, v) F(v)


-i2rv


(uz+vy) dx dy


(3-19)


This is the visibility function at a frequency determined by the Fourier transform on 7 and

contains all the information necessary to map the source at frequency v (Hjellming and


Basart, 1982).


It is only necessary to calibrate the bandpass function F(v) by observing


a sufficiently strong continuum source, i.e. one whose intensity doesn't vary appreciably

over the (narrow) range of frequencies included in the bandpass.

As a final note in this discussion of interferometry, it should be pointed out that there


are two "resolutions"


associated with an interferometer array:


that set by the diameter


of the individual antennas, and that set by the size of the synthesized aperture of the


entire array.


The first, known as the primary beam, sets the effective field of view for the


radio observations, and is usually defined as the half-power beamwidth of the antenna,


OHPBW.


For the


VLA antennas,


which are 25 m in diameter, this is approximately


1982; England,


-00








The synthesized resolution determines the final spatial resolution of the observations

and is a function of the lengths of the various baselines of the interferometers making up


the array.


The VLA'


antennas are moveable, and can be arranged in four different-sized


configurations, from compact to extended.


The most compact, the D-array configuration,


has a maximum baseline length of 1.03 km and a synthesized beam of approximately


(arcseconds), while the most extended, the A-array


has a maximum baseline of 36.4


km and a synthesized beam of approximately


Since the surface brightness sensitivity of a radio telescope goes as the inverse of

the solid angle of the beam, there is a trade-off between resolution and sensitivity that


must be taken into account when planning observations.


The flux density detected by a


radio telescope can be written as


BP, dO


(3-20)


where


B is the


source


brightness


and Pn


normalized antenna


power pattern.


Rewriting B in terms of the brightness temperature


2k
-TB


and substituting this into equation (3-20),


(3-21)


we find:


STBP, dfl


(3-22)


minimum


detectable


density


therefore depends on


minimum detectable


change in the temperature


ASmin


(AT)


Pn dQ


(3-23)


mt. n n. .. ad a ad a L~ 1 a a 1. a n a e a 4 a en a a a a a


it *5 nAr~ 4 n aln 1 rnn at*l Cmw n -p4.ada aa- -..


/I f






32

Integrating equation (3-23) over the beam solid angle 0j and rearranging, we find


Smin


(3


From this, it can be seen that at a given wavelength, a larger (synthesized) beam can


detect smaller changes in T.


Therefore, although the largest configuration (the A-array)


provides the best resolution, the most compact (the D-array) provides the best sensitivity

to low levels of broad emission.


Imaging


As discussed above, a radio interferometer observes the complex visibility function


corresponding to a source's


brightness distribution.


Once these


visibilities have been


recorded, they must be corrected for instrumental effects (calibrated) and then Fourier


transformed to produce images (maps) of the intensity distribution of the source.


These


images are actually of the convolution of the true brightness distribution and the synthe-


sized beam (cf.


equation (3-16)); and thus reproduce the true brightness distribution the


beam must be deconvolved from the images.


Brief descriptions of each of these steps


in the reduction of the data are given below.

Calibration


As in any observations, a method of detecting and correcting for instrumental effects


is needed.


At the


VLA, this is done by


observing a primary (or flux) calibrator,


well as secondary (or phase) calibrators and using them to calibrate the amplitude and


phase response of the array.


The amplitude response of the antennas can vary from






33

zero is analogous to a slight change in the pointing position of the pair, and a consequent

decrease in the amplitude response as the source moves away from the beam center.


calibrator is


a very


strong


source


a known,


stable


flux,


phase calibrators are sources with known


fluxes and accurately


determined positions.


These calibrators are used to adjust the system response to correct for any instrumental

instabilities that might occur in amplitude or phase over the time of the observations.


At 21-cm, the array response should be calibrated every


observing run to ensure that the system's


30 40 minutes during the


phase and amplitude responses are known as


a function of time.

In spectral line observations, the signal is divided into n channels of narrow frequency


width (


v/n).


One of these channels


, called channel zero, is a pseudo-continuum channel


consisting of the average signal from the inner three-quarters of the entire bandpass and


is therefore a broadband channel.


Since the array sensitivity is proportional to the inverse


of the observed frequency range (equation (3-24)), the sensitivity in channel zero is much

greater than for the individual narrow band channels: ~7x for 64 channels, and ~10x


This increase in sensitivity allows for better calibration, so the amplitude and


phase calibrations are determined using channel zero and then applied to the spectral

line channels.


a first


calibration


individual


calibrators


examined


obvious


problems


such


interference.


Each


point,


visibility,


corresponds


to the


signal


from


one antenna


over


integration


time


(usually


between


seconds).


redundancy


present








assumed


have


a known


value)


calculated


center


frequency


being


observed.


Once


of the


primary


calibrator


been


established,


antenna


(amplitude and phase) solutions for the array as a function of time can be determined.

We can approximate the baseline-based complex gain Gy(t) by


Gi,(t)


= ai(t)ay(t)


-& (l))


(3-26)


where a(t) is an antenna-based amplitude correction normalized so that


Eai(t)


, (t) is


an antenna-based phase correction normalized so that


= 0, and ti are the closure


errors from the gain solutions (Fomalont and Perley


1989; Martin,


986).


The smaller


the closure errors, the better the approximation of the complex gain Gi(t) is.

In practice, calibrating is an iterative process wherein one tries to minimize the closure


errors.


The results of a calibration run are examined, baselines producing large closure


errors are discarded, and the calibration is repe

are at or below a level deemed acceptable.


This continues until the closure errors


For these projects, amplitude errors below


about


10-


and phase errors below about 8


- 10 degrees were usually achieved.


These errors correspond to approximately a


level for most of the calibrators used.


After determining a satisfactory gain solution for the array, the fluxes of the phase

calibrators are determined using the flux calibrator, and the calibration is applied to the


entire dataset, including the source data.


This is usually done using a running boxcar


average over entire set of the observations, which usually consist of alternating scans of


the phase calibrator(s) and the sourcess.


However, for some sources observed for the


i(~i(t)


c~i(t)






35

In those cases where the data consisted of two sets of observations of the same source

done hours apart, the calibration interpolation was done separately for each observation.


Recall that all this calibration has been done using the channel zero data set.


calibration can now be applied to the line data set, which consists of a number of narrow


frequency channels.


The last step in calibration is to correct for any variation in the


instrumental response across the frequency bandwidth observed; i.e.


channel to channel.


any variations from


Since the flux calibrator has been chosen to have a constant flux across


the bandwidth, any variations in flux are due only to the response of the instrumental


bandpass.


A bandpass correction is calculated by dividing the line data set for the flux


calibrator by the channel zero data set.


The bandpass correction in amplitude and phase


is then applied to the line data for the source.


Imaging


Once the data are calibrated, an image, or map, of the source's


brightness distribution


can be obtained by Fourier transforming the visibility data set (cf. equation (3-15)).


As the


data sets involved in spectral line interferometry are very large, a Fast Fourier Transform


(FFT) is used rather than a Direct Fourier Transform (DFT).


The FFT, which performs the


transform on data that has been gridded first, requires computational times proportional


to NxNylog(NxNy),


where NxNy is the size of the image in pixels.


The DFT however,


which evaluates the transform at each individual data point, requires times proportional


to N NyN v,


where


is the total


number of visibilities (data points) in


the data


set. Since this number can be on the order of hundreds of thousands for VLA data, the








In order to use an FFT


, the data must be gridded into an Nx by Ny complex array


where Nx and Ny are powers of two. However, first the data is smoothed (via convolution

in the (u, v) plane) to suppress aliasing and so that it can be uniformly sampled at the


grid points


Unsampled regions are assigned a value of zero, which introduces extensive


sidelobes into the synthesized beam, producing what is known as the "dirty beam"


provide good sampling, the cell size (pixel size) for the images should be chosen so that


there are approximately 3 4 cells


per synthesized beam (Hjellming and Basart,


1982;


England,


1986).


The application of the FFT to the gridded complex visibility results in what is known


as a


"dirty


" image: this is the source intensity distribution convolved with the dirty beam


equation (3-16)).


The dirty beam is the Fourier transform of the sampling function.


For spectral line data, a cube of dirty images with one image for each frequency channel

is produced; the three axes are right ascension, declination, and frequency or velocity.

These images contain not only the emission from the line being observed (i.e. 21-cm),

which is frequency dependent and so varies from channel to channel, but also continuum


emission from


"background"


resolved or unresolved


point sources


that is continuous


across all the channels.


The continuum emission is subtracted out, usually by subtracting


the average of several channels at each


continuum emission.


"end" of the cube that are known to contain only


This results in a cube containing only the line emission from the


source being observed.

Once the continuum emission has been subtracted, the images must be corrected for


the distortions introduced by the dirty beam.


This is done using a CLEAN algorithm,






37

convolving the beam with a point source containing some specified fraction of the peak


emission (usually 0.1, or 10%), and subtracting the result from the image.


This is repeated


iteratively until the peak emission reaches a specified level, usually one or two times the


r.m.s. noise on the image.


The location and amount of flux subtracted is kept track of, and


these components are then convolved with the "clean" beam (usually an elliptical gaussian


fitted to the primary response of the dirty beam) and added back into the image.


Since


the clean beam does not have the extended sidelobes of the dirty beam, this procedure

removes such artifacts as well as secondary grating responses from the image.


The calibrated,


continuum subtracted,


and CLEANed data cube is now ready for


any analysis judged necessary and/or useful.


Integrating the cube in velocity produces


a "zeroth"


moment map of the column


density


(see equation


(3-7));


taking the first


moment with respect to velocity results in a moment map of the velocity field (equation

(3-10)); and taking the second moment results in a moment map of the velocity dispersion


(equation (3-11)).


These moment maps can be analyzed to determine the location and


amount (mass) of HI, as well as its large-scale motions such as rotation.

The data for both projects done for this study were obtained and reduced in accordance


with the general methods outlined above.


Specifics for the survey project are discussed


in Chapter 4, and those for the BCD-LSBD project in Chapter 5.













CHAPTER


HI SURVEY PROJECT


Introduction


Although dwarf galaxies are thought to be the most numerous type of galaxy, there are


many indications that they are underrepresented in current surveys.


Optical surveys tend


to miss objects that are of small optical extent and/or of low surface brightness, with this

bias increasing at greater distances. Hence, compact but high surface brightness systems


as well as large but low surface brightness systems may not be detected (e.g.


., 1988; Davies and Morgan, 1994).


Binggeli et


Dwarf galaxies, which are both small and generally


of low surface brightness, tend to suffer strongly from these selection effects.

Observations of dwarf irregular galaxies in the Virgo cluster and in the field indicate

that the luminosity function for dlrrs is flat or even possibly decreasing (Sandage et al.,


1985;


Tammann,


985; Binggeli et al.,


1990).


Tyson and Scalo (1988) state that this


observed turnover at MB


-14 in the magnitude distribution for dIrrs


is due not to


an inherent decrease in the number of galaxies at fainter magnitudes, but is the result


of a combination of selection effects due to


angular size.


limiting apparent surface brightness and


They further state that these effects will be more severe for galaxies that


are undergoing sporadic bursts due to SSPSF.


As pointed out by Searle et al. (1973),


one of the implications of SSPSF is that a








optically much less visible due to the lack of luminous (and therefore short-lived) stars.


Smaller, less massive galaxies,


which burst less frequently,


will spend even more time


in a quiescent stage,


making them even less likely to be detected at optical wavelengths.


Therefore,


the bursting systems are just a very small part of a much larger,


optically


faint population of galaxies.

This suggestion that small galaxies spend only a small fraction of their lives in an

optically visible state led Tyson and Scalo (1988) to postulate that existing catalogs, based


on optical observations, were missing most of this presumed faint parent population.


order to predict the "true"


number of dwarf galaxies, they used the SSPSF scenario to


model starbursts in a sample of 10 dwarf galaxies.


They assumed a power law frequency


distribution of galaxy sizes (radii) of the form


OcrT


(4-1)


so that 7 is now the variable of interest to be determined.


stochastically


sampling


applying


optical


selection


effects


(apparent


magnitude, surface brightness, and angular size) to their parent population (undergoing

SSPSF), they created a simulated catalog that could be compared to a real catalog of


dirrs based on actual observations.


They then adjusted the parameters for their model


parent population until the simulated catalog most closely matched the real catalog of

galaxies, so that they felt confident that their modelled parent population was an accurate

reflection of the true (postulated) parent population represented by the observed catalog.


They found the best fit for a value of


so that the


"true" frequency


A;ctrwl it"nn nf


Ilrllc9'7a IC'P ;


-4









This


frequency


distribution


represents


a luminosity


function


dwarf


irregular


galaxies that rises steeply for smaller (i.e. fainter) galaxies.


(See Figure 4.1


below).


I I I 1


I I I I


I 11I


1I t -i


1 11


Radial Frequency Function
f(r) = 3r


I I I I I I II I I I I I


.4
Radius (kpc)


Figure 4.1:


Radial frequency function determined by


Tyson and Scalo (1988).


By integrating this function over all galaxy sizes,


K.r


-4.2


Tmin


Kr_-3'


for rmnax


where Kr was determined to be 3 for a space density n in Mpc


rmin


(4-3)


, if r is in kpc.


From this,


Tyson and Scalo estimated that the space density n of galaxies could range from 10 to


I I






41

1985), then these galaxies could exist in high enough numbers to provide enough


mass to close the universe:


Rdwuarf


In their paper, Tyson and Scalo assumed a constant space density for dIrr galaxies:


their simulated sample was distributed evenly throughout space.


This uniform distribution


is contrary to that observed for brighter galaxies,


scales.


which exhibit "clumping"


on several


Normal (non-dwarf) galaxies are clustered on both small and large scales.


tend to occur in groups such as our Local Group;


and in clusters such as


They


Virgo.


turn, these groups and clusters form larger and larger groups and clusters (superclusters)


as one looks on larger and larger scales.


The large scale structure of the universe is a


complex network of what appears to be intersecting "bubbles"


, with galaxies distributed


preferentially along the surfaces of bubbles enclosing large voids where few or no galaxies


have been


found.


In an effort to explain this large-scale structure in the distribution of bright galax-


ies, the concept of biased galaxy formation was introduced.


Biased galaxy formation


proposes "large-scale segregation between luminosity (= luminous galaxies) and mass (=


dark matter)"


(Binggeli et al.,


1990, p. 42): mass is postulated to be uniformly distributed


throughout space, but luminous matter (bright galaxies) does not follow the mass distri-

bution, being clustered instead.

In 1986, Dekel and Silk, using cold dark matter biasing, developed a model showing


that galaxies that form from small amplitude fluctuations (~-


will become dwarf galaxies,


l a) in the mass distribution


whereas normal (bright) galaxies form preferentially from


arge (~2,


- 3a) deviations.


Therefore they proposed that dwarf galaxies will trace the


Pcre






42

Project Description


In order to examine the validity of Tyson and Scalo's


luminosity function (1988), we


initiated and carried out a search for this large population of quiescent dwarf galaxies.

Although these objects are optically faint, they contain large amounts of HI gas which


make them "bright" at the radio wavelength of 21-cm. We therefore conducted a 21-cm

wavelength survey of three separate areas (fields) using the VLA. Although not subject

to the strong selection effects that bias optical surveys, HI surveys are sensitive to the


amount of flux, and so are subject to a flux bias.


Since the


"surface density"


of the


atomic hydrogen (i.e.


the column density NHI


see equation (3-7)) and therefore the HI


mass (see equation (3-9)) is a function of the flux, HI surveys are subject in essence to


a gas mass selection effect.


These surveys will miss objects with either low HI contents,


such as dEs, and/or objects with low column densities of HI.

Number Density


Using the radial frequency distribution found by Tyson and Scalo (1988) (equation


(4-2) above),


we were able to predict the number of galaxies we should detect within the


volume of space encompassed by the primary beam of the VLA in the following manner.


The total number, N,


of galaxies with radii greater than rmin within a volume V can


be written as


f(r) dr dV


(4-4)


where f(r) dr is


Tyson and Scalo's


radial distribution function for galaxies (equation (4-


Tmin








(For an instrument such as the VLA,

the section on Observations, below.)


w is just the solid angle of the primary beam; see

Since the detectable HI mass is a function of the


distance (equation (3-9)),


the survey volume is also a function of the HI mass.


Lower


mass


galaxies can only be detected


in nearby volumes,


so that the effective


volume


searched for lower mass systems is smaller than that for higher mass systems.


When


predicting the number of galaxies we expected to see, we had to take this dependence of


the volume on the HI mass into account.


The minimum detectable HI mass, Mhmin, is


Mhmin


(4-6)


where


Fmin dv


(4-7)


Fmin is the minimum acceptable flux for a detection, and dv is the velocity width in km


one channel.


Equation (4-6) can be rewritten in terms of the total mass, Mr, rather than the HI

mass by using the empirical relation


= 5.36Mh


(4-8)


determined by


Tyson and Scalo from their catalog of observed dwarf galaxies.


Hence,


we now have


MT(min


= ks


2, (4-9)


where the constant k has become


x kh:


= 5.36


x 105)


rI


Fm in dv


(4-10)








and differentiating this with respect to MT,


we find the following expression for ds as


a function of MT(min):


(MT(min


dMT(min)


We can now write the volume element as a function of the minimum detectable


(total) mass M by substituting equations (4-11) and (4-1

(equation (4-5)):


2) into the expression for dV


= ws2 ds


(Mmin')


dMmin


(4-13)


where we have dropped the subscript T for clarity

with radii between rmin and rmax within a volume


. So the total number N of galaxies

V becomes


f(r) dr dVm


Tmin


M(Smax) 7max


M(Smin) rmrn


f (r) dr (Mmin)


dMmin


(4-14)


The limits for the volume integration, M(sm) and M(smin) are the minimum detectable


total masses at the maximum and minimum distances surveyed.


These quantities are


found from equation (4-9) above.

Because there is a relationship between the mass and the radius of a galaxy, we must

rewrite the radial distribution f(r) dr as a function of mass (f(M) dM) before evaluating








where log(KM)


= 8.06 0.15 and q


= 1.8


+0.2


for M in solar masses and r in kpc.


Solving for r,


= (-
VM/


(4-16)


and differentiating with respect to M, we obtain the following expression for dr:


1=M(
= 1M
q(KM)


(4-17)


Substituting these expressions for r and dr into the radial distribution function (equation

(4-2)) allows us to transform


f(r)dr


= Kr


r 'dr


(4-18)


tmin


Mmax


f(M) dM


q(KM)


M(-1) dM.


(4-19)


Mmin


Evaluating the integral for f(M) dM in the limit Mmax

as a function of Mmin:


Mmin allows us to findf(M)


f(M) dM


Kr (7 + 1)


(Mmin )


(4-20)


(KM)


which is the number of galaxies per cubic Mpc with masses greater than Mmin.


Using this


result, we can now write the integral in equation (4-14) completely as a function of Mmin:


_(wKr
\2kI


(KM)-1
(7 +1) -
Kg,)


M(smax
!


(Mmin) i2


dMmin


(4-21)


(8mm))


The integration limits M(smin) and M(smax) were determined from






46

where Fmin for this project was defined to be 5.12 times the r.m.s. noise (o-) on a single


channel map


. For the estimated values of the observational parameters a,


the single


channel width dv


, and Smin and Smax,


we used a


= 0.6 mJy,


=41 km/s


, and smin and


smax are


2.5 and 53 Mpc, respectively.


We therefore find that


8w&in


sma x)=


x 108 M .


(4-23)


Using the value determined (see Observations section, below) for the VLA'


primary


beam solid angle,


= 9.6014


x 10-5 steradians, and recalling that Kr


= 108.06


- 4.2, and q


1.82, we find from evaluating equation (4-21) that the estimated total


number of galaxies that are detectable by the


VLA in one of our survey fields is 9.1.


The uncertainties associated with this number are difficult to assess, as several of the

uncertainties in the quantities that go into the determination are correlated, preventing

an accurate determination using straightforward propagation of errors. However, a rough


estimate obtained in this way results in an uncertainty on the order of


per field.


+40 galaxies


The upper limit indicated by this value would be easily detectable and can be


ruled out by the results of this and other surveys, as will be shown below.


The lower


limit would indicate an extremely low space density of dwarf galaxies, and would be

of no cosmological interest, as the fraction of dwarf galaxies in the Universe would be

insignificant compared to their larger more massive brethren.

Another uncertainty in this numerical estimate is the result of a bias analogous to


the u wll-lnnnrn Mnnlmrnict hinac (Is/fholct nrtn flhRinnti 10Q1


1~rl iirn~na.nrt in;


= 3, KM


3A 3\






47

the mass-radius relation means that, for a given radius, some galaxies will actually have


masses slightly lower that than dictated by the mass-radius relation.


also means that, similarly,


This uncertainty


there will be galaxies with masses slightly higher than the


one predicted by the mass-radius relation.


The galaxies with slightly higher masses will


be detectable out to a greater distance, and so are visible over a volume that is slightly


larger than the nominal one.


volume.


These systems will be included in a survey of the nominal


Conversely, the galaxies with slightly lower masses aren't detectable over the


entire nominal volume, and will be excluded. Since the higher mass systems are sampled

throughout a larger volume than the lower mass systems, we are including more higher

mass systems than we are excluding lower mass systems. This causes a net increase


in the total number of galaxies of a given radius that are detectable.


greater for galaxies with smaller radii,

radial distribution function. We have i


This bias will be


due to the steep increase in the (Tyson and Scalo)


lot accounted for this bias in the derived numerical


estimate, and so in this sense, the 9.1 galaxies per field is a lower limit.

Spatial Distribution


In addition to investigating the number of


dwarf


galaxies,


we were interested in


examining their spatial distribution as well, to


see whether these small systems are indeed


more uniformly distributed than the brighter normal galaxies as predicted by Dekel and


Silk'


models (1986) for biased galaxy formation.


Therefore the survey was designed to


encompass three different extragalactic environments.


The first region is located within


a void, the second in a cluster of galaxies, and the third in the well-known interaction


field of M81/M82.


This last field was included to test the idea that dwarf galaxies may






48

detection of 3 previously uncataloged low surface brightness dwarf galaxies, including


one in the M81


group2, and more recent work on the possible formation of dwarfs in


the tidal tails of interacting systems (Duc and Mirabel,


Hibbard et al


1994; Mirabel et al.,


., 1994) has provided support for the idea that dwarf


1994; and


galaxies can form


through galaxy-galaxy interactions.

If the theory of biased galaxy formation is correct, then our survey should detect


essentially the same number of galaxies in the void and in the cluster fields


and if dwarfs


do indeed form more readily in interaction fields, then we should find an enhancement

in the M81/M82 interaction environment.




Observations


Each of the three fields was chosen to include a known dwarf galaxy; the presence of

some signal in the observations provided a means to check that the array was operating


correctly and the data were reduced properly.


In the void field, the observations were


centered on


UGC


10805,


a dwarf irregular


located near the edge of the


void.


cluster field was centered on UGC 2014, a dwarf irregular in a nearby cluster; and the

interaction field was chosen to include M81 Dwarf B (hereafter M81dB), one of the two


dwarf galaxies detected by Lo and Sargent (1979).


Table 4.1 presents physical properties


of these systems as reported in the Third Reference Catalogue of Bright Galaxies (known


as the RC3


de Vaucouleurs et al


., 1991).


In Table 4.1


, a and 6 are the right ascension and








Table 4.1:


Physical Properties of target galaxies.


UGC 10805 UGC 2014 M81 Dwarf B
(Void Field) (Cluster Field) (Interaction Field)
a (B 1950) 17h 17' 34s 02h 29m 48s 10h 01tm 24s
6 (B1950) +140 26' 47" +380 27' 00 +700 37' 00 "
Common names DDO 207 DDO 22 UGC 5423
D25 1.66' 2.04' 0.87'
BT 15.3 15.65 15.19 a
Av20 (km s-1) 55 5 67 + 7 67 + 7
Av50 (km s-l) 37 + 7 49 + 12 39 + 7
V (km s-l) 1554 4 565 6 340 5
d (Mpc) 16.86 6.85 4.54
MHI (MQ) 4.23 x 108 8.95 x 107 1.87 x 107


a me rather than BT.


declination for equinox B1950. D25

where the surface brightness level is


is the apparent major isophotal diameter measured


.0 B-magnitudes per square arcsecond. BT is the


total apparent magnitude in the B system.


The following two lines,


Av2o and Avso, are


the full-widths of the HI line as measured at the 20% and 50% levels of the peak signal,


respectively.V


is the mean heliocentric radial velocity derived from HI observations,


and d is the distance as determined by the velocity corrected to the galactic standard of


rest (VGSR) as defined in the RC3, and using Ho


= 100 km s-1 Mpc-1


We have chosen


to use this value for Ho both to be in accord with Tyson and Scalo (1988), and because

it provides us with a conservative volume estimate.


In order to provide both reasonable velocity resolution (channel


width) and wide








.5 MHz.


This bandwidth corresponds to a velocity range of about 2500 km


S-1; which


is a distance range of


Mpc, using H0


= 100 km s-1


Mpc-


To extend the volume


surveyed,


we observed each field at two different center frequencies, separated by


MHz. Since the two sets of observations covered adjacent frequency ranges of 12.5 MHz


(2500 km


s-1), the combination of the two sets of observations had a total bandwidth of


MHz and thus a total combined velocity range of approximately 5000 km


The center frequencies chosen for the two sets of observations done for each field


were


1401 MHz for the high redshift (4100 km


low redshift (1500 km


-1) observations.


therefore approximately 230 km


1) observations and 1413 MHz for the


The total velocity range actually observed was


to 5371 km


, so that the distance range surveyed


for each of the three fields was from about


3 to about 53.7 Mpc.


The total volume3


surveyed per field was then


1
= -(Dm
3- -m a


(4-24)


where w is the beam solid angle of the primary beam of the VLA. Approximating the

VLA primary beam as a 2-D Gaussian with a FWHM of 31.6', we find that the beam


solid angle is 9.6041


x 10-5 steradians.


Using the minimum and maximum distances of


3 and 53.7 Mpc, the maximum total volume per field is 4.96 Mpc3


volumes vary from this slightly


The actual survey


one or more channels at the end of the bandpass were


sometimes discarded due to the loss of sensitivity produced by the bandpass roll-off.


Observations for the cluster and interaction fields were done on Jan.


21/22


1990,


and observations for the void field were done on May


15/16,


1991.


After preliminary








reduction of the cluster and interaction fields, the high redshift observations were found to

be contaminated by the presence of an internal interference spike very close to the center


frequency of 1401 MHz.


Since these (Jan.


1990) observations had been done in auto-


correlation mode, it was impossible to isolate and remove the effects of this interference.

Subsequently, time to reobserve these data sets was applied for and granted, and the high


redshift observations for the cluster and interaction fields were retaken on August


1992.


As this was a detection experiment, high sensitivity to low levels of emission was


required.


Since the minimum detectable flux is inversely proportional to the array size


(see equation (3-25)), the most compact array configuration, the D-array,


the observations.


was used for


Each of the three fields was observed for approximately 8 hours


hours at each center of the two center frequencies. We th

and low redshift observations for each of the three fields.


lerefore had 6 data sets:


The expected r.m.s.


noise at


the one-sigma level in one channel is:


a (mJy)


(4-25)


- 1)nAt


where C is a system constant which was


10 for the January


1990 observations and 9.4


for the May


1991 and August 1992 data. N is the number of antennas used, which was


generally 27


n is the number of IF pairs,


which was 1/2;


t is the total observing time


in hours, and Av is the width of one channel in MHz,


which was 0.195.


Evaluating


this for a 4-hour observation predicts an r.m.s noise of 0.6 mJy for each of the six sets

of observations.


Data Reduction








and then calibrated and Fourier transformed to produce a set of images, which were then


analyzed as described in the following section.


here,


The general procedures used are discussed


with specifics mentioned in the section on survey results.


As discussed in Chapter 3, the data calibration is carried out using the


"channel-zero"


data, which is the average of the inner three-quarters of the total bandpass observed.


This


increases the sensitivity of the calibrator data, and therefore provides a better calibration

of the source line data.

The channel-zero data for each calibrator and source were examined and any anoma-

lous data points (usually identified by a flux value far from the mean) were removed.


Once the calibrator data were edited satisfactorily, the gain, phase, and bandpass cali-

brations were performed according the precepts in Chapter 3. The calibration was then


applied to the line data for each source data set.


The channel-zero editing was also applied


to the line data sets to remove any problem data identified by the channel-zero data.


After calibration,


line data sets were ready for editing and


transforming into


images. Examination of some of the data sets revealed the presence of solar interference


when the observations were done during daytime.


This type of interference is common in


D-array data due to the short baselines used, and can be diagnosed by the systematically


high flux values of the daytime data from the shortest baselines in the array.


was identified and removed from the data sets in question.


Such data


The amount of data affected


was small, since only the very shortest baselines are sensitive to solar emission.

In each of the line data sets, several channels from across the entire bandpass were

also examined to locate any frequency-dependent interference that might be present. As






53
high (several tens of Janskys) flux values. T

worst of the contamination to one or a few

Removal of the affected data was done bv


he narrowness of the feature restricted the

channels in the middle of the bandpass.

using the AIPS task CLIP to remove all


data points with flux values greater than a specified level (generally around 0.6 Jy).


the highly affected central channels,


channel.


this removed approximately half the data for the


The effect is to raise the r.m.s. noise level on the channel; effectively reducing


the sensitivity in those channels,


and thus increasing the lowest signal detectable in the


affected channels.

After editing the line data, each data set was reduced in the following way: channels


without obvious signal were combined in the (u,


v) plane data and then imaged (Fourier-


transformed) to produce a map of the continuum emission:


emission from background sources.


the frequency-independent


After imaging the line data, this continuum emission


map was subtracted from each of the line channel maps,


producing a cube of images


containing only line emission. In the case of the interaction field data sets (those centered


on M81dB),

galaxy M82.


there was also strong sidelobe emission present from the nearby starburst

This was removed by CLEANing a map centered on M82; since CLEANing


produces a model of the emitting source, it was then possible to subtract this model of

M82 from the (u, v) data. Since the source flux was no longer present in the (u, v) data,

there was no beam response to produce sidelobes during imaging, so that the resulting

maps were no longer contaminated.


Before analysis


of the data could


proceed,


one more


in the


reduction


necessary.


Because of


wide


bandpass


MHz)


used for these observations,


was








in velocity.


Hanning smoothing is a running weighted average over three channels of


form


1
=f-In


-1 +


1 1
j'n + -In+1
2 4


(4-26)


where I is the intensity of a particular pixel in channel n, and InH is the intensity of that


pixel in the Hanning smoothed channel at the same velocity as channel n.


reacting "ringing"


Besides cor-


, Hanning smoothing also reduces the noise in each channel. Propagation


of errors shows that the noise in a Hanning smoothed map will be approximately 0.6124


times the noise in the unsmoothed data.


This type of smoothing is often used to reduce


noise and enhance signal (as in the second project, discussed in Chapter 5).


The price


paid for this improvement in the signal to noise is the loss of some velocity resolution.


According to Rohlfs (1990, p.


159),


the velocity resolution of Hanning smoothed data


will be twice the channel separation of the unsmoothed data. As the channel separation


of the unsmoothed data for this project is


~ 41


, the resolution of the Hanning


smoothed data is 82 km


It should also be noted that since the first and last channels


cannot be smoothed this way, they are blanked in the Hanning smoothed data set, thus


reducing the velocity coverage by 41 km


at each end.


After continuum-subtraction and smoothing, any apparent signal in the maps


CLEANed to remove the effects of the dirty beam (see Chapter 3).


only the target galaxies were CLEANed.


In general, this meant


Any possible detections that were identified


during analysis of the data later were weak enough that they did not produce a strong


was






55

Analysis


Noise


In any set of observations, there are errors associated with the data.


As described


by Fomalont in Synthesis Imaging in Radio Astronomy (1989), these errors are of two

types: (1) stochastic (random) errors due to the instrumentation limits; and (2) systematic


errors due to instrumental imaging defects.


Imaging defects, if present, are corrected as


well as possible during the calibration, editing, and imaging of the data.


errors (or "noise"


The stochastic


) determine the background emission level of the data maps, and for


a correlation-type detector, such as is used in the


VLA, these errors should follow a


Gaussian distribution in the image plane and are quantified by the r.m.s.


intensity level


associated with each pixel in an image.


A Gaussian distribution is characterized by its mean, p,


aV2F


and standard deviation, a:


(4-27)


A pixel with a value far from the mean would not be following a Gaussian distribution,


and can be attributed to a signal.


A detection is thus defined as a signal that appears at


a certain level above the background noise.

In order to use Gaussian statistics to describe the significance of a possible detection

and thereby decide whether it is valid, it must first be shown that the background level, or

noise, of a channel map does indeed follow a Gaussian distribution. A Gaussian function


was fitted to the emission (pixel intensity values) in an "empty"


signal, therefore containing only noise.


channel:


This is shown in Figure 4.2.


one with no


The filled circles







56

comparing a completely random set of data points to the specified function (a Gaussian in


this case) is 38


As a perfect fit should have a reduced X


of 1 and a probability of 50%,


the model fit is quite good.


Therefore, the noise on a channel map can be considered to be


Gaussian in nature, and so a possible detection can evaluated in terms of its significance

(i.e. level above the background noise) as determined by Gaussian statistics.


I I


I I I


I 1 I


I 1 1


I I I


Gaussian Fit to Noise


* Measured data
- Gaussian Fit


I I I I I


Il l 1 1


I I I I


I I I I


I I I I


I I I


0
Intensity (mJy/Beam)


Figure 4.2:


Gaussian fit (solid line) to the noise in a channel with no signal emission.


Detection Criteria


In order to minimize spurious detections, several criteria were defined and applied


to the data during reduction and analysis.


There are two basic characteristics to examine


when attempting to distinguish between noise and signal:


flux level and velocity (or


channel) continuity.

Since the noise follows a Gaussian distribution, establishing an appropriate flux level


' I








Gaussian distribution, the probability that x will have a value within p a is given by
p+ar


P(x)


1
o~-------


(4-28)


p-a.


Evaluating this integral shows that approximately 68


of the values of x will fall within


11+0


Letting t


--, the probability function can be recast to find the probability


that a value of x falls within t:


P(t)


(4-29)


where


is the


well-known error function.


Evaluating


the probability


function


determine the number of pixels expected to fall outside the 3a interval (i.e. t


= 0), shows that 0.2


= 3 for p


7% of the data should have values greater or less than three times the


noise (30ch).


The channel maps used for the survey project consist of 256


x 256 pixels,


or a total of 65,536 pixels per channel; therefore one expects (65,536


x 0.0027 =) 176.9


pixels to appear with such values for a map containing only noise. At the 5cr level, this


probability decreases to 5.734


for 65,536 pixels.


This is equivalent to only 0.04


pixels per channel expected with values greater or less than SUch.

with values at or above 5ach can be defined as significant: signal


Therefore, any pixels


, instead of noise.


velocity


continuity


criterion demands


that a signal appear in more than one


channel.


The observed velocity width of a galaxy is a combination of the channel width


Avch of the observations and the intrinsic velocity width of the HI spectral line of the

galaxy (which is a function of both the turbulent and rotational motions of the gas; see

Chapter 5 for details)ve:


r








(AVUob


x41


= 82


s ) requires an intrinsic velocity greater than


~ 35 km


which is quite low (cf. Gallagher and Hunter, 1984).


It is therefore reasonable to expect


all but the most extreme dwarfs to appear in more than one channel of the unsmoothed

data.

In general, noise spikes, or anomalous high-flux pixels, can be identified and elim-


inated based on their appearance in only one channel.


However,


the identification of


noise spikes in the survey data was complicated by the Hanning smoothing of the data.

As this is a running average of every three channels, a one-channel noise spike will show

up in the two adjacent channels as well after Hanning smoothing.

A 5ach noise spike in a channel of the Hanning smoothed data would appear at


5.1240a


' signal in the unsmoothed data,


where a'


is the noise in one channel of the


unsmoothed data.


Hanning smoothing a one-channel spike of this level will result in


the appearance of "signal" at the levels of 3.3Och, 5ach, and 3.3och in three consecutive


channels of the Hanning smoothed data.


Therefore,


the Hanning-smoothed data cube


was examined for pixels with intensities greater than 5oach


when such a pixel was found,


pixels at the same location in the two adjacent channels were examined.


If these were


found to be at a level greater than 3.5 7ch, it was considered to be a possible detection.

Once the entire data cube was examined, channels with possible signal were blanked


and then integrated.


The blanking is done to avoid integrating up the noise as well as


the signal, and was performed using a conditional blanking technique.


In this method,


a blanking mask is created by convolving each map in the data cube with a Gaussian


with a FWHM twice that of the beam.


The blanking is then performed by testing each






59
version of the unconvolved cube, containing only pixels whose absolute values on the


mask were


> 2,m.


After blanking, any channels suspected to contain signal were integrated using the


AIPS task XMOM. A flux limit was used, so that only pixels with intensities IFI


were included in the integration.


>2.5


Negative values were included to avoid introducing


a positive bias in the final moment map.


XMOM produces zeroth,


first, and second


moment maps; the zeroth moment is an image of the integrated flux, or column density;

the first moment is an image of the velocities; and the second moment is an image of the


velocity dispersions associated with each pixel (see equations (3-7), (3-10),


and (3-1


Once the moment maps were created, two further criteria were applied to any possible

detections: the object had to have a peak integrated intensity greater than five times the

r.m.s. noise on the zeroth moment map (oxmom); and the HI mass of the object had to

be greater than five times that expected from the integrated flux due to the noise in one

beam (aOHI).


The 5a limit was determined as follows: a point source (i.e.


1 beam) signal of 3.5a


So', 3.5a appearing in three consecutive channels will add coherently: 3


.5a + 5a + 3.5a


= 12a


. The noise will add approximately as


where N


= number of channels


Thus the signal-to-noise


S


= 6.9.


This assumes a point source where


the signal overlaps exactly.


exactly, the signal will add as (


For a source with single-channel peaks that do not overlap


)a 50*


assuming the overlap is at


the half-power point.


The noise adds as before, and so the signal-to-noise


= 8.57


S
.va


= 4.9.


Therefore, to be classified as a valid detection, the peak integrated flux value on








It should


mentioned


that since


was


Hanning


smoothed,


the data


consecutive channels is correlated, not independent, and so the noise during the integration


doesn't add exactly as the square-root of the number of channels.


To determine the noise


level on the integrated moment map more accurately,


the unblanked signal


channels


were integrated without using any flux limits, so that all pixels in the relevant maps were


included in the integration.


The AIPS task TVSTAT was then used to determine the r.m.s


level (c7xmom) of this "noise"


map.


This measured level was higher than that calculated


using v; so the 57xmom criterion is somewhat conservative.

Finally, the HI mass of the object under investigation had to be greater than five times


that expected from the flux due to the noise in one beam (OHI).


This was determined by


the HI mass corresponding to the flux at the one-sigma level in one beam.


The general


equation for the HI mass is (cf. equation (3-9))


MHI


S dv


(4-31)


where D is the distance to the galaxy in Mpc,


is the velocity width of the signal in km


S is the signal flux in Janskys, and dv


The expected r.m.s. associated with this


integral can then be found from:


5 D2ozmom


(4-32)


where 0xmom is the noise on the integrated zeroth moment map.

To summarize, the detection of a signal required:

(1) the appearance of a signal at levels greater than 3.57ch, 5rch, and 3.5 ach








(3) that the integrated HI mass be greater than SaIm,


where am is the HI mass


expected from a lCrxmom signal in one beam.


Survey Results


The results of the analysis of the three observed fields are discussed in the following


section.


The data for each of the six sets of observations was edited, calibrated, and


reduced as described above.


82 km


The velocity resolution of the Hanning smoothed data is


the spatial resolutions varied for each set of observations and are discussed


individually below.


Velocities were converted to the galactic standard of rest (GSR) using


the precepts set forth in the RC3 (de


Vaucouleurs et al


., 1991), and distances were then


calculated from the velocities using Ho


= 100km


Mpc-'


All volume calculations


were done using equation (4-24).

Void Field


Observations in this field were centered on a catalogued dwarf irregular located at


the edge of the Local Void.


UGC 10805 (also known as DDO 207) has a position of a


(B 1950)


17" 34.4s


, 6 (B1950)


= +140 26'


47.0"


, and a heliocentric velocity of


1554 km


Table 4.1).


were done on May


15/16,


Observations of both the low and high-redshift data sets


, and the data were calibrated, edited, and reduced as


described above. After Hanning smoothing, the single-channel r.m.s.


for the low redshift


data set was 0.428 mJy per beam (B),


and 0.383 mJy B-


for the high redshift data set.


Low redshift Void field data set.


The spatial resolution of this data set is 91


87.4";


the position angle of the beam is


-46.60


(measured from the north through the


17"









each


"end" of the bandpass was discarded during Hanning smoothing (see discussion on


Hanning smoothing, above), and an additional 3 channels at the edge of the bandpass


were discarded due to the poor quality


of the data resulting from the roll-off


of the


bandpass response.


The total volume observed is 0.76532 Mpc3.


To locate possible signal (other than UGC 10805 itself,


which appears in this data


set and is discussed below), the AIPS routine IMEAN was used to find the statistics for

each channel, including the peak pixel intensity and r.m.s. (ach) for the entire channel.

A plot of the peak signal-to-noise as represented by the peak pixel intensity divided by


the r.m.s.


for each channel (ach) is presented in Figure 4.3.


The data for the galaxy


has been excluded from this plot.


It can be seen that there are no points with values


greater 5ach in this data set;


therefore, the only detection for this set of


observations


UGC


10805


itself.


I I I


IIII


I I 1


IIII


I I A


Void Field
va Data Set
Without Galaxy


I I I I I I I I I I I II li


was


I


nAn


rrnr


A A J


1111111 1 kl\ll ')111\11 r)c~llrr









-1 I


I I I I~


I I I


I I


I I I 1


Void Field
vt1 Data Set
With Galaxy


I


1000


1500 2000
Velocity (Ve) (km/sec)


2500


Figure 4.4:


Peak signal-to-noise per channel for the low redshift data set


for the Void field observations; including the data for UGC 10805.


UGC 10805.


UGC 10805 was located in the center of the observed bandpass, as is


shown in Figure 4.4: the plot of peak pixel intensity divided by the r.m.s. noise in each


channel.


This figure shows the same data as that in Figure 4.3, but this time, with the data


for the galaxy included. Signal from the galaxy was observed over 4 channels; figure 4.5


shows the flux spectrum of the galaxy signal from the blanked data cube.


error bar shows the velocity resolution (83 km


The horizontal


s-'); the vertical error bar indicates the


one-sigma variation ( 0.0018 Jy) in the summed flux in each channel.


The channels containing signal were integrated in velocity to produce moment maps

of the galaxy. Figure 4.6 shows the zeroth moment map, which is the integrated intensity


Sn^rjmn ltn nan n-^ Z. r, an an4 nc*an il Z4 nn at 11 nd-a-.n


N' L a n r -- a 1..


I I


II



































1200 1400 1600 1800 2000
Velocity (Ve) (km/sec)


Figure 4.5:







14 31

30

29


Flux spectrum of the blanked data cube for UGC 10805.


0 1 2 3






65
The derived properties for UGC 10805 are as follows:


Peak column density NHI = 4.89 + 0.12


x 1020 atoms cm-2


Peak signal-to-noise (NHi/Oaxmom) = 40.9


Systemic (flux-weighted) heliocentric velocity


Distance D =


1552.5 0.8 km s-1


16.85 Mpc


HI mass MHI = 4.86 + 0.17


x 108


HI mass signal-to-noise (MHI/OHI) = 83.9


AV50 =


36.0 +


1.4 km s-1


The velocity width Avso has been corrected for the velocity resolution (cf. equation (4-30)


above).


The poor velocity resolution prevents us from making an accurate determination


of the


velocity width at the


20% of peak


level.


velocity uncertainties are


conservative statistical errors which reflect the uncertainties in the pixel intensity values

due to the noise on the maps. Systematic effects such as those from errors in measurement


of the spectrum width are not included.


The major and minor axes of the HI distribution


dimensions


(after


deconvolution


beam


from


image)


are 97.1"


84.7"


respectively, and are oriented at a position angle of


--8 30


. All of these properties are


also listed in Table 4.2 in the Discussion section, along with those for the other detected

galaxies.


Comparison


quantities


from


RC3


listed


Table


shows


close


agreement with the results presented here:


HI mass we derive is slightly higher


than the 4.23


x 108


M in the RC3.


High redshift Void field data set.


The spatial resolution of this data set is 61.7"


Vo-









is from 2960.7 to 5376.0 km


these are distances of 30.93 and 55.08 Mpc. As for the


low redshift data for this field, one channel from each end of the bandpass was discarded

during Hanning smoothing, and an additional 3 channels were discarded due to the poor


quality of the data resulting from the roll-off of the bandpass response.


The total volume


observed for this data set is 4.402 Mpc3.


Using the same method as for the low redshift data set, the map cube was searched

for any signal greater than 5ach; the plot of the peak pixel intensity per channel in terms


of the r.m.s. in each channel is shown in Figure 4.7


There is a possible detection at the


high velocity end of the bandpass, where there is signal with values greater than 3.5,

and 3.5Och in three consecutive channels.


I I


I I


I I I I


I


I


Void Field
va Data Set


I I I I I I I I I I


I


3000


3500


4000 4500
Velocity (Vo) (km/sec)


5000


Figure 4.7:


Peak signal-to-noise per channel for the


high redshift data set for the Void field observations.









the signal passed the initial detection criterion, it failed the last two:


the signal on the


integrated map was below 5axmom in terms of both the peak column density (NmH


-8.6


x 1019


atoms cm


= 3.5axmom) and in terms of the HI mass (MrIl


4. laOH, at a distance of 51.8 Mpc). A search of the NED database4 revealed no catalogued


objects within a


radius.


The object'


spectrum is included below (see Figure 4.8), for


completeness.


.002




.0015




.001




.0005




0


4400


4600


4800
Velocity (V,


5000
(km/se


5200


5400


Figure 4.8:


Flux spectrum of blanked cube for possible detection in the high redshift Void field.


Results for the Void field.


Owing to the loss of the end channels in both the high


and low redshift data sets, there is a slight gap in velocity coverage between them:


maximum distance for the low redshift data set is 28.86 Mpc; the minimum for the high


redshift set is 30.93.


Adding the volumes from both data sets results in a total observed


l-

Possible Detection
Void Field ve


lc-
S --



-4








volume for this field of


.17 Mpc3


Only the target galaxy, UGC 10805,


was detected.


There is the possibility of another object in the data set, but it did not integrate up to levels


above 5ao in either HI mass or column density.


However, since this possible detection


is at the end of the observed bandpass where the sensitivity is beginning to drop off,


there is a remote possibility that this object really does exist.

centered at its heliocentric velocity would settle the question.


study,


Follow-up observations

For the purposes of this


however, it cannot be regarded as a detection.


Cluster Field


The observations of this field were centered on at a (B 1950)


= 02h 29m 48s


, (B 1950)


= +380 28' 00"


, to target a catalogued dwarf irregular located in a cluster of galaxies.


UGC 2014 (also known as DDO 22) has a heliocentric velocity of 565 km


1 (see Table


4.1).


Observation of the low data set was done on Jan.


21/22,


1990; the high redshift


data set was taken on August 2/3,


1992.


The data were calibrated, edited, and reduced as


described above.


After Hanning smoothing, the single-channel r.m.s. for the low redshift


data set was 0.597 mJy per beam (B),


and 0.450 mJy B-


for the high redshift data set.


Low redshift Cluster field data set.


The spatial resolution for this set of observa-


tions is 59.00"


x 52


the beam position angle is 60.500


The channel separation is


41.6 km


and so the resolution of the Hanning smoothed data is 83


.2 km


Only one


channel at each end of the bandpass was discarded (as a result of the Hanning smoothing)


and so the heliocentric velocities range from 256.0 to


2754.3 km


The corresponding


distance range, calculated from the GSR velocities, is from 3.76 to 28.74 Mpc.


This is








from UGC 2014,


which appears in this data set, has been excluded from this plot.


points above Scrh at the high velocity end of the bandpass were investigated, and proved

to be residual emission from a continuum source that was incompletely removed during


continuum subtraction.


The peak emission producing the high signal-to-noise in the line


data set coincided with the position of a strong source visible in the continuum map; a


search of the NED database identified it as the radio source B3 0231+385.


As a check, the


channels with the residual emission were blanked and integrated, and the column density


and HI mass signal-to-noise levels were checked.


These both proved to be below 5 (NHI


= 4.4rxmom; MHI

I I I
5.2 -

5


= 1.5aHi).


Therefore the only detection for this data set was UGC 2014.


500 1000 1500 2000 2500
Velocity (Ve) (km/sec)


Figure 4.9:


Peak signal-to-noise per channel for the


low redshift data set for the Cluster field observations.


UGC 2014.


Figure 4.10 shows the peak pixel signal-to-noise per channel of the








map is presented in Figure 4.12.


Derived properties for UGC 2014 are:


Peak column density NmH


= 8.82 0.40


x 1020 atoms cm-2


Peak signal-to-noise (Nm/axmom) = 22.3

Systemic (flux-weighted) heliocentric velocity V


Distance D


= 6.85 Mpc


HI mass MHI


= 6.13 0.33


x 10


HI mass signal-to-noise (MHI/OHI)


= 50.4


tM'50


= 47.6 +


1.9 km s-1


The major and minor axes of the HI distribution are 97


and 34.8", oriented at a position


angle of 179.80


. These data are also shown in


Table 4.2.


Velocity uncertainties are as


for UGC


10805:


conservative statistical estimates only.


Comparison with


Table 4.1


, the data listed for this system in the RC3,


shows that


we are detecting about 68


of the listed flux.


However, our value is within the range of


fluxes listed in Huchtmeier and Richter's


HI Catalog (1989).


Our value for Avso agrees


very well with the one in the RC3, as do the heliocentric velocity and distance.

30 -
Cluster Field
ivt Data Set
25 -With Galaxy


= 565.3 + 0.1 km


L
































300 400 500 600 700 800 900 1000
Velocity (Ve) (km/sec)


Figure 4.11


Flux spectrum of the blanked data cube for UGC 2014.


0.5 1.0 1.5












High redshift Cluster field data set.


The spatial resolution of this data set is 70.2"


x 55.9"


the east).


the position angle of the beam is -88


The channel separation is 42.3 km


(measured from the north through


, and so the velocity resolution of the


Hanning smoothed data is 84.6 km


discarded during Hanning smoothing.


data set is from 2954.2 to 5495


Mpc, respectively.


. One channel from each end of the bandpass was

The heliocentric velocity range covered for this

-l; corresponding to distances of 30.74 and 56.15


The total volume observed for this data set is 4.738 Mpc3.


The plot of the peak pixel intensity per channel in terms of the r.m.s. in each channel


was searched for any data points with values greater than 5o-ch


none were found.


This


plot is shown in Figure 4.13.


I*I I


I I I


I I T


I


Cluster Field
v2 Data Set


I ~I


I I I i I I I iI


I I I IJ


3000


3500


4000
Velocity (Ve)


4500
km/sec)


5000


5500


Figure 4.13:


Peak signal-to-noise per channel for the


C t1 f fl C f


I I








The combination of the two data set volumes results in a total volume surveyed


for this field of 5


Mpc3


Again,


only the target galaxy,


UGC 2014,


was detected.


possible detection


low redshift


data set was proved


to be an


incompletely


subtracted continuum source.


Interaction Field


The observations of this field were centered on at a (B1950)


(B 1950)


= +700 37' 00"


, to target the catalogued dwarf irregular M81dB (UGC 5423).


This galaxy is located near M81 and M82, which make up an interacting system that also


includes NGC 3077


M81dB has a listed heliocentric velocity of 340 km


Table


4.1).


Observation of the low data set was done on Jan.


21/22,


1990; the high redshift


data set was taken on August 2/3, 1992.


The data were calibrated, edited, and reduced


as described above. After Hanning smoothing, the single-channel r.m.s.


high redshift data sets were 0.595 and 0.568 mJy B-

Low redshift Interaction field data set. The spat


for the low and


, respectively.


ial resolution for this set of obser-


vations is 54.11


41.6 km


the beam position angle is 44.280


. The channel separation is


and so the resolution of the Hanning smoothed data is 83.2 km


Only one


channel at each end of the bandpass was discarded (as a result of the Hanning smoothing)


and so the heliocentric velocities range from 256.1 to 2754.3 km


The corresponding


distance range, calculated from the GSR


velocities, is from 3.68 to 28.67 Mpc.


This


corresponds to a volume of 0.753 Mpc3


Initial


visual


inspection of the data cube revealed the


presence of


definite signal


= h02 0







74

a plot of the peak signal-to-noise in each channel, excluding the signal from both M81dB


and UGC 5455


, is shown in Figure 4.14.


There is one data point greater than 5Och,


located near the very end of the bandpass.


I I I '


1 I I I


I I I I I


Interaction Field
11 Data Set


-.1 I II


I I I I I I II III


1000 1500
Velocity (V0)


km/se


2000


2500


Figure 4.14:


Peak signal-to-noise per channel for the low redshift data set


for the Interaction field observations, excluding M81dB and UGC 5455.


The end channels


were blanked and


inspected,


and the


last three channels were


integrated.


The spectrum of the blanked cube is presented below in Figure 4.15; the


vertical error bars represent fla variation.


They are plotted separately as the noise in


these end channels rises steeply towards the end of the bandpass and so an average value

is not truly representative for the three channels.

The integrated signal did not pass the final two detection criteria, and no catalogued


object was found in the NED database within a


radius of its position.


Although the


I


I 1 1 1


I I I


I I








bandpass, or whether it is an artifact of the high noise prevalent in the end channels.


poor quality of the data would tend to indicate the latter.


As for the possible detection


in the Cluster field, this object fails two of the detection criteria and so is not considered

a valid detection for this experiment.


300 400 500 600 700 800 900 1000
Velocity (Vo) (km/sec)


Figure 4.15:




M81dB.


1100


Flux spectrum of blanked cube for possible detection in the Interaction field.




Figure 4.16 shows the peak pixel signal-to-noise per channel of the Hanning


smoothed data, including the emission from M81dB (high velocity end) and UGC 5455


(center of bandpass).


The channels containing the emission from M81dB were blanked


and integrated to produce a moment map of the integrated intensity.


of the blanked cube is shown in Figure 4.17


The flux spectrum


and the moment map is presented in Figure


































500 1000 1500 2000 2500
Velocity (Vo) (km/sec)


Figure 4.16: Peak signal-to-noise per channel for the low redshift data set for the
Interaction field observations; including the data for M81dB and UGC 5455.


400 600 800 1000
Velocity (Ve) (km/sec)


1200


- ---













70 41


40


39


10 02 15


01 45


Grey scale flux range:
Peak contour flux =


Levs


15.35)


= 1.5175E+02


RIGHT ASCENSION (B1950)


-0.231


00 45


2.355 Kilo JY/B*M/S


2.3548E+03 JYIB*M/S


2.000,


5.117, 8.528,


Figure 4.18:


Integrated HI column density map of M81dB.


Contour levels are 1


.2 (2o),


and 9


x 1020 atoms cm-2


Derived properties for M81dB are:


Peak column density Npn


=8.92 +0.


x 1020 atoms cm-2


Peak signal-to-noise (Ni/axmom)


= 15.5


Systemic (flux-weighted) heliocentric velocity V


Distance D


= 349.7 + 2.7 km


= 4.62 Mpc


m m mK









The major and minor axes of the


HI distribution are 48


and 31.8".


oriented at a


position angle of 131.60


These data are also shown in Table 4.


Velocity uncertainties


are, again, conservative statistical estimates only.


Comparison with Table 4.1 shows that we are detecting about 94% of the flux listed


in the RC3


, and our value for Avso agrees fairly well with the one in the RC3.


heliocentric velocity and distance are slightly different than the published ones; this may

be due to the poorer quality of the data since the signal appears at the end of the bandpass.


UGC 5455.


Figure 4.16 shows not only the signal from M81dB, but also strong


emission from UGC 5455; another dwarf irregular galaxy whose presence in this field


was not realized until the data were reduced.


The channels containing emission were


blanked and integrated, and the spectrum and integrated intensity maps are presented in

Figures 4.19 and 4.20.





.0 UGC 5455
.02 \-



.015 Av -



.01



.005 -



0-


- -


*i1 i1 J'1i) 1 Ani r fll i fllf


ll


r nnn rr


1 r, r


----


lrl








Derived properties for UGC 5455


are listed below and in


Table 4.2;


the column


density and HI mass have been corrected for primary beam attenuation.


5455 lies approximately 21


Since UGC


from the pointing center of the field, the sensitivity of the


primary beam is reduced by roughly a factor of 3.5,


and so the measured values were


corrected by this amount.


Peak column density Nm =

Peak signal-to-noise (NHI/a


12.19 1.23


xmom)


x 1020 atoms cm-2


= 9.9


Systemic (flux-weighted) heliocentric velocity V


= 1293


+ 6.6 km


Distance D


= 14.06 Mpc


HI mass MHI


= 3.69 0.15


x 108


HI mass signal-to-noise (Mm/oa


Av50


= 24.9


= 46.9 + 8.0 km


-- -- - -- -


..









The major and minor axes of the


position angle of 144.1


HI distribution are 85.0"


o. These data are also shown in Table 4.2.


oriented at a


Velocity uncertainties


are conservative statistical estimates only.


The HI mass listed in the RC3 for this system is 3.69


agreement with the HI mass reported above.


which is in exact


The listed 50% velocity width of 57 + 12


is also in reasonable agreement.


High redshift Interaction field data set.


spatial


resolution


of this data set


118.3"


x 48.4"


the position angle of the beam is


-44.10


(measured from the north


through the east).


The channel separation is 42.4 km


, and so the velocity resolution


of the Hanning smoothed data is 84.8 km


was discarded during Hanning smoothing.

this data set is from 2834.6 to 5376.1 km s


54.88 Mpc.


. One channel from each end of the bandpass

The heliocentric velocity range covered for

'; corresponding to distances from 29.47 to


The volume observed for this data set is 4.473 Mpc3


I


I I


I I


I I I


I I I I


I I I I J


Interaction Field
v2 Data Set


4 l


& II


I








The plot of the peak pixel intensity per channel in terms of the r.m.s. in each channel

was searched for any data points with values greater than 5uch; the plot is shown in


Figure 4.21.


As can be seen,


there is one such point,


in the center of the bandpass.


The data were blanked and integrated;

either column density or HI mass. The


but the integrated signal was not above 5a in


signal-to-noise levels were 3.4 in column density


1.3 in HI mass;


therefore this does not constitute a valid detection.


In addition,


the spectrum of the blanked cube showed that signal from only two channels was being

included in the integration; and a NED search turned up no catalogued objects within


radius of its position.


Results for the Interaction field.


As for the other two fields, the loss of channels


from each end of the bandpass due to Hanning smoothing has resulted in a slight gap


in velocity coverage between the low and high redshift data sets.


The combination of


the two data set volumes results in a total volume surveyed for this field of 5.23 Mpc3


Unlike the other two fields, however, we detected a galaxy other than the target, M81dB.


UGC 5455 was observed in the low redshift data set along with M81dB.


A possible


detection in the high redshift data set did not integrate up to a significant level and is


probably


a noise spike.


Discussion


In this project, we have attempted to place limits on the luminosity function proposed


Tyson and Scalo in their


1988


paper.


Using the radial distribution function they


determined combined with the sensitivity limits inherent in our VLA observations, we








these systems as derived from the observations are presented in


Table 4


Each field


encompassed approximately


Mpc3


, and so the actual total volume surveyed was 15.65


Mpc3


. This gives us an observed number density of 0.26 galaxies Mpc-3


Table 4.2:


Derived Properties of detected galaxies.


UGC 10805 UGC 2014 M81dB UGC 5455

Avso (km s-1) 36.0 1.4 47.6 1.9 46.4 + 5.4 20.3 + 8.0
Vo (km s-1) 1552 0.8 565.3 0.1 349.7 2.7 1293.2 6.6
Nm 4.89 + 0.12 8.82 0.40 8.92 0.57 12.19 1.23
(atoms cm-2) x 1020 x 1020 x 1020 x 1020
Nm/anxmom 40.9 22.3 15.5 9.9
d (Mpc) 16.85 6.85 4.62 14.06
Mm (107 M) 48.6 1.7 6.13 0.33 1.76 0.08 36.9 1.5
MHI/aHI 83.9 50.4 23.1 24.9


There were four possible detections investigated:


for the


one in the high redshift data set


Void field, one in the low redshift Cluster data set, and one each in the low and


high redshift data sets of the Interaction field.


The possible detection in the Cluster field


was shown to be the remnants of a poorly subtracted-out continuum source; and the one

in the high redshift Interaction data set was at such a low level that it showed up in only


two channels of the blanked data cube and is most likely a noise spike.


The other two


possible detections, in the high redshift Void data and the low redshift Interaction data,

are near or at the end of the bandpass, where the sensitivity falls off and the data quality


is poor.


This makes it difficult to determine the validity of the detections, and follow-up


observations would be necessary to settle the question.


However, for the purposes of


d.L ....n: an4 nn A ~ a *a ji, a An*an4 an n4 tat4 a octal..l 0kaA (a.. 4 natkar af flac~a tnn








It should be


stressed that the survey presented here


is sensitive


masses, and so examines the faint end of the luminosity function.


This is the area in


which Tyson and Scalo's


radial distribution function is steepest.


Therefore, our essentially


null results,


while not definitive, place a limit on


Tyson and Scalo's


radial distribution


function: it would seem to predict too many small galaxies.


Other surveys have reached


the same conclusion:


that although


there are


many


dwarf


galaxies,


which are often


overlooked in traditional surveys, there is not the large number indicated by the steep


function suggested by


Tyson and Scalo.


Reviews of searches for both low-mass HI-rich


galaxies and "intergalactic HI clouds" (concentrations of HI with no discernible optical


component) are given by Brinks (1994), Briggs (1990),


and Roberts (1988).


Briggs, in


particular, concentrates on searches for dwarf irregulars, and concludes that present HI


surveys are sensitive enough to have detected a large population, if such exists.


these searches,


However,


while occasionally detecting objects, do not support Tyson and Scalo'


luminosity function (see, for example,


Weinberg et al.,


1991).


Several authors have investigated the faint end of the luminosity function using the

form proposed by Schechter (1976):


@(L)


exp (-


L/L*)d(L/L*)


(4-33)


In this expression,


P(L)dL is the number of galaxies per unit volume in the luminosity


interval


from L to L+dL,


is the number of


galaxies


per unit


volume,


is the


luminosity


at which


the function changes slope (in the (log$


log L)


plane),


and a


is the slope of the


luminosity function


when L


<< L*. The parameters


~ ~r (Ll L* )"






84
(1988), the faint end of the luminosity function for clusters is well-fit by a ~, -1.25


and M*


while that for field galaxies has a flatter slope, with a


-1.0. According


to Fisher and Tully (1981) and Staveley-Smith et al.


(1992) however, the very faint end


of the luminosity function is represented by a steeper slope of a


1-i-i


Staveley-Smith


et al.


use this to derive a (conservative) space density of 3


Mpc


, assuming a lower


absolute magnitude cut-off of


-10.


The number of systems detected in this experiment, one each in the Void and Cluster

fields, and two in the Interaction field, is too low to draw conclusions about the spatial


distribution of


dwarf irregular galaxies.


Several studies of the clustering of both low


surface brightness galaxies and blue compact dwarfs have been undertaken by various


authors (e.g.


Salzer and


Rosenberg,


1994;


Pustil'nik et al.


, 1994;


Alimi,


1994;


Roukema, 1994); and a good overview of current research is given by Hopp (1994).


consensus is that although dwarf galaxies, both low surface brightness and blue compact,


appear to be slightly less clustered than brighter,


the voids.


more massive galaxies, they do not "fill


" This rules out any strong biasing, such as is suggested by Dekel and Silk


(1986) in their Cold Dark Matter models.

There are two possible explanations for the lack of detections in this and other HI

surveys: either there is no large population of small galaxies, or these small systems are


not gas-rich, and therefore are not detectable at 21-cm. As discussed in Chapter


it may


be that small, low-mass galaxies lose their HI as a result of a vigorous star-formation

episode. If such an event caused the HI reservoir associated with the system to expand,


it could fade into "invisibility"


at radio wavelengths once the column density became too













CHAPTER 5


BLUE COMPACT


AND LOW SURFACE BRIGHTNESS DWARF PROJECT


Introduction


The possibility that low mass dwarf galaxies suffer expansion and perhaps loss of

their HI gas as a result of an episode of vigorous star formation prompted us to undertake

an investigation of the distribution and kinematics of the HI associated with such systems.

To examine the effects of star formation on the HI properties of low-mass dwarf galaxies,


we present here the results of VLA observations of the HI associated with


16 dwarf


galaxies, of which 8 are believed to be undergoing significant amounts of star formation

and 8 are thought to have low star formation rates currently.


As mentioned in Chapter


it has


been


proposed that dwarf


galaxies undergo a


bursting mode of star formation (SSPSF), followed by a long quiescent period.


Under


SSPSF, star formation occurs in regions known as cells; a cell that is currently forming


stars can trigger star formation in a neighboring cell; there is also a stochastic probability


that a cell will be begin forming stars spontaneously


The star formation within a cell will


cease once the HI gas (out of which the stars form) is either exhausted or dispersed as a

result of energy injected into the ISM as a result of the starburst (e.g. from the evolution


of massive stars).


Once the star formation has stopped, the cell, depleted of HI, cannot


undergo any more star formation until the HI is replenished somehow,


perhaps through