Title: Tidal interactions between M81, M82, and NGC 3077
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Title: Tidal interactions between M81, M82, and NGC 3077
Physical Description: v, 94 leaves : ill. ; 28 cm.
Language: English
Creator: Killian, David John, 1951-
Copyright Date: 1978
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Subject: Galaxies   ( lcsh )
Physics and Astronomy thesis Ph. D
Dissertations, Academic -- Physics and Astronomy -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by David John Killian.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 90-93.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099388
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000075003
oclc - 04748599
notis - AAJ0278

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TIDAL INTERACTIONS BETWEEN M81, M82, AND NGC 3077


By

DAVID JOHN KILLIAN














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














UNIVERSITY OF FLORIDA

1978














ACKNOWLEDGEMENTS


The extensive computer calculations on which this dissertation was

based were carried out on the IBM 370/165 at the Central Florida Regional

Data Center (CFRDC), Tampa, Florida, and the Amdahl 470/V6 at the

Northeast Regional Data Center (NERDC), Gainesville, Florida. Special

thanks for assistance in utilizing the combined CFRDC and NERDC system

is extended to C.J. Young, Assistant Director NERDC, and J.G. Schudel,

Systems Programmer NERDC.

The author also wishes to thank H.W. Schrader and J.T. Pollock for

photographic assistance. Thanks is also due to two people who had a

more indirect effect on the completion of this degree: Ms. Eileen Wyman,

the author's second grade teacher, who taught the author the value of

reading during his protracted childhood illness, and Dr. J.F. Smeltzer,

the author's undergraduate advisor, who truly introduced the author to

astronomy.















TABLE OF CONTENTS


ACKNOWLEDGEMENTS. ..

ABSTRACT . . .

CHAPTER


I INTRODUCTION . . . . . .

II THE MODEL .. . . . . . . . . . .

III THE GALAXIES . . . . . . . . . . .

The Galaxy M81 (NGC 3031). .. . .........

The Galaxy M82 (NGC 3034) . . . . . . . . .

The Galaxy NGC 3077 . . . . . .... . . .

IV RESULTS OF THE MODELLING . . . . . . . . .

The M81-M82 Models . . . . . . . . . .

The NGC 3077 Model . . . . . . . . . .

V CONCLUSIONS . . . . . . . . .. . .

APPENDIX . . . . . . . . . . . . . .

BIBLIOGRAPHY . . . . . . . . . . . . .

BIOGRAPHICAL SKETCH . . . . . . . . . . . .


Page

ii

iv


. . . ... . . . .

. . . .. . . .











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


TIDAL INTERACTIONS BETWEEN M81, M82, AND NGC 3077

By

David John Killian

August 1978

Chairman: Stephen T. Gottesman
Major Department: Physics and Astronomy

The system of galaxies consisting of the galaxies M81, M82, and

NGC 3077 is a peculiar system. The principal member, M81, is optically

a large beautifully symmetrical spiral galaxy. The other two members

belong to the rare and optically unusual IO or Irll class of galaxies,

and they are noted for their peculiar structure and stellar distribution.

Radio observations have revealed a vast cloud of neutral hydrogen (HI)

that envelops all three galaxies, as well as extensive HI bridges con-

necting the two smaller members of the system with M81.

Numerical models of this system have been made to see if the HI

bridges could be products of a tidal interaction between the three

galaxies. In such an encounter the gas in the outermost regions would

be most heavily affected. Therefore, the galaxies were modelled by rings

of massless test particles originally in circular orbits about a central

mass. The rings were initially confined to an annular region whose inner

radii were approximately the Holmberg radii of the respective galaxies

and whose outer radii varied with each galaxy. The central masses were

then launched at one another on a predetermined orbit, and the motions

of the test particles were followed by integration of the restricted









three body equations of motion. The resulting models were compared for

structural and kinematical similarity with the best available observa-

tional studies.

The consequences of these models are potentially important in the

interpretation of this system of galaxies. The HI bridges can be built

tidally, and many of the large scale HI features are duplicated by the

models. During the course of the interactions, a large number of par-

ticles penetrated the nuclei of the two minor galaxies. If the gas

followed similar trajectories, such an event could have precipitated an

era of rapid star formation, which in turn could have modified the mor-

phology of the galaxies. The models also indicate that the systemic

velocity of M82 is closer to +210 km/sec heliocentricc) and that the

orientation of NGC 3077 in the sky is considerably different than that

deduced observationally. The position angle of the kinematical major

axis of 3077 found in this study was 1610 with 3077 inclined 400 to the

line of sight (southeast nearest the observer). Though the HI bridges

and large scale structures are successfully constructed with the models,

the large HI envelope in which the galaxies are immersed is not produced,

nor does it appear to be able to be produced, by the interactions. The

outer structure of M81 has been modified drastically first by the passage

of NGC 3077 approximately 6 x 108 years in the past and then by M82 about

2 x 10 years ago. The outer spiral arm-like features of M81 are

probably the result of these modifications.















CHAPTER I

INTRODUCTION



Intergalactic bridges and tails of stellar and gaseous matter are

common occurrences in systems of two or more closely associated galaxies.

The most widely held theory on the origin of these structures has been

that the gravitational forces between the galaxies have raised tide-like

distortions in each system and thus drawn out the bridges and tails.

The roots of this theory have been traced by Toomre (1974) back to the

early part of this century, but the demonstration of the plausibility

of the theory awaited the advent of the high speed digital computer.

The gaseous extent of a spiral or irregular galaxy is normally much

greater than the corresponding optical image where the bright stellar

components and the bulk of the mass currently attributed to the galaxy

are located. In this region far from the nucleus, it is reasonable to

suppose that gravity is the controlling factor. The gas density is low,

minimizing the importance of hydrodynamic effects. Combes (1978), using
2 3
a typical particle density of 10- cm-3, estimated the importance of four

forces that most reasonably could affect the gas in such regions: the

gravitational and magnetic forces of the parent galaxy, gas pressure

arising from turbulence in the gas, and self-gravitation of the gas.

Considering the force per unit volume of each type, Combes estimated

that the magnetic force was an order of magnitude less than that of

both the pressure and self-gravitation, which were of comparable size









but in turn an order of magnitude less than the gravitational force.

Combes' estimate of the gravitational force per unit volume in a typical

bridge in the NGC 4631 group was 3 x 10- Nm-3

Since the gravitational forces of the principal galaxies appear to

dominate the gas motions in any galactic tidal encounter, a simplistic

model of the encounter can be constructed. The gas may be represented

by "massless" test particles in initially circular orbits in an annular

region about a central mass. The inner radius of the annulus is large

enough to place the innermost particles clearly in the gaseous, non-

stellar region of the galaxy where the model is applicable; the outer

radius can be determined from observational extent of the gas in the

actual galaxy. The circular orbits portray adequately the low disper-

sion velocities typical of the gas motions in spiral galaxies (,' 10

km/sec). The motions of the test particles when two such galaxies

approach one another can then be followed by numerical integration of

the restricted three body equations of motion for each particle. To

model adequately the gas, however, a large number of particles in each

galaxy are required, necessitating the use of a high speed computer to

calculate the motions of the particles.

The system of galaxies consisting of M81, M82, and NGC 3077 exhibits

extensive neutral hydrogen (HI) bridges. Observations by Gottesman and

Weliachew (1977) and Cotrell (1977) clearly demonstrated that one such

bridge appears to connect the principal member, M81, to M82. Cotrell

(1976) also found the neutral hydrogen distribution of 3077 to be dis-

torted towards M81, and van der Hulst (1977), working at a higher sensi-

tivity and with a wider range of sampled velocities than Cotrell, found

that 3077 also was connected to M81 by an HI bridge. The evidence of









apparent tidal interactions between these galaxies and the fact that

both M82 and 3077 belong to the peculiar and rare IrII-IO type of

galaxy were considered by Gottesman and Weliachew (1977) perhaps to be

related phenomena. They reasoned that the results of a tidal encounter

could be to alter violently the gas structure of both M82 and 3077 and

thus induce structural changes that transformed the galaxies from normal

spirals or irregulars into IrlI-1O galaxies.

To test this hypothesis, computer programs were developed to model

the system in the previously described manner. The principle aim of the

modellingwas to see if the observed bridges could be constructed. The

secondary aim was to see if any peculiar particle motions or distribu-

tions were the result of the encounters. Since the two minor galaxies,

M82 and NGC 3077, belong to the structurally unique IrrII-IO class, any

unusual gas motions or distributions predicted by the models could have

some bearing on the evolution of these peculiar objects.

Details of the construction of the models, orbital considerations,

and methods of kinematical and structural comparison of models and ob-

servations are detailed in Chapter II. An observational summary of the

galaxies is given in Chapter III, and the results of the modelling are

discussed in Chapter IV. Chapter V presents the conclusions that may

be drawn from the modelling of the system.














CHAPTER II

THE MODEL



The model chosen for this work was a rather simplistic one. Each

galaxy was assumed to consist of rings of massless test particles

originally in circular orbits in an annular region about a central mass.

The central masses were then "launched" at one another on a predetermined

orbit. As the masses approached one another, the test particles each

experienced an acceleration which, from the restricted three body problem

(cf., Danby 1962), can be expressed as


-GM1 (r r) GM2 (r r2
r = 3 - (Eq. 1)
Ir rI1 Ir r2 3


In Equation (1), M1 and M2 are the masses of the two central masses, G

is the universal gravitation constant, rl and r2 are vectors locating the

central masses with respect to their center of mass, and r and r are

respectively the position and acceleration vectors of one of the test

particles with respect to the M1-M2 center of mass (see Figure 1).

To follow the motions of each test particle, one need only inte-

grate the system of equations described above with respect to time from

some initial time to some final time. For any choice of orbit, the

initial time should be such that M1 and M2 are widely separated so that

one term of Equation (1) is essentially zero for the particles orbiting

each central mass; i.e., Equation (1) reduces initially to the circular


























x

Gx" plane

plkne of orlit


Figure 1. The vector diagram for the restricted three body problem.









centripetal acceleration of the test particles about their central

masses. An initial model time of 8 x 108 years before perigalacticon

was found to produce adequate separation for the models in this study.

The choice of a final time is model dependent and will be discussed

later.

The chief difficulty in integrating Equation (1) is that one must

constantly evaluate r and r2 as a function of time. If one chooses M1

as the origin of an arbitrary x-y-z coordinate system as in Figure 1,

R = Ir2 i1 can be evaluated from the equations that describe the orbit

geometrically; the direction of the vectors comes from the orientation

of the orbital plane with respect to the coordinate system. For example

(see Danby 1962 for details for all conic section orbits), the separation,

R, of the major masses in the case of a hyperbolic orbit is

R = (e 1)-1 q (e cosh B 1) (Eq. 2)


where e is the orbital eccentricity, q is the distance of closest ap-

proach, and B is the eccentric anomaly position angle. The eccentric

anomaly is related to the time elapsed from the time of closest approach,

T, by Kepler's equation for hyperbolic orbits:


[C (e 1)3 q-3]1/2 T = e sinh B B (Eq. 3)

where C = G (M1 + M2). Equation (3) can be solved numerically for B for

assumed values of the other parameters, and then Equation (2) may be

solved for R, leading to an evaluation of r and r2 from the definition

of the center of mass of the M1-M2 system.

From this point, the integration can proceed in any number of ways.

For this work, a Fortran IV computer program was built around a









Runge-Kutta integration algorithm developed by Dr. Erwin Fehlberg at

the Marshall Space Flight Center. Fifth order Runge-Kutta integration

of Equation 1 were then carried out by high speed computer. Each par-

ticle was integrated independently so that the step size used in the

integration could be optimized for it. The results were typically of

greater accuracy (6 to 7 significant digits) than could be utilized

entirely in the subsequent analysis.

During the course of any integration, however, strict watch must be

kept on the denominators of Equation (1). If one of the test particles

approaches one of the central masses too closely, the evaluation of

Equation (1) is dominated by the term whose denominator is vanishing.

At this point, the future behavior of the particle is suspect, and little

weight should be given to its future integration. The motions of such

particles could be preserved by regularization of the equations of motion

to remove the singularity near each mass (Szebehely 1967), but this

was not felt to be necessary for this work. The particles which ap-

proached within some limiting distance, rmin' of the mass centers during

the course of the integration were simply flagged for future identifica-

tion. The value of rmin was found by numerical experimentation. For any

particular central mass, there was a radius within which, for the scale

assumed, the calculations were of insufficient precision to maintain

circular orbits in an unperturbed situation for the time span of a

normal model without some kind of regularization. Therefore, this radius

was chosen as r min because all particle motions within it were suspect.

The exact results of any calculation of this type are dependent on

several parameters which can be broken generally into two categories.

The orbital group determines the behavior of the test particles during









the calculations. The viewing group governs how the results will be

compared to the observations.

Figure 2 illustrates these two groups by showing the orbit of M2 rela-

tive to M1. Mass M1 is at the origin of an x-y-z coordinate system.

The x-y plane is the plane of the test particles initially about M ;

therefore, the initial spin angular momentum of the model galaxy is along

the z-axis. The orbit of M2 about MI has eccentricity e, is inclined to

the plane of the galaxy by an angle i and has its ascending node on

the positive x-axis. The minimum separation of the two masses is q,

and this point is located in the plane of the orbit by the angle w the

argument of pericenter, which is measured from the ascending node in the

direction of motion of M2. At some time T from closest approach, M2 is

located by the vector R from M1. The direction of R depends on angles

i and w which orient the orbit with respect to the x-y plane, but the
g g
magnitude of R can be found from Equation (2) and from the equation for

a general conic:


R = q (1 + e) (1 + e cos v)-1 (Eq. 4)


The angle v, the true anomaly, is measured in the plane of the orbit from

the position of closest approach to M2 and is related to the eccentric

anomaly, B, in the case of a hyperbola by


cos v = e cosh B (e cosh B 1)-1 (Eq. 5)

and by

sin v = (e2 1)1/2 sinh B (e cosh B 1) (Eq. 6)


The viewing angles, ) and 0, determine how the system would appear to

the observer, i.e., how the system would be projected onto the sky. The










toobserver


Figure 2. The orbital and viewing angles relative to the plane of a
galaxy.









position angle of the line of sight in the plane of the galaxy is q, and

the angle e is the inclination of the line of sight to the z-axis.

Observations can be used to couple the orbital parameters to the

viewing parameters. A well-observed galactic system will have the

following parameters defined: M1 and M2; z, the relative radial velocity

of M2 with respect to M1; R the projected separation of M1 and M2 in

absolute units (if the distance to the system is known, R0 is the distance

to the system multiplied by the angular separation of the centers of

mass for each system); one of the viewing angles for each galaxy, el

and e2, the inclinations of the galaxies to the plane of the sky; and

finally, d the position angle of M2 measured in the plane of the sky

relative to the major axis of M1.

Figure 3 illustrates the orbit in the sky. Mass H1 again is at the

origin, but in this X-Y-Z coordinate system, the X-Y plane is the plane

of the sky. Again the ascending node is on the X axis, and R, v, q, and

e are as previously defined. However, the inclination is and argument

of pericenter ws are now defined with respect to the sky frame.

The problem is geometrically similar now to that of a spectro-

scopic binary (cf., Smart 1965). In Figure 3, it is clear that

z = R sin (v + w ) sin is = (R2 R2)1/2 (Eq. 7)


Differentiating Equation (7) with respect to time

z = R sin is sin (v + ws) + R sin is cos (v + w ) v (Eq. 8)


As already shown in Equation (4), R is related to v by the equation for

a general conic. The conservation of angular momentum in the two body

problem relates v to R:






-11-

3.


Figure 3. The orbital angles relative to the plane of the sky.









= [q (1 + e) C]/2 R-2 (Eq. 9)

Differentiating Equation (4) and substituting Equation (9),

R = C1/2 [q (1 + e)]-1/2 e sin v (Eq. 10)

Solving Equation (7) for sin is,

sin is = (R2 R2) 1/2 [R sin (v + w )]1 (Eq. 11)

and substituting Equations (4), (9), (10),and (11) into Equation (8)

C1/2 (R2 2 )1/2 [cos (v + w) + e cos w ]
z = o- (Eq. 12)
[q R2 (1 + e)]1/2 sin (v + ws)

Therefore, for an assumed set of {e, T, q}, Equation (3), which is

a smoothly varying function of B, can be solved by numerical root solving

methods for B. Once B is known, Equations (2), (5), and (6) can be

solved for R and v. Differentiating Equations (2) and (3), an expres-

sion for R2 + RB, the kinetic energy, can be found and evaluated. If

R is greater than or equal to Ro and the kinetic energy is greater than

or equal to z2, Equation (12) can be solved by numerical methods by sub-

stituting the values of R and v and treating Equation (12) as a function

of ws only. Over the range -n/2 + v< v + ws < i/2 + v, Equation (12) is

a smoothly varying function which, in the simplest case (v = 0), reduces

to the ctn function multiplied by constants. If the value of ws found

from this solution also satisfies Equation (11), the parameter set

{e, T, q, is, w s completely describes an orbit which will fit through

the observations.









Figure 4 illustrates the relationship between the orbit with re-

spect to the sky and the orbit with respect to the plane of the galaxy.

Once i and w are known, the angle, d, between the ascending node in

the sky and the projected position of M2 can be found from


tan d = cos is tan (v + w ) (Eq. 13)


Once d is known, the spherical triangle ABC in Figure 5 can be solved

for the values of i g and F necessary to use in the calculations of

the particle perturbations and the subsequent projection for viewing.

A similar process will yield ig2 and wg2, the orbital angles with re-

spect to M2.

For any set of ({M, M2' e, T, q}, the values of R and the angles v

and B are uniquely determined, as described above. However, for exactly

the same values of these parameters, variations of i and w can pro-
g g
duce vastly different results for the motions of the test particles.

The greatest perturbations occur when the interacting mass, M2, approaches

M1 in the plane of the galaxy and in the direction of the galaxy's ro-

tation. In this case, i is zero, and the orbital and galaxy spin

angular momentum vectors are aligned. Significant reductions in the

amount of disturbance results when these vectors are anti-parallel.

This effect can be illustrated by imagining a particle on the line joining

the two masses at the moment of closest approach. In the first case, the

particle's rotational motion carries it in the direction of motion of

the perturber, effectively increasing the time that the perturbing mass

has to accelerate it. In the latter case, the particle and the per-

turbing mass are separating in opposite directions and consequently

reducing the perturbation time. The perturbation is also reduced as





















































Figure 4. The combined sky and galaxy coordinate systems.












































orbit








Figure 5. The spherical triangle ABC, which relates the orbital angles
in the sky frame to the orbital and viewing angles in the
galaxy frame.









the plane of the orbit becomes more inclined to the plane of the galaxy

so that the perturbing accelerations do not act in the same plane as

that in which the particles are initially moving. Further reductions

in the disturbance can be produced in the case of inclined orbits by

letting w approach 900. As w increases, the point of closest approach,

which is also the point of maximum perturbing acceleration, migrates away

from the plane of the galaxy, thereby again decreasing the amount of

perturbing acceleration in the plane of motion of the particles.

At this point, the problem becomes much more complex than a spectro-

scopic binary. For a given set of observed parameters, one can find an

infinite number of the sets {e, T, q, is, w s which will satisfy the

observations geometrically, and there is no reasonable hope of obser-

vationally solving this dilemma as is done in the stellar case. However,

since each of these sets of orbital parameters produces a different per-

turbation of the galaxies, the models can hopefully be differentiated by

detailed comparison with the observations, as discussed below. Also,

some of the sets can be rejected for a number of other reasons. For

example, generally no effects can be noted prior to the first passage

of M2 through closest approach. Therefore, T is virtually restricted to

values greater than the first time of closest approach. A lower limit

to the eccentricity can be roughly calculated for each q value from

energy considerations. The total energy of the M1-M2 system is constant;

therefore, by summing the kinetic and potential energies, it can be

shown that

(2 + R22)/2 C/R = -C (1 e) (2q) (Eq. 14)

The minimum value of the kinetic energy is z at an actual separation of









R which for a given q, lets Equation (14) be expressed as


2q (z C/R ) C- + 1 = em (Eq. 15)


If no perturbations of one galaxy are observed within a distance R of

the center, numerical experimentation will yield a minimum q for which

no perturbations are induced by the interacting mass in a ring of test

particles of radius R. Finally, if e is too large, the interaction will

take place so rapidly that the perturbations induced will be minimal.

The model galaxies, as previously mentioned, were made up of cir-

cular rings of test particles, and initially these rings were confined

to an annular region of inner radius R1 and outer radius R2. Since the

model applies most realistically to regions far from the nucleus of the

galaxy where Keplerian motions might be expected to dominate the gas

motions, R1 must be large enough to place the first ring clearly in this

region. Arbitrarily, the Holmberg (1958) radius of maximum photographic

extent of the respective galaxies was chosen to approximate R It is

reasonable to suppose that the bright stellar material and hence most

of the mass currently attributed to the galaxies lies within this radius.

In the case of M81, however, R1 was taken as 10 kpc because at this

radius irregularities begin to appear in its HI distribution (Gottesman

and Weliachew 1975; Rotts and Shane 1975). The outer radius was gener-

ally taken to be twice R1, though in some models the outer radius varied

in size in order to duplicate some of the observed features with the

models.

Each ring was loaded initially with equally spaced particles. The

total number of particles in each ring was proportional to the ring

radius, and the same constant of proportionality was used for each ring.









By keeping the angular spacing of the particles initially constant in

this manner, it was felt that the effects of the interaction would be

more visible, particularly in the outer regions where the perturbations

are most severe.

This model was applied primarily to the HI structures of the galaxies

involved in this study. In the regions of the galaxies which the models

consider, the gas atoms are good physical approximations of the restricted

three body test particles. Combes (1978; see Chapter I for a discussion

of this work) demonstrated that the gravitational force of the central

masses clearly dominates the motions of the gas far from the nuclear

regions. Therefore, where surveys of the kinematics of the extended

hydrogen structure of an interacting galaxy pair exist, direct compari-

son of the model to the observations is possible. For structural

similarity, one would hope to find the final projected particle distri-

bution conforming well to the observed distribution of the gas. For

kinematical similarity, one can compare the radial velocity distribution

of the particles within a given area to the corresponding radio spectra

of the area.

If the model represents the gas motions correctly, one would expect

to see good correspondence between the gas distribution at a given radial

velocity and the particle distribution at that same velocity. In this

work this was accomplished by numerically sweeping a "beam" the size of

that used in the observations across the projected particle distribution.

The beam could be gated to accept radial velocities only within certain

limits, and the positions of beams which contained the appropriate par-

ticles were plotted for positional comparison to similar single channel

maps of the actual system.









Naturally, discrepancies between the predictions and the actual

observations will occur. Little information generally exists, par-

ticularly in highly disturbed systems, about the gas distribution prior

to the interaction. Spiral structure in disc systems, for example,

normally has an associated HI concentration, but such a distribution

can not be imposed on the particle distribution of the model without fear

of introducing some sort of spurious effect on the model since the orien-

tation of the spiral structure at the time of the encounter cannot be

reasonably assumed. The encounter could also produce conditions in the

gas where the effects of turbulent gas pressure and self-gravitation of

the gas are no longer negligible as the model assumes. If there are

significant gas motions in the systems not due to gravitational forces

assumed by this model, these, too, would cause the model kinematics to

differ from the observed kinematics. Besides such intrinsic effects,

instrumental variations in sensitivity and resolution can alter the

observed extent of the gas and the amount of detail seen at any par-

ticular frequency.

With these complexities in mind, the best course of action appears

to be to assume an initially smooth distribution like this model and to

look for general trends instead of specific reproduction of the small

scale observational details. Therefore, the final model one chooses is

not an absolutely unique model, but one that represents the system well

geometrically, structurally, and kinematically in comparison with the

observations according to some criteria. The criteria used for this work

were simply to make the shape of the final particle distribution conform

well with the extent of the observed HI structure and to make the radial






-20-


velocity distributions of the particles conform well with the extent of

the observed gas at particular velocities.

The use of this type of model for the large scale gas dynamics in

galactic interactions is not unusual. The first use of it can probably

be traced to Pfleiderer and Siedentopf (1961) and Pfleiderer (1963) in

which it was used to show that transient spiral structure can arise from

tidal interactions in strictly planar encounters. Wright (1972) used

a similar model to study the types of structures possible from these

interactions of the orbital parameters for strictly planar elliptical

orbits. Eneev et al. (1973) and Yabushita (1971) did similar work for

hyperbolic orbits, and Yabushita (1977) used this model to study the

possibilities of the formation of galactic binary systems after a close

passage of two galaxies. These post-Pfleiderer authors were all inter-

ested in the production of galactic bridges and tails instead of spiral

structure. Toomre and Toomre (1972) applied the model to several extra-

galactic systems and successfully modelled the structures of M51, Arp 295,

NGC 4676, and NGC 4038/39. The important requirements for galactic

bridge and tail formation found by these studies were summarized by

Toomre (1974): the encounters must be close, the masses must be unequal,

and the relative velocities of the galaxies during the close approach

must be small.

Attempts have been made to treat galactic tidal interactions in a

more complex manner. Clutton-Brock (1972) used a multi-term potential

function to calculate the motions of the test particles. However,

Clutton-Brock discovered that this innovation for mimicking self-gravi-

tating particles led to the production of diffuse bridges and tails,

instead of the generally observed thin filaments. Clutton-Brock reasoned









that the self-gravitating model could perhaps reflect the motions of

the stars in a perturbed galaxy, but that the gas motions were best

represented by a model with low velocity dispersion of the particles,

i.e., rings of particles in a fixed potential field. Tashpulatov (1970a,

b) attempted a more hydrodynamic approach. His model galaxies consisted

of homogenous prolate ellipsoids, but he worked under the rather arti-

ficial constraint that mass could exit the system only at the vertices

of the ellipsoids. However, he did demonstrate that bridges and tails

could be produced for a wide range of masses and distances of close

approach. Neither of these more complex approaches have demonstrated

applications to actual systems, and the success of the Toomre and Toomre

models clearly argues in the favor of the simpler model used by this

project.

Some users of this type of model have tried to make the initial

particle distribution correspond more nearly with the current concepts

of galactic structure. For example, van der Hulst (1977) modified the

gravitational potential of each central mass to the form -GM (r2 + a2 1/2

where G is the gravitation constant, M is the mass of the galaxy, r is

the distance of a point from the center of the galaxy, and a is a con-

stant called the softening parameter. This modification achieves two

things. For r less than a, the circular orbital velocity increases more

or less with r, much like the rotation curves of many spiral galaxies do

in the inner regions. Also it simplifies the integration by preventing

the denominators of Equation (1) from vanishing as r approaches zero.

Combes (1978) used a similar approach but used three such potentials

to represent the gravitational field in different radial zones from the

central masses. In this manner, Combes tried to account for the









gravitational effects of a massive, spherically symmetric galactic

stellar halo as well as the optical disc and forced the initial par-

ticle distribution to reflect the observed rotation curve of the galaxy.

Combes also allowed the population of the rings to decrease exponentially

with increasing ring radius to reflect the assumed distribution of mass

in the galaxies.

These attempts to reflect "reality" may be questioned on several

grounds. In interacting systems there is some question that the observed

rotation curve actually reflects the rotation curve of the unperturbed

galaxy. Particularly in the region in which the model is applicable,

extensive perturbation of the gas can be expected; therefore, imposing

the observed rotation curve on the particle distribution may be as

artificial as imposing a spiral structure on it. The introduction of

the parameter a and the mass of a galactic halo only add more variables

to an already complex problem. Particles which enter the interior of

the galaxy at which the modified potentials are effective have already

left the region in which the model may reasonably be applied. In order

to get a reasonable number of particles in the exterior rings for the

perturbations to be easily visible, an exponential variation of the

number of particles, while perhaps reflecting the variation of mass in

the galaxies, dramatically increases the total number of particles, and

thus the total computation time. Since the model can at most reflect

general trends, these modifications are felt to introduce unnecessary

complexity and length to the calculations.













CHAPTER III

THE GALAXIES



The three galaxies involved in this study, NGC 3031 (M81), NGC 3034

(M82), and NGC 3077 are members of the M81 group in Ursa Major, one of

the closest groups of galaxies to our own. De Vaucouleurs (1975) de-

scribed this group as consisting of a few large late type spirals and

irregulars and a large number of smaller dwarf systems scattered over an

area 40" x 20' in the sky. Tammann and Sandage (1968) placed the dis-

tance to this group at 3.25 Mpc, which will be adopted as the distance

to the principal member of this group, M81, for this study.



The Galaxy M81 (NGC 3031)


M81 (1950.0 = 9h51m30s; 1950.0 = +69'18') is a large, beautiful,

early type spiral galaxy (see Figure 6). Holmberg (1958) classed it as

a Sb type system and gave its optical dimensions as 35 x 14.4 arcmin.

It has an integrated spectral type of G3 (Humason et al. 1956) and can

easily be resolved into stars and HII regions (Sandage 1961). Morgan and

Mayall (1957) and Morgan (1958) found M81's blue-violet spectral region

to be dominated by light characteristic of K-type giants and therefore

classed it as a k-type spiral. Extensive photometry by Brandt et al.

(1972) revealed that the spiral arms could be optically traced to within

3 arcmin of the nucleus.






























Figure 6. The galaxy M81 (NGC 3031), as photographed with the
University of Florida .75 m telescope at Rosemary Hill
Observatory. Photograph was provided by Dr. A.G. Smith.






N




I 1 .E

10 arcmin





;*r7'~~
~1. 1

i;









The galaxy has been extensively studied for its geometrical param-

eters and systemic velocity, both optically and in the radio spectrum.

Rotts (1975) has tabulated the results of the studies to date, and

general agreement exists on all parameters. For this study, an inclina-

tion of 580 and a position angle of the major axis of 151' (Gottesman and

Weliachew 1975) will be assumed to describe the system geometrically in

the sky. A systemic velocity of -40 km/sec (Rotts 1975) will also be

adopted. According to de Vaucouleurs (1959) the southwest side of the

galaxy is the nearest to the observer.

Roberts' (1972) HI observations with a 10 arcmin beam revealed that

M81 was immersed in a vast cloud of hydrogen distorted in the directions

of its two nearby companions, M82 and NGC 3077. Higher resolution

studies by Gottesman and Weliachew (1975) and Rotts and Shane (1975) have

revealed a wealth of HI data. Both studies have shown an excellent cor-

respondence between the peaks of the HI distribution and the optical

spiral arms. Both found a neutral hydrogen density depression at the

nucleus of the galaxy. They also found a well-behaved rotation curve

for the galaxy from the nucleus out to about 10 kpc from which they de-

duced a systemic mass of approximately 1011 solar masses. Beyond 10 kpc

the regularity of the system breaks down. There is evidence of a local

depression of neutral hydrogen mass surface density, the appearance of

two new outer spiral arm-like features different from the inner spiral

arms, and a marked discrepancy between the northern and southern rotation

curves (Rotts 1975). Gottesman and Weliachew (1975) and Rotts (1975)

felt these outer region differences were due to possible interactions

tidally between M81, M82, and NGC 3077.









M81 has been observed in many other spectral regions as well.

Kleinman and Low (1970b) listed it as one of their sources of extra-

galactic IR emission. The disk of the galaxy but not the spiral arms

is detectable at 4.8 GHz, as well as a nuclear source (von Kap-herr

et al. 1975). At 1.415 GHz, van der Kruit (1975) found the nuclear

source as well as the spiral arms, remarking that the northern arms

appeared twice as bright as the southern ones. The nuclear source is

variable on a time scale of a month (Kellerman et al. 1976; Crane et al.

1976; de Bruyn et al. 1976), and there is evidence for nuclear kinematics

quite different from those of the disk (Goad 1976). Geldzahler et al.

(1977) believed that the nuclear sourcewasa compact object similar to

those found in other extragalactic systems.

Besides its two major companions, M81 has at least two accompanying

dwarf systems. One is an apparently spheroidal system 29 arcmin south

of the M81 nucleus, and the other (DDO 66) is an irregular 10 arcmin to

the east. Both have been resolved and have a maximum extent of about 4

arcmin in diameter (Bertola and Maffei 1974).



The Galaxy M82 (NGC 3034)


M82 (a~950.0 = 9h51m54s; 1950.0 = +69056') is the archetype of its

own group of irregular galaxies (see Figure 7). The fusil shaped, dust

curdled image of this galaxy has been classed by Holmberg (1958) as an

IrlI and by de Vaucouleurs and de Vaucouleurs (1964) as an 10. The

IrlI-IO class of galaxies is characterized by red color, dust, and a

smooth luminosity distribution (Chromey 1974a). M82 lies approximately

37 arcmin north of the M81 nucleus, and its turbulent image is not

resolvable into stars (Sandage 1961).
















Figure 7. The galaxy M82 (NGC 3034), photographed by Dr. A.G.
Smith with the University of Florida .75 in telescope
at Rosemary Hill Observatory.


E-


5 arcmin


Figure 8. The galaxy NGC 3077, photographed by J.T. Pollock with
the University of Florida .75 in telescope at Rosemary
Hill Observatory.






5 arcmin





N




E












The Holmberg (1958) dimensions of the galaxy are 13.4 x 8.5 arcmin.

From this Lynds and Sandage (1963) suggested that M82 was an intrinsic

disk system inclined at 8023' with the northwest side nearest the ob-

server. Heckathorn (1972) placed the optical major axis at a position

angle of 64.50, in close agreement with the direction of alignment of

compact radio sources in the nucleus (Kronberg and Wilkinson 1975).

For a nearly edge-on disc system, however, the optical structure of

the galaxy is very peculiar. Its smooth non-uniformly illuminated sur-

face is laced with dark absorption lanes. Its A5 type integrated

spectral class (Humason et al. 1956) contrasts strongly with its B-V

color of +.91 (de Vaucouleurs 1961). Morgan and Mayall (1959) explained

this discrepancy by assuming that the galaxy was filled with vast quanti-

ties of dust, and indeed estimates of the optical extinction of the

hydrogen optical emission lines in the direction of the assumed nucleus

exceed 3 magnitudes (Peimbert and Spinrad 1970; van den Bergh 1971).

A system of faint filaments visible in Ha and continuum light also

makes the optical image peculiar. The filaments trail out somewhat ran-

domly along the minor axis, reaching a maximum extent of 4 to 5 arcmin

from the principal plane. Elvius and Hall (1962) reported that the fila-

ments were highly polarized with the electric vector generally perpen-

dicular to the minor axis and that there was a similarly polarized

galactic halo. These results were confirmed by several later studies

(Sandage and Visvanathan 1969; Elvius 1972; Schmidt et al. 1976). Though

once thought to be rather massive phenomena (Lynds and Sandage 1963;

Burbidge et al. 1964), the nature of the filaments is a matter of current

debate. Schmidt et al. (1976) showed that the contrast of the filaments

is less than 25% above the mean background emission and argued that the









filaments may be nothing more than random collections of efficient light

scattering particles. Another peculiar feature of the filaments is the

extremely narrow (less than 6 Angstroms) half-width of the polarized Ha

emission from them (Visvanathan and Sandage 1972).

The stellar distribution in the galaxy is clearly abnormal for a disk

system. In a normal system, HII regions and associations of bright stars

are generally confined to the disk and are found rather far from the

nucleus. Infrared observations of M82, however, reveal immense HII

regions and dozens of knotty structures which are probably young associa-

tions of very hot stars, but none are found in the outer regions of the

galaxy (van den Bergh 1971). Burbidge et al. (1964) deduced that the

sudden switch in integrated spectral type and the switch from an emission

to an absorption spectrum with no evident corresponding morphological

change as one goes outward from the nuclear regions also indicated a

preponderance of early type stars in the nucleus. Peimbert and Spinrad

(1970) found significant differences between the size of the Balmer jump

and the degree of interstellar ionization between the nuclear and outer

regions. Both of these factors they attributed to the presence of a

large number of stars earlier than type B1, perhaps thousands more 0 type

stars than exist in our own galaxy. Also, the nuclear regions are an

intense source of infrared emission. Kleinman and Low (1970a,b) and

Harper and Low (1971) believed that the galaxy's IR luminosity of over

2 x 1044 erg sec- was due to dust being heated by thousands of 0 type

stars. The presence of these early type, short lived stars in the nucleus

probably indicates that the nuclear regions underwent a period of ex-

tremely rapid and active star formation within the last 108 years (O'Connell

and Mangano 1978).









M82 has been heavily observed spectroscopically and in radio emission.

Emission and absorption line studies (Mayall 1960; Lynds and Sandage

1963; Burbidge et al. 1964; Heckathorn 1972) reveal a general progression

of radial velocities along the major axis attributable to galactic rota-

tion, though peculiar gas motions are evident. Lynds (1961) first iden-

tified M82 as the radio source 3C 231. The GHz observations of the

nuclear regions (Wilkinson 1971; Hargrave 1974; Kronberg and Wilkinson

1975; Geldzahler et al. 1977; and references in all) reveal a number of

compact nuclear sources and a distinct non-thermal nuclear source which

dominates the emission. The nucleus has also been detected in HI absorp-

tion (Guelin and Weliachew 1970; Weliachew 1974) and is the source of an

intense OH maser stronger than any known in our galaxy (Rieu et al. 1977).

Rickard et al. (1977a,b) have detected molecular HCN and CO emission from

the galaxy. They stated that the CO emission was confined to the optical

image and clearly displayed a velocity gradient in the sense of the

assumed galactic rotation. They also found that the [HCN]/[CO] ratio

was consistent with Galactic values, but the intensity and spectrum of

the CO emission implied the presence of large molecular clouds with high

interstellar density. For example, Gottesman and Weliachew (1977) quoted

a molecular hydrogen content of 103 atoms/cm-3 to collisionally excite

the CO emission. M82's HI emission has been observed several times

(Volders and Hogbom 1961; Roberts 1972; Davies 1974; Gottesman and

Weliachew 1977; Cotrell 1977). The HI emission structure is clearly

distorted from the optical image, and even the rotational component of

the kinematics is not particularly prominent (Gottesman and Weliachew

1977). However, it is possible to associate approximately 109 solar

masses of HI with the optical image (Gottesman and Weliachew 1977;









Cotrell 1977). The details of the HI distribution will be discussed in

more detail in a later section.

The systemic velocity of the galaxy is difficult to determine.

Results of the optical research to date have been tabulated by Weliachew

(1974). The optical research suffers from the fact that there is no

clearly defined optical nucleus to use as a reference, and there is no

reason to assume in such an unusual system that the center of light and

the center of mass are coincident (Burbidge et al. 1964). Radio observa-

tions have suffered from the extreme disorder of the system, especially

the HI distribution. For example, Volders and Hogbom's (1961) 36 arcmin

beam produced a systemic velocity of +184 km/sec which differs extremely

from the widely accepted value of +240 km/sec (Heckathorn 1972; Weliachew

1974) derived from optical emission and HI absorption studies. Though

Volders and Hogbom's difference can be understood in terms of confusion

between the galaxy and the M81-M82 hydrogen bridge revealed in detail by

later studies (Gottesman and Weliachew 1977; Cotrell 1977), even the

accepted value for the systemic velocity is suspect. Rickard et al.

(1977a) found the CO spectrum was symmetrical about a velocity of +206

km/sec. They also found that the CO and HI absorption spectra were

broadened the same width, even though the galaxy was optically thin to

the CO emission and a much wider velocity range of galactic rotation

would be sampled in the CO spectrum. Hence they reasoned that the fore-

ground HI must be undergoing a variety of motions to cause the necessary

broadening. Even Burbidge et al. (1964) distrusted the use of their

optical emission spectrum position-velocity diagram as a galactic rotation

curve and referred their data instead to the Mayall (1960) H and K ab-

sorption line rotation curve, hoping the absorption spectrum was arising








in more distant regions free of peculiar motions. O'Connell and Mangano

(1978) also pointed out that Heckathorn's (1972) systemic velocity was

close to the heliocentric velocity of one of the central bright HII

regions not at the nucleus.

Since the rotation curve of the galaxy is so ill determined, the

systemic mass is also. However, Burbidge et al. (1964) made some crude

estimates based on the velocity extremae of their emission line studies

and derived a systemic mass of approximately 1010 solar masses. Van der

Hulst (1977) attempted to estimate the mass from the mass-luminosity

relationship, but the clearly anomalous stellar distribution and heavy

obscuration make this procedure questionable. The Burbidge mass would

give a HI mass to total mass ratio of about 14% (Gottesman and Weliachew

1977), which would be consistent with the interpretation of the galaxy as

a late Sc or irregular (Solinger et al. 1977; Gottesman and Weliachew

1977; O'Connell and Mangano 1978). A mass of 1010 solar masses will be

assumed to be the mass of M82 for this study.

The explanations of the anomalies of M82 can be grouped into three

types: (1) explosive, (2) drifting through dust, and (3) interactive. The

objective of the first two types is essentially to explain the polariza-

tion of the halo and the filaments. The explosive models (Lynds and

Sandage 1963; Burbidge et al. 1964; Solinger 1969) start with some sort

of nuclear explosion which ejects matter and vast quantities of rela-

tivistic electrons perpendicular to the plane of the galaxy. The polar-

ized emission then arises from synchrotron radiation by the high energy

electrons. The initial success of these models led Krienke and Hodge

(1974) to propose that there was an explosive subclass to the Irll

galaxies. The explosive theories, however, had difficulty explaining









the extremely narrow Ha lines (Visvanathan and Sandage 1972), which led

Sanders and Balamore (1970) to propose that the halo polarization rose

from dust scattered light from a Seyfert-like nucleus. It now appears

that a good deal of the light originates in the disk of the galaxy as

well as the nucleus (Solinger and Markert 1975; Schmidt et al. 1978).

The dust scattering models (Elvius 1972; Solinger et al. 1977) explained

the polarization also by having nuclear and disk light being scattered by

dust. However, they required that the dust in the halo be extra-M82 in

origin. O'Connell and Mangano (1978) pointed out that dust usually

arises in regions of active star formation and that it was difficult to

imagine how the necessary amountof dust could be dispersed into the inter-

galactic medium in a group of galaxies as sparse as the M81 group. They

also stated that the dominant scattering component was concentrated to

M82 itself and not more uniformly distributed as an exterior cloud might

be. The tidal explanations placed all the blame on gravity. The

M81-M82-NGC 3077 system has long been known to be immersed in a vast HI

cloud (Roberts 1972; Davies 1974). Gottesman and Weliachew (1977) and

Cotrell (1977) clearly demonstrated the existence of a HI bridge between

M81 and M82 as well as significant irregularities in the HI structures

of both galaxies. These authors proposed that the bridge was a direct

product of a tidal encounter between M81 and M82 and that the other

phenomena were by-products produced by the disruption of the two systems.



The Galaxy NGC 3077


NGC 3077 (see Figure 8) is perhaps the least known of the three

galaxies. It lies about 47 arcmin (a1950.0 = 9h59m24s; 61950.0 = +6858')









southeast of the M81 nucleus. Holmberg (1958) placed 3077 among his Irll

galaxies also, and he gave its dimensions as 8.8 x 8 arcmin, though

Barbieri et al. (1974) found a maximum photographic extent of 10 arcmin.

Its amorphous visual image, however, has caused some difficulty in its

classification. Van den Bergh (1976) classed the galaxy as an E2p, siding

against Holmberg's Irll and de Vaucouleurs and de Vaucouleurs' (1964) 10

classification. The detection of a great deal of neutral hydrogen associ-

ated with the galaxy has supported the irregular classifications (Lewis

and Davies, 1973; Cotrell 1976; van der Hulst 1977).

The geometrical parameters of the galaxy are also difficult to deter-

mine because of the lack of a well defined structure. From his HI obser-

vations with a single dish, Davies (1974) placed the position angle of

the major axis at 60. The more detailed optical work of Barbieri et al.

(1974) placed the position angle at 45. If the galaxy is an intrinsic

disk system, its inclination may be about 45 (Barbieri et al. 1974;

Cotrell 1976).

The optical image bears some resemblance to its classmate M82. The

central regions are filled with bright condensations visible in Ha light,

but there is no well defined nucleus (Demoulin 1969), though one of these

sources, asymmetrically placed with respect to the center of light,

dominates the emission (Barbieri et al. 1974). Around the central bright

region is a generalized halo filled with apparently randomly oriented

filaments, arches, and radial lanes as well as several semistellar con-

densations which may be star clusters (Demoulin 1969; Barbieri et al.

1974). In blue light Barbieri et al. (1974) found a wide absorption lane

laced with filaments on the southern border of the strong central source

as well as several more bright condensations which did not correspond to





-37-


any Hu feature. One of the blue knots, however, corresponds in position

with a nuclear 1.415 GHz source detected by van der Kruit (1971).

Spectroscopically the galaxy has long been known as unusual. Seyfert

(1943) and Humason et al. (1956) noted it for its broad emission lines

and early type spectrum, but Burbidge (1968) demonstrated the galaxy was

not of the Seyfert type. De Vaucouleurs (1961) noted that 3077's B-V

color of +0.70 made it the bluest of the IO galaxies. Demoulin (1969) and

Barbieri et al. (1974) could not find any motions attributable to galactic

rotation in their spectral studies. Working from available spectral

data, Chromey (1974b) was able to construct a model stellar distribution

for the galaxy. He found the system could be best represented by a

population composed primarily of solar neighborhood stars and blue

globular cluster stars with the young stars concentrated toward the

central regions.

Roberts (1972), Lewis and Davies (1973), and Davies (1974) clearly

demonstrated the presence of HI associated with the galaxy. An inter-

ferometric study by Cotrell (1976) revealed a HI distribution skewed with

respect to the optical image and the existence of a narrow HI spike ex-

tending over 10 arcmin northward from the main body of the galaxy. More

sensitive interferometry by van der Hulst (1977) showed the same features

and an HI bridge extending westward from the southern part of the galaxy

and seeming to merge with the outer spiral arms of M81. Cotrell (1976)

was able to associate 4.1 x 108 solar masses of neutral hydrogen with the

main body and the northern spike whereas van der Hulst (1977) found

7.3 x 108 solar masses of hydrogen within the same area. Van der Hulst's

southern bridge contained 5 x 108 solar masses of hydrogen. Both Cotrell

and van der Hulst proposed a tidal origin for the HI features.


~









Because of the structural and kinematical confusion in the system,

both the systemic velocity and the total mass are not reliably known.

The optical systemic velocity of the assumed nucleus found by Barbieri

et al. (1974) is -10 km/sec which is also the HI velocity at that posi-

tion (van der Hulst 1977). However, the centroid of the HI distribution

associated with the main body of the galaxy is +15 km/sec from Cotrell

(1976) and +10 km/sec from van der Hulst (1977), values consistent with

earlier work by Lewis and Davies (1973). Since there is no well defined

rotation curve, the mass of the galaxy is equally difficult to estimate.

Cotrell (1976) attributed the slight velocity gradient along his assumed

major axis to rotation and then calculated a mass of 6 x 109 solar masses by

assuming the galaxy was an intrinsic disc system. Van der Hulst (1977)

used the mass-luminosity relationship to derive a mass of 1010 solar

masses. Though both of these parameters are ill-determined, a systemic

velocity of +15 km/sec and a mass of 1010 solar masses will be adopted

for this work.














CHAPTER IV

RESULTS OF THE MODELLING



Following the methods described in Chapter II and the observational

constraints assumed from Chapter III, the system of galaxies was modelled

in two steps. The first step was the modelling of the M81-M82 system;

the second was the modelling of M81-NGC 3077's interaction. No three

system models were attempted though the results of the two system models

clearly indicate the need for such treatment in the case of M81's outer

regions. However, the two system models appear to serve as good fiducial

indicators of what the three system effects would be. In the case of

M82, the models represented refinements of previously reported work

(Killian and Gottesman 1977). The systems were modelled first for an

attempted reproduction of the large scale neutral hydrogen features in

each. Structural similarity was judged by direct comparison of the

maximum shape and extent of the particle distribution to the best avail-

able observations of the HI structures. This procedure was applied first

to the low mass galaxies, M82 and NGC 3077, whose HI structures have

distinctive patterns. Once a satisfactory structure for these galaxies

was obtained, the corresponding M81 model was created to see if the

observed bridge structures could be reproduced.

If a combined minor galaxy and M81 model passed the structural com-

parisons, the particle distribution was then examined in detail for

position-radial velocity correspondence to single channel maps of the


~~









HI distribution. If the model adequately represents the gas motions

induced by the tidal encounter, then good correspondence between the

single channel maps and the distribution of the test particles at the

corresponding radial velocity should exist.

Two types of comparisons for velocity correspondence were made.

First, the distribution of the particles was examined for positional

correspondence with the HI features as revealed by the single channel

observations. The particle distribution then was "scanned" numerically

with a square, untapered "beam" of a size similar to that used by the

observers at half beam intervals in right ascension and declination.

The beam centers of the beams which contained particles at the desired

velocity were plotted as a function of beam position. Beams which con-

tained more than three particles, and thus represented particle "con-

centrations," were plotted with larger symbols so that the "peaks" of the

distribution were accentuated. Intercomparisons between these maps and

the observations should also yield good positional correspondence, pro-

vided one assumes that the real gas is nearly as optically thin as the

particle "gas."

Models which passed both comparisons adequately were then subjected

to a variation of the orbital and systemic parameters. In particular,

the effects of a different assumed mass and/or a different assumed

systemic velocity were studied. Also considered were changes in the

perigalacticon, q, and the orbital eccentricity, e.

The modelling results presented here are the end product of over

350 simulations of the systems. These models, though by no means unique,

are representative of the best results obtained for structural and

velocity intercomparison. They also have some interesting implications








for the structure of the systems before and after the interaction. For

easy reference, the systemic and orbital parameters for all the models

discussed in this chapter have been tabulated in Table I.



The M81-M82 Models


M82 presented some immediate difficulty in modelling because of the

indeterminacy of its systemic velocity. As a result, two modelling lines

were followed. Model 1 assumed the systemic velocity of Weliachew (1974)

and Heckathorn (1972) of +240 km/sec. Model 2 assumed +210 km/sec as the

systemic velocity, a value closer to the CO central velocity determined

by Rickard et al. (1977a).

The next difficulty was the orbit itself. Using the above systemic

velocities and the assumed masses of M81 and M82, a quick calculation of

the kinetic and potential energies of M82 relative to M81 in the plane of

the sky at the assumed separation clearly indicates that the total energy

is positive and the orbit is therefore a hyperbola. Hyperbolic orbits

tend not to produce extensive bridges because of the great velocity at

which the perturbing mass moves relative to the other mass during

closest approach.

The hyperbolic orbit placed some immediate constraints on the orbit.

Since the aim was to build a bridge from M81 to M82, the orbit must be

one which maximized the limited amount of perturbations caused by M82;

the low mass ratio of M82 to M81 (1/10) and high relative velocity of

M82 in a hyperbolic orbit about M81 were not conducive to building

bridges. The best cases, therefore, were close, direct (in the direc-

tion of M81's rotation) approaches with low inclination with respect to

M81 and an argument of pericenter nearly in M81's plane.

















TABLE I

MODEL PARAMETERS



M81 M82 M82 NGC 3077
(all) (fModel 1) (Model 2)

Total Mass (x 1011 solar masses) 1.0* 0.1* 0.1* O.1*

Apparent Separation from M81
(kpc @ 3.25 tpc) 35* 35* 44.2*

Position Angle of Major Axis () 151* 65* 65' 161

Inclination to Line of Sight () 58* 10* 10* 40

Systemic Velocity
heliocentricc, kin/sec) -40* +240* +210* i15*

Model Annulus Data
Inner Size (kpc) 10 4.0 4.0 4.0
Outer Size (kpc) 20 9.5 9.5 7.0
Number of Rings 9 12 12 7
Ring Spacing (kpc) 1.25 0.5 0.5 0.5
Total Number or Particles 540 324 324 154

Perigalacticon to M81 (kpc) 15 15 22.5

Eccentricity of Orbit 3.5 2.9 0.95

Display Time of Mdel (x 108 yrs)
(after Perigdldcticon) 2 2 6

Inclination of Orbit in the Sky
(Is. 1) 67.6 67.1 58.1
Inclination of Orbit to M81
(ig. ) -13.2 -10.1 17.9
Inclination of Orbit to Minor System
(ig2', ) 80.9 85.8 -72.6
Argument of Pericenter in Sky
(ws. ) -23.1 -28.7 -7.0
Argument of Pericenter with
Respect to M81 ( g, ) 18.3 -4.1 89.0

Argument of Pericenter with Respect
to Minor System (wg2, 9 ) 52.0 48.6 -178.1

Viewing Angle ( o) -43.8 -63.1 -5.3

Note: Orbital and Viewing Angles are as defined in Chapter 11. Values marked
with anasterisk () are adopted or derived from observation; see
Chapter [II for references.









A limit on the distance of closest approach was provided by obser-

vation and numerical experimentation. Rotts (1975) found thatat8 to 10

kpc from the M81 nucleus the symmetry of the inner HI spiral structure

began to break down. If this deviation is caused, as Rotts supposed,

by the tidal encounter, the model would hopefully produce a disturbance

at about 10 kpc. However, since the galaxy is beautifully symmetric

within this region, the model disturbance should be minimal closer to

the M81 mass center. By numerical experimentation, it was found that a

ring of particles at a distance of 10 kpc from the M81 mass center began

to be perturbed when q, the distance of closest approach, was approxi-

mately 15 kpc. This was taken as the approximate minimum value for q.

A particular structural feature in M82 was also important. Both

Gottesman and Weliachew (1977) and Cotrell (1977) found a "spike" of

neutral hydrogen rising northward almost perpendicular to the galaxy's

major axis at its eastern extremity. This spike is quite prominent in

the single channel maps of Gottesman and Weliachew (1977; hereafter

called GW), extending over 10 arcmin from the optical major axis.

The GW brightness temperature maps also indicate that the northern

tip of the spike might be a clump or concentration of gas since the

brightness temperature contours of this region are detached from the

main body of the galaxy.

The models of M82 characteristically had an s-shaped distortion

after close approach to M81, with the body of the s along the galaxy's

major axis, the west end pointing toward M81, and the east end pointing

northward like the spike. Generally, this northward feature would begin

to become evident about 108 years after the close approach, growing

larger but staying relatively intact until about 3 x 108 years after









close approach when the rotational and peculiar velocities of the par-

ticles had dispersed it. This model feature was assumed to be the

counterpart of the GW hydrogen spike. Its position and size were used

as timing and structure marks in the analysis of the models.

Many parameters affected the development of this spike in the models.

If the distance of close approach were too great, the spike would not

develop sufficient height. Successive attempts at different q values

brought M82 closer and closer to M81 at their minimum separation in an

attempt to increase the size of the spike. Finally, the q value reached

the 15 kpc limit imposed by the HI structure of M81, but the spike still

did not extend to the observed height. At this point, the migration of

the minimum separation was halted. The time after perigalacticon was

then adjusted within the 1 to 3 x 108 year range imposed by the co-

herence of the spike. A time of 2 x 108 years was found to give the

greatest height of the spike with the greatest concentration of par-

ticles in the spike feature. With T and q fixed at these values, the

position angle of the spike could be adjusted somewhat by variation of

the eccentricity of orbit which produces a change in the orbital angles

of the encounter as explained in Chapter II. In this manner, the best

positional agreement between the model spike and the observed spike was

obtained. The extent of the spike was then obtained by simply increasing

the size of M82, which produced another interesting effect. The outer-

most rings of this enlarged galaxy rose directly into the spike and were

twisted into a clump at the spike's northern tip, a clump suggestive of

that in the GW observations. Using the information gleaned from this

structural study, the value of q was increased and similar attempts at

structural duplication were attempted. However, no significant









improvements were found, and in fact, these more distant approaches made

alignment of the model and observational spike very difficult, when it

could be done at all.

The best structural results of the M81-M82 models are displayed in

Figures 9 and 10, which illustrate the +240 and +210 km/sec systemic

velocity models, respectively. The models are quite similar, showing

the northern spike as well as a well developed intergalactic bridge.

The maps of Cotrell (1977) and GW indicate that the bridge is clumpy, and

the models suggest, particularly southwest of M82, that the clumps could

be due to an intermixing and/or superposition in the line of sight of

materials from both galaxies.

Though structurally similar, the two models differ greatly in the

kinematics. Figures 11 and 12 show the particle radial velocity dis-

tributions in a 40 arcmin square about M82. In these figures, the

particles have been plotted if their radial velocities were within a

21 km/sec "bandwidth" of a given central velocity. The central veloci-

ties and bandwidth are those of the GW single channel maps. To aid

further in the comparison of the model to the GW maps, the particle dis-

tribution was then scanned numerically with a square 4.4 arcmin beam at

half-beam intervals. The coordinates of each beam which detected par-

ticles within the given velocity range were then plotted. Those beams

which contained more than 2 particles were plotted with a larger symbol

so that the "peaks" of the distribution's particle density were visible.

The results of these scans of both distributions are displayed in

Figures 13 and 14. The reader should note that apparent gaps and dis-

continuities in Figures 11 through 14 between features in the same

velocity range could be due to the finite number of points in each

galaxy model as well as the calculated effects of the interaction.




























Figure 9. Particle distribution for Model 1 of the M81-M82 inter-
action at 2 x 108 years after perigalacticon. Circles
denote particles which were initially about M81; M82's
particles are marked with asterisks. The large crosses
indicate the Holmberg (1958) dimensions of the respective
galaxies as well as the assumed orientation of the galaxies.
The solid line indicates the orbital path of M82 about M81,
and the arrow indicates the perigalacticon with respect to
M81's center. The coordinate tic marks are at 10 arcmin
intervals from the center of M81.



N




E












+ 40


T o ,I I



<. 4 Lt




+
























cl q) !, Iv e ", cg l
S''C,
4 ++ ** *

4 4


C ,
L. l,, '.





+ KD
, ^ v "* ,









C, c l 1U. % L
U"- m C ,' ', --





+, C' -C',,+








c "' "' "' -


I___. ._I






























Figure 10. Particle distribution for Model 2 of the M81-M82
interaction at 2 x 108 years after perigalacticon.
Plotting conventions are the same as those in
Figure 9.


N




E











I- -- F m-I--


.' c ,
*. S Cc-


RIGHT ASCENSION





























Figure 11. Radial velocity distribution of particles in Model 1
near M82. Particles were plotted if their radial
velocities were within a 21 km/sec bandwidth centered
on the velocity listed in the lower left corner of
each plot. The cross indicates the Holmberg (1953) dimensions
of M82 and the assumed orientation of the galaxy.
Coordinate tic marks are at 10 arcmin intervals from
the center of M82.








































/ .~





2 IM C

r














La l~M/~ C

























.1'*








01 NM/S C


**





i *I *

8-T1, --T- - -lo


^/


r~~J 0? N


*jb* IJ[. P 1 -




rI


20 nMSC






/ ../


33p K/,SC , i


22? N M I


L-
*


I


-~^/ .


Sllu hy M .-C































Figure 12. Radial velocity distribution of the particles in
Model 2 near M82. Plotting conventions are the
same as in Figure 11.






















, sc.
hO~hn/~C.~


/ .


~i? Ml C Fjff]
[ F I -1 IL j

T"





1.








r
r


WA:ii


Pp ~1




L _


S/ "*









op


.r





1 1 I
























.B.


/0











C p


SF





2---r? kh





























Figure 13. Beam-smoothed radial velocity distribution of the
particles in Model 1. The particle distribution in
Figure 11 has been scanned with a 4.4 arcmin square,
untapered beam at half-beam intervals in right
ascension and declination. If the beam contained a
particle, the beam center was plotted. Beams enclosing
more than two particles were denoted by plotting the
beam center with a larger symbol. Other plotting con-
ventions are as in Figure 11.
























































--I -r r--1-- r

Y
O







.....
.
-

-




181h~/5~C
r- I I





.











"'' Re
_-~L~ 11I_~_1



T-'~T-T-~


..


...
...
....



hn/
OP""/sfiI qr(








..


[i7lhn/5EC _

















33?y /sc iC


-T ---r


'.: :






*0 *
_1rj. . I





^ ^__CLII-i:_




















r - "
1 T


'"'










.....



~_.shC '; 9R
I IT
u
O






.....
.....


i


~1 ~I


rn IE
__. %


....
....
..


I' ''


.....
....


31p" tsc h ,


-3S4 H/Si C .





























Figure 14. Beam-smoothed radial velocity distribution of
particles in Model 2. The particle distributions
of Figure 12 have been scanned with a 4.4 arcmin
beam as described in Figure 13.

























HOI HM S





















mi.
fl
O






































rmr r m T1
r--t T-- 7
Q









.em.

*--.






.




,,;
iy7^n/5^ ' ',' ' R



u

.o.
* .






:** r r


,?5 rn'S ^


.






- l






m .... -


* F T*












_.---,_-^

*** ,
****














..
Q.
*o *n * '
*
* -~
*

^^i:;:




?? nS,[ , i


33V nns L ,/


TO rM rjljT








_, = .. .,
-m

. . ; "










i- --- ----- r- -7-







22 INh/S C A__ Ff
ivro
***




i|i





*I
-,. ,,*
,* .





i- $ i


II_""_,"


-4- 1 --_4 -









Above 144 km/sec the model radial velocity distributions consist

primarily of particles associated with M82. One clear cut difference be-

tween themodels is that Model 1 shows a definite skewing of the velocity

distribution toward higher velocities, particularly in the 292 km/sec

map. Comparison with the GW maps clearly shows that the radial velocity

distribution of Model 2 follows the observational distribution more

closely than Model 1. One feature is common to both distributions at

velocities near 250 km/sec. Long chains of particles at similar veloci-

ties run northward from the major axis along the northern spike. Cotrell

(1977) remarked that the isovelocity contours in this region became

nearly perpendicular to the major axis with a velocity gradient nearly

parallel to the minor axis, a result clearly indicated by the models.

The worst agreement in either model is in the low velocity maps.

The large concentrations of material at velocities of 144 km/sec or less

are conspicuously absent in the bridge. The bulk of the material at

these low velocities in the models comes from the outer portions of M81.

If the gas concentrations in the bridge did originate with M81, the

original gas distribution in M81 must have been quite different than that

assumed by this model. This point will be discussed further in Chap-

ter V.

Perhaps the most intriguing event occurring in both models is the

large amount of infall of particles from both galaxies that occurs in

M82. During the course of the encounter in Model 1, 43 particles from

M81 and 92 particles from M82 entered the inner 2.5 kpc of M82. In

Model 2, 51 M81 particles and 92 M82 particles entered the same region.

At the same time, the infall into a similar region about M81 was 2

particles for Model 1 and 1 particle for Model 2. In other words, in









both models nearly 16% of the total number of particles in both galaxies

and 28% of the particles in M82 alone had trajectories that brought them

into the nuclear regions of M82. The possible implications and impor-

tance of this event will also be discussed in Chapter V.

Both models follow similar evolutions after the time illustrated.

The distribution around M82 continues to expand and become more diffuse.

By 4 x 108 years after perigalacticon, the distributions increase their

projected linear dimensions by nearly half. The coalescing of the M81

particles in the southwest part of that galaxy clearly evident in both

models eventually forms a spiral arm-like feature that persists for a

few galactic rotations.

While these final models were being perfected, studies were also

performed to see the effects of changing the mass of M82, its tilt, and

the position angle of its major axis. For any assumed {e, T, q} the

effect of changing the mass is to change the orbital angles. In the

case of the M82 direct orbits about M81 at about 2 x 108 years after

perigalacticon, decreasing the mass increases the inclination of the

orbit with respect to M81. This has an immediate adverse effect on the

production of the M81 bridge. Increasing the mass has the opposite

orbital effect, but the increased circular velocities of the particles

in M82 due to the larger mass are immediately visible in the radial

velocity field. In both cases, the positioning of the northern spike

of M82 becomes more difficult. Variations of the mass of M82 of 20% and

50% were attempted. Though models were found that were similar to

Models 1 and 2 for the 20% variation, the 50% mass variations produced

either too high of a velocity distribution, in the case of the increased

mass, or an insignificant M81 bridge, in the case of the low mass models.









The orientation of M82 in space deduced by observation seems to be

consistent with the results of these models. Variations of the position

angle of the major axis of up to 5 degrees produced little effect.

Assuming M82 is a nearly edge on disc system, the position angle of the

major axis probably can not be more than 5 degrees in error from the

64.50 measured by Heckathorn (1972). The assumed tilt of the galaxy of

100 (northwest near the observer) is close to that deduced by Lynds and

Sandage (1963). Variations of this angle by 100 or more in either direc-

tion produce easily observable structural changes. The northern spike,

in particular, is affected, suffering shortening and broadening by the

changes in inclination.

Little direct evidence is available about the motions of the gas in

the plane of the sky. However, Solinger et al. (1977) compared the

distribution of light in the M82 halo to that produced by a model galaxy

embedded in a dusty medium. From this analysis, they deduced that the

flow of gas in the plane of the sky around M82 was about 140 km/sec

southwest to northeast. Figure 14 shows the plane of the sky velocity

field for Model 2, and Figure 15 illustrates the details of this field in

and around M82. The magnitude and direction of the flow around M82 is

quite similar to that predicted by Solinger et al. (1977).



The NGC 3077 Model


NGC 3077 proved a much more difficult object to model for several

reasons. Its low systemic velocity allows solutions for ellipses,

parabolas, and hyperbolas. The lack of any structural information about

its orientation in space introduces the tilt and position angle of the





























Figure 15. Plane of sky velocity vectors of particle distribu-
tion of Model 2 shown in Figure 10. Each vector
begins at a particle and indicates the direction and
scaled magnitude of that particle's motion in the
plane of the sky. Vectors which would extend beyond
the bounds of the plot or whose magnitudes were less
than about 30 km/sec (the size of the arrow head) have
been omitted from the plot. Other plotting conven-
tions are the same as in Figure 9.










E


































































VELOCITY VETO[ SCRL[
100 kM/SEC UNITS

HIGH ASCENSION





-63-


































^L LLLI_ 1 \
VELOCITY VECTOR SCALE
i I- I-











RIGHT ASCENSION


Figure 16. Detail of plane of sky velocity vectors of Figure 15 in

and around M82. Cross indicates the Holmberg (1958) dimen-
r -
























sions and assumed orientation of M82. Coordinate tic marks
are at 10 arcmin intervals from M82's center.
-3--- F i-~---
tK r





RIGH RSCNSI0

Figure ]6 ealo n o k eoiyvctr fFgr 5i
an aoud 82 Cos idcate th omeg(15)dmn
sion an sue rinainu12 oriat i ak
are at1 rmnitras rm18' etr








major axis of the galaxy as two more "free" parameters to be considered.

In addition, it was found that both retrograde and direct orbits of

3077 about M81 produce similar disturbances in M81 and that the slightest

change in orbital parameters could drastically alter the nature of the

particle distribution.

The bridge to 3077 from M81 provided a great deal of orbital and

timing information. The bridge appears to be kinematically associated

more closely to the material in the outer portions of M81 than to the main

body of 3077 (van der Hulst 1977; hereafter denoted as vdH). Assuming

that the bulk of the bridge material does come from M181, the effects of

several types of 3077 passages on M81 were studied. Retrograde passages

of 3077 produced only diffuse particle distributions to the east of M81;

even the most destructive cases, when 3077 was nearly in the plane of

M81, produced only a suggestion of a bridge feature. No retrograde orbit

was found to produce a bridge of the size and extent observed by vdH.

The direct orbits were definitely favored for the production of

the bridge. The geometry of the observations dictated an orbital solution

with a northern perigalacticon for 3077 relative to M81 for the assumed

systemic masses, relative velocity, and projected separation for times

near perigalacticon. Hence, the effects of 3077's passage were to

elongate the rings of test particles in the northern sections of M81 to

the east, in the direction of 3077's motion. For this material to

develop into the observed bridge, the time elapsed since perigalacticon

had to be relatively long so that the combined effects of galactic rota-

tion and the perturbing accelerations of 3077 could carry the particles

into the region indicated by the observations. Times between 4 and

6 x 108 years after perigalacticon were found to be sufficient to









produce the bridge-like feature. At earlier times, the bridge did not

extend far enough; at later times, the rotational and peculiar motions

of the particles simply dispersed the bridge.

Within this time bracket, variations of the orbital parameters had

a great effect on the nature and composition of the bridge. The value

of q, the distance of closest approach, was still restricted to values

greater than 15 kpc, as in the case of the M82 models, to preserve the

M81 structure at 10 kpc. Increasing the value of q caused the bridge

particles to be drawn from the more distant rings. Geometrically, in-

creasing the value of q for a given eccentricity, lowered the plane of

3077's orbit into the plane of M81, thereby increasing the amount of

destruction of M81 both by having 3077 more nearly in the plane of the

particles and by lowering the velocity at which the interaction occurred.

Varying the orbital eccentricity for a given q also changed the nature of

the bridge geometrically. In general, the near parabolic orbits had the

lowest inclinations with respect to M81's plane, thus making them the

most destructive from that standpoint.

Another artifact of the production of the bridge on the eastern side

of M81 was the creation of a spiral arm-like feature on the western side

of the galaxy. This feature was well defined structurally from about

4 x 10 years after perigalacticon and persisted usually for a few

galactic rotations. Its shape, extent, and position could also be

altered by adjustment of the orbital parameters. Close passages early

in the time bracket produced the arms with the greatest length and

breadth in the region of the inner rings of M81. Later and/or more

distant passages shortened the arm and moved it further away from the

M81 nucleus. This feature is quite similar to the outer spiral arm-like









feature in M81 observed by Rotts and Shane (1975) and Gottesman and

Weliachew (1975) in both shape and extent.

The interaction also perturbed a number of particles from M81 to

great distances from both galaxies. Since the entire M81 system is im-

bedded in a neutral hydrogen cloud (Roberts 1972), at first this event

might seem a possible explanation for the origin of the hydrogen envelope.

However, the particles at great distances are found almost exclusively

northeast of M81. Within the time bracket allowed for the development of

the bridge, the model would appear to be incapable of producing the more

uniform distribution observed by Roberts.

Though the prograde orbits could structurally reproduce the M81

phenomena for a wide range of orbital parameters, the reproduction of the

3077 features were much more difficult. As in the M82 models, the low

mass ratio (1/10) makes the result of the interaction very severe for 3077

structurally. This problem is further complicated by the low relative

velocity of the two galaxies at close approach dictated by the geometrical

solutions for the orbits.

Both Cotrell (1976) and vdH found the 3077 HI structure to have a

distinctive shape consisting of a spike of neutral hydrogen extending

northwestward from the eastern side of the galaxy's main body. Reproduc-

tion of this spike proved to be exceedingly difficult at first. The

difficulty was coupled primarily to the assumption that the major axis

of the galaxy was within the range of 45" to 600 indicated by the obser-

vations of Barbieri et al. (1974) and Davies (1974). The solutions for

the orbital parameters with respect to 3077, assuming the position angle

was within this range, led to particle distributions which bore no









resemblance to the observations structurally. For direct passages,

3077 was elongated more or less along its major axis. These types of

distributions could be broadened or narrowed by varying the tilt of the

galaxy, and they could be lengthened or contracted by changing the dis-

tance of closest approach. For q values of 18 kpc or less these types of

passages were catastrophic for 3077, the bulk of the material being

captured in a very tight orbit about M81 or dispersed widely through the

area to the east of M81. The retrograde passages with respect to 3077

produced a distorted galaxy but also failed to produce the spike.

After a wide range of tests at various values of T, e, and q within

the assumed range of the position angle of the major axis of 3077, it was

decided that if the spike was a result of the interaction, the orbital

geometry, and hence the position angle of the major axis, must be quite

different than what had heretofore been assumed. The position angle of

the major axis was gradually increased, and the nature of the disturbance

was observed for each new orbital geometry.

Once the position angle passed 160, the spike feature became a

natural consequence of the interaction for the direct passages for a

wide range of values of q and e. Like the M82 models, its position

and shape could be altered by changing the inclination of the galaxy and

the orbital eccentricity. Models in this range also produced a second

spike feature at nearly right angles to the first one. This new feature

extended generally westward from the main body of the galaxy and into

the M81 bridge. The extent, shape, and breadth of the spikes could be

controlled by variation of the tilt of the galaxy, though tilts with the

southeast edge of the galaxy nearest the observer were preferred for best

shape control.









The geometrical constraints also appear to be quite stringent for

the value of the position angle of the major axis. For example, for

e = 1, q = 17.5 kpc, and T = 5 x 108 years after perigalacticon, if the

position angle of the major axis equals 131', 3077 is cataclysmically

destroyed, while with the position angle at 1610 the interaction produces

the spike. The common geometrical parameters between the spike producing

models seem to be the inclination of the orbit to 3077 and its respective

argument of pericenter, nearly all the models which produced the spike had

an orbit inclined nearly 90 to 3077 with the close approach occurring

nearly in the galaxy's plane.

Since the spike occurred for such a wide range of parameters, it now

became necessary not only to position the spike, but also to regulate the

size of 3077. Cotrell (1977) and vdH have mapped the spike only to about

10 arcmin north of 3077. Depending on the size of the galaxy, however,

the model spike could easily extend several times this length for dif-

ferent values of q. For example, in the q = 17.5 kpc model quoted above,

a ring of radius 8.5 kpc was drawn almost 40 arcmin northward of the

galaxy. Therefore, each model had a different maximum ring radius in

order to maintain the 10 arcmin spike length.

Figure 17 shows a typical model particle distribution for the 3077

passage. The bridge and spike are both present, as well as the spiral

feature west of M81. This model has been selected because of its struc-

tural similarity to the observations. The spike in vdH's observations is

nicely centered within the model spike, and this distant passage (q =

22.5 kpc) is capable of sustaining a rather large 3077 so that the effects

could be noted more easily for a moderate amount of computation. Figure

18 shows the gated radial velocity maps of this distribution. The





























S.wcLn a
J e-- Ol Jr
4-)U --- ) 4-


r- 0 0)
tn rO S. C P4-
S- Q. O *i- w 3
0) .n 0o *r- U


r a (a O i-

Oi- CUO -L

C 4CD ) 0)



m 0 u +1 Co

03 4-' 0 Z-


0) o *


-- 0 CO
o c 0 4c U4 -
- r-- Sn- N- : C
0, u c m3O 0o


0o 0 0



-a Lc a-'
OCO S 00 )



SW -) 03r4-'



4-C) r- U tC
- 0 01 C C
C U cC) 4-' s-




CO 0 0)
1- a m 0





m O OC rO
*r- _Q f O *-







U- 0 ) -r- 0) 0)

*I-- 4 C* )E o*

O- 0- 0 -EU rU 0-







S.-
re i Er u a v





0 -

a-
cn

i"i_
CD l 0a
*~ro ~~ c
L.L.


03












NOIIUN[1330






























Figure 18. Radial velocity distribution of particles near NGC 3077
shown in Figure 17. Particles were plotted if their
radial velocities were within a 20 km/sec bandwidth
centered on the velocity listed in the lower left corner
of each plot. Cross indicates Holmberg (1958) dimen-
sions and assumed orientation of 3077. Coordinate tic
marks are at 10 arcmin intervals from 3077's center.


















?pOMh'EC FA


-89KM/SEC A


- 0iM/i EC A 1-0 hEC A
SI Il--r


-I o n/EC A I 0-10 Mn EC
II i '


.2%. *1






-6 iI'C


r-



-U MI/S CA


o0 KM, C 120, IM/sy ,


uo, KM/SC 6


a

;jC~'


60, Kw/sqc ,


80so, n/syc ,









bandwidth of the gate was 20 km/sec which was centered on the radial

velocities used by vdH in the construction of his single channel maps so

that the model and observations can be intercompared. No beam-smoothed

maps were constructed for this model since vdH's beam was approximately

the size of the points plotted on the graphs.

Because of the discreteness of the model distribution, intercompari-

son with the high resolution observations of vdH is difficult. Struc-

turewise, the model follows the trend of the observations well. Kine-

matically, the distribution of radial velocities around 3077 at small

positive and negative velocities is really similar, though the detail is

missing and the distributions are somewhat broader as expected due to the

coarseness of the model when compared to the observations.

Perhaps the most interesting point of this model, as in the case of

the M82 models, was the large amount of particles that enter the nuclear

regions. The inner 2.5 kpc of 3077 was penetrated by 65 or 42% of its

own particles and 9 particles from M81. In the same time period, only

4 particles entered a similar region about M81. The importance of this

event will be discussed in Chapter V.

The chief failures of this model are probably associated with M81's

distribution. The model fails to produce the observed breadth and high

negative velocity distribution of the bridge, and the western spiral arm

is not exactly coincident with the outer spiral features of M81. Both of

these problems could be model related. As previously mentioned, time,

eccentricity, and distance of close approach can all affect the nature

of the bridge and spiral arm. Since the M82 model proved tractable by

variation of these parameters, it seems reasonable to suppose that some

improvement could be gained by further modelling. Also, the inherent






-74-


discreteness of the model could be reduced by increasing the number of

rings and particles at the expense of a great deal of computation time.

Since the 3077 models are so sensitive to the slightest change in

orbital parameters, it seems more reasonable, however, to take a model

such as this one as an indicator of what is possible than to push the

model to try to duplicate observations as detailed as those available for

3077.













CHAPTER V

CONCLUSIONS



The results reported in the previous chapter clearly indicate that

it is possible to build models which can adequately mimic both the ob-

served structures and radial velocity distribution in the system, par-

ticularly of the minor galaxies. If these models are similar to the

actual events they are attempting to duplicate, much can be inferred

about the consequences of the tidal encounters for each of the three

galaxies.

Perhaps the most important consequence of the models is the large

amount of infall of particles to the inner regions of the minor galaxies.

Provided the gas follows similar trajectories, the central regions of both

galaxies have received a large injection of gas as a result of their close

approach to M81. Though the models are not strictly applicable in inner

region of the galaxies, this event suggests the following scenario.

The tidal forces experienced by the minor galaxies perturbed a great

quantity of gas into free fall toward the nucleus of each. This free

falling material radically changed local conditions in the interstellar

medium as it plunged inward. The new gas injection raised the inter-

stellar gas density and induced shockwaves in the interstellar medium.

The shockwaves compressed the enriched interstellar medium and initiated

a new era of star formation. In these regions of star formation, dust

also formed and was mixed into the medium by the turbulence of the gas

flow.









It is not possible to estimate the mass of gas that the injection

involves in the case of either of the minor galaxies. The particles which

reach the nuclear regions come from many radii and do not form as a group

any well defined area distribution in the original models. Hence, it is

not possible to use some average HI mass surface density and area occupied

by the particles to estimate the mass. However, the number density of

the particles reaching this region at least indicates the relative im-

portance of the sources of the gas. In the case of 3077, the bulk of the

infalling material comes from itself. For M82, however, a significant

number of the infalling particles come from M81. Since M81 is so much

larger than M82, it could be that the mass contributed by M81 to the M82

nucleus is comparable to that produced by the collapse of M82 itself.

The differences between M82 and 3077 can be attributed to time and

the nature of the infall. Since the model indicates that 3077 was

originally somewhat smaller than M82 and that it received little material

from M81, it is reasonable to suppose that total mass of the injection

was small compared to that of M82. Also the time scale of the models

indicates that 3077 has had much longer to recover from the effects of

the interaction than M82. Any 0 and B stars produced by the 3077 inter-

action would have long since evolved away. The dust and filament struc-

tures in the galaxy (Demoulin 1969; Barbieri et al. 1974) and the stellar

distribution skewed toward Population I stars of type A or later in the

nuclear regions (Chromey 1974a,b) are simply the remnants of the inter-

action. In M82, however, the injection was both more massive and more

recent according to the models. The great amount of dust and the vast

number of early type stars seems to indicate that 182 has undergone a very

rapid era of star formation within the last 108 years (O'Connell and








Mangano 1978). Since this time is comparable to the nodelled time since

close approach and the onset of the infall, it appears that the star and

dust formation are natural consequences of the interaction.

As noted in Chapter IV, it was difficult for the M82 models to

kinematically reproduce the bridge features at low velocities. This is

possibly due to the fact that the M81 structure had already been signifi-

cantly altered by 3077 by the time M82 reached close approach. The outer

spiral arm feature of M81 produced by 3077 provides a much denser particle

distribution in the region from which M82 draws the M81 bridge; hence, it

is probable that the production of the M81-M82 bridge is, in detail,

quite dependent on the exact time between the passages of the two galaxies

and the orientation of the 3077 produced spiral feature at the time of

M82's close approach.

One HI feature that the model also fails to produce is the large

clump northeast of M81 observed by Gottesman and Weliachew (1975) and

by Rotts and Shane (1975). This clump could have been perhaps pro-

duced by the M82 modification of the 3077 disturbance in the northern

part of M81 as noted above. Kinematically, this clump has similar

velocities to the 3077 features. Interestingly, if the size of the 3077

annulus is allowed to increase to the size of M82, the spike feature of

the 3077 distribution extends nearly into this region. However, the

observations of the region from the tip of the 3077 spike to the clump

are incomplete and can not verify this possibility. Gottesman and

Weliachew (1975) also pointed out that the clump was near in position to

that of one of the dwarf systems, DDO 66. This companion might also be

produced by the interactions, but it could be an actual satellite of

M81. Since dwarf companions can be important in the development of

a model (cf. Combes 1978), the possibility that this clump









and perhaps some of the others in the system are due to the dwarf

systems can not be disregarded.

The models also seem to indicate that neither interaction is respon-

sible for the large HI envelope around the system observed by Roberts

(1972). Though 3077 is most successful at moving material to great

distances around the galaxies it does not produce the more uniform gas

distribution that is observed, nor does it appear to be capable of doing

so. The periods of the near parabolic, distant passage orbits that

position the spike well in the 3077 models are typically a few time 1010

years. Closer orbits result in the nearly complete destruction of 3077

on the first passage, making it doubtful that any HI structure would be

observed at all during subsequent passages. Therefore, the models' time

and structure dictate that both galaxies are going through their first

close approach and are therefore incapable of producing the envelope by

periodic interactions with M81. If the envelope was drawn from M81 and

is not simply the natural extent of the M81 hydrogen structure, then the

tidal agent which produced the envelope is not immediately obvious.

The effects of 3077 and M82 on each other are probably minimal. As

pointed out by Toomre (1974) the production of bridges and tails requires

a close, slow passage of unequal masses. Considering the 3077 model and

Model 2 of M82, it appears unlikely that the two minor galaxies meet

Toomre's conditions. Since the masses are equal, the interaction would

be minimal, and even at closest approach, the galaxies are separated by

approximately 65 kpc with a relative velocity of about 70 km/sec.

Model 2 of the M82 interaction seems to argue strongly for the re-

vision of the systemic velocity of M82. The value of +210 km/sec

heliocentricc) used by Model 2 is near the CO velocity field center of









symmetry determined by Rickard et al. (1977a). Since the CO observa-

tions reflect the characteristics of a normal disc system more than the

hydrogen or optical emission structures do, it is probably better to use

the +206 km/sec Rickard et al. (1977a) velocity as a fiducial indicator

of the systemic velocity than any other available criteria in this highly

disturbed system. The success of Model 2 in reproducing the Gottesman

and Weliachew (1977) radial velocity field near M82 using a system velocity

near this value seems to indicate that systemic velocity of M82 is at

least 30 km/sec lower than the accepted value of +240 km/sec based on

the work of Heckathorn (1972) and Weliachew (1974).

The only previously developed models of this system have been for-

mulated by van der Hulst (1977). The trends of his 3077 model are quite

similar to the one presented here. The M81 bridge to 3077 and the spiral

arm of M81 are both produced in a similar manner to the one described in

this work. His failure to find the spike distribution of 3077 can be

traced to his assumed position angle of the major axis and the orbital

geometry that results. His M82 model fails entirely to produce the

observed distribution for M82 or the bridge. This can be traced to his

assumption of a mass for M82 of 5 x 1010 solar, which the models in this

work indicate is too large, and his model time of 5 x 108 years after

perigalacticon, which likewise is too long. Van der Hulst's aim with

his M82 model appears to have been to increase the particle density of

the bridge from M81 to 3077 by having M82 contribute its perturbations of

the M81 distribution to 3077's. Though he accomplished his aim, the

result was to ignore the M82 features entirely.

In summary, this work has presented possible models of the tidal

interactions between M81, M82, and NGC 3077. The models indicate that









the HI bridges, but not the HI cloud in which they are immersed, are

natural consequences of such an interaction. The large scale HI struc-

tures of the three galaxies are also reproducible in the context of

these interactions. Kinenatical comparisons with the available obser-

vations show that the models are quite similar to what is found obser-

vationally. In the case of M82, the models argue that the systemic

velocity should be lowered to around +210 km/sec heliocentricc) at least.

Reproduction of the 3077 structure requires the position angle of major

axis to be approximately 1600 with an inclination of about 400 to the line

of sight (southeast nearest observer). As a result of the interactions,

both minor galaxies receive a large injection of particles into the

nuclear regions. If the gas in the systems followed similar trajectories,

this event could have precipitated an era of rapid star formation which

could be responsible for morphological changes that cause the systems to

be classified as the IO-IrrIl type.

Some further work could probably be done on the system of galaxies.

For example, though the minor galaxies probably do not interact signifi-

cantly, the simultaneous effects of 3077 and M82 on the development of

the outer M81 structures are important. Adjustment of the orbital param-

eters of 3077 could possibly produce a more favorable bridge to M81,

though intercomparison with the observations is more difficult because

of the coarseness of the model when compared to the observations. How-

ever, the models produced in this work do demonstrate that the observa-

tions can be explained within the framework of a tidal interaction between

the galaxies, and they do serve as fiducial indicators of the structural

and morphological changes that are the result of such interaction.












APPENDIX


The analysis of the models presented in this work depends heavily

on direct comparison of the models to the HI observations of the three

galaxies M81, M82, and NGC 3077. This appendix contains diagrams from

the observations of Gottesman and Weliachew (1977) and van der Hulst

(1977) which were extensively used as comparisons for the models.

Structural and radial velocity information in these diagrams will aid

the readers in following the discussion in Chapters IV and V and in

evaluating the models for themselves.




























Figure 19. Map of the integrated HI over the M81/M82 region at
4.4 arcmin resolution by Gottesman and Weliachew (1977).
The minimum contour unit is 10.8 x 1019 atoms cnm- on
the sky. The dashed contours indicate regions of higher
intensity than might be indicated by the cross-hatching.
The coordinate system is with respect to the center of
M81. This figure was reproduced by permission of Drs.
S.T. Gottesman and L. Weliachew and The Astrophysical
Journal.







































BEAM 0
S20-





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Figure 20. Brightness temperature maps of the neutral hydrogen near
M82 at different velocities with a 4.4 arcmin resolution
and 21 km/sec velocity resolution by Gottesman and
Weliachew (1977). The size of the cross at the center of
the field is close to the optical center of M82 and is
equal to the synthesized beam at half power. The oblique
line drawn through the center is the Holmberg size of M82
at the assumed position angle of the major axis. The
angular scale is given by the first map. The contour
unit is 0.5 K, and the lowest contour level is 0.5 K
except when indicated (in K). The full contours are above
3o, and the dashed contours are between 2 and 3a. The
velocities in km/sec are indicated in the bottom left
corners of the maps. This figure was reproduced by per-
mission of Drs. S.T. Gottesman and L. Weliachew and
The Astrophysical Journal.





















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BIBLIOGRAPHY


Barbieri, C., Bertola, F., and di Tullio, G. 1974, Astr. & Astrophys.,
35, 463.

Bertola, F., and Maffei, P. 1974, Astr. & Astrophys., 32, 117.

Brandt, J.C., Kalinowski, J.K., and Roosen, R.G. 1972., Ap. J. Sup.,
24, 421.

Burbidge, E.M. 1968, A.J., 73, 890.

Burbidge, E.M., Burbidge, G.R., and Rubin, V.C. 1964, Ap. J., 140, 942.

Chromey, F.R. 1974a, Astr. & Astrophys., 31, 165.

Chromey, F.R. 1974b, Astr. & Astrophys., 37, 7.

Clutton-Brock, M. 1972, Astrophys. & Space Sci., 17, 292.

Combes, F. 1978, Astr. & Astrophys., 65, 47.

Cotrell, G.A. 1976, Mon. Not. Roy. Astr. Soc., 174, 455.

Cotrell, G.A. 1977, Mon. Not. Roy. Astr. Soc., 178, 577.

Crane, P.C., Guiffrida, T.S., and Carlson, J.B. 1976, Ap. J. (Let.),
203, L113.

Danby, J.M.A. 1962, Fundamentals of Celestial Mechanics (New York:
The Macmillan CoY).

Davies, R.D. 1974, in IAU Symposium #58, The Formation and Dynamics of
Galaxies, ed. J.R. Shakeshaft (Boston: D. Reidel Publishing Co.),
119.

De Bruyn, A.G., Crane, P.C., Price, R.M., and Carlson, J.B. 1976,
Astr. & Astrophys., 46, 243.

Demoulin, M.H. 1969, Ap. J., 157, 81

De Vaucouleurs, G. 1959, in Handbuch der Physik, Astrophysics IV:
Stellar Systems, ed. S. Flugge (Berlin: Springer-Verlag), 311.

De Vaucouleurs, G. 1961, Ap. J. Sup., 5, 233.









De Vaucouleurs, G. 1975, in Stars and Stellar Systems IX: Galaxies and
the Universe, ed. A. Sandage, M. Sandage, and J. Kristian (Chicago:
University of Chicago Press), 557.

De Vaucouleurs, G. and de Vaucouleurs, A. 1964, Reference Catalog of
Bright Galaxies (University of Texas Press).

Elvius, A. 1972, Astr. & Astrophys., 19, 193.

Elvius, A. and Hall, J.S. 1962, A.J., 67, 271.

Eneev, T.M., Kozlov, N.N., and Sunyaev, R.A. 1973, Astr. & Astrophys.,
22, 41.

Geldzahler, B.J., Kellerman, K.I., Shaffer, D.B., and Clark, B.G. 1977,
A J. (Let.), 215, L5.

Goad, J.W. 1976, Ap. J. Sup., 32, 89.

Gottesman, S.T. and Weliachew, L. 1975, Ap J., 195, 23.

Gottesman, S.T. and Weliachew, L. 1977, Ap. J., 211, 47.

Guelin, M. and Weliachew, L. 1970, Astr. & Astrophyt., 9, 155.

Hargrave, P.J. 1974, Mon. Not. Roy. Astr. Soc., 168, 491.

Harper, D.A. and Low, F.J. 1973, Ap. J. (Let.), 182, L89.

Heckathorn, H. 1972, Ap. J., 173, 501.

Holmberg, F. 1958, Medd. Lunds Astr. Obs., Ser. 2, No. 136.

Humason, M.L., Mayall, N.U., and Sandage, A.R. 1956, A.J., 61, 97.

Kellerman, K.I., Shaffer, D.B., Pauliny-Toth, I.I.K., Preuss, E., and
Witzel, A. 1976, Ap. J. (Let.), 210, L121.

Killian, D.J. and Gottesman, S.T. 1977, Bul. Am. Astr. Soc., 9, 364.

Kleinman, D.E. and Low, F. 1970a, Ap. J. (Let.), 159, L165.

Kleinman, D.E. and Low, F. 1970b, Ap. (Let.), 161, L203.

Krienke, O.K. and Hodge, P.W. 1974, A.J., 79, 1242.

Kronberg, P.P. and Wilkinson, P.N. 1975, Ap. J., 200, 430.

Lewis, B.M. and Davies, R.D. 1973, Mon. Not. Roy. Astr. Soc., 165, 213.

Lynds, C.R. 1961, Ap. J., 134, 659.

Lynds, C.R. and Sandage, A.R. 1963, Ap. J., 137, 1005.









Mayall, N.U. 1960, Ann. d'Ap., 23, 344.

Morgan, W.W. 1958, PASP, 70, 364.

Morgan, W.W. and Mayall, N.U. 1957, PASP, 69, 291.

Morgan, W.W. and Mayall, N.U. 1959, Science, 130, 1421.

O'Connell, R.W. and Mangano, J.J. 1978, Ap. J., 221, 62.

Peimbert, M. and Spinrad, H. 1970, Ap. J., 160, 429.

Pfleiderer, J. 1963, Zeit. fur Astrophys., 58, 12.

Pfleiderer, J. and Siedentopf, H. 1961, Zeit. fur Astrophys., 51, 201.

Rickard, L.J., Palmer, P., Morris, M., Turner, B.E., and Zuckerman, B.
1977a, Ap. J., 213, 673.

Rickard, L.J., Palmer, P., Morris, M., Turner, B.E., and Zuckerman, B.
1977b, Ap. J., 214, 390.

Rieu, N.Q., Mebold, U., Winnberg, A., Guibert, J., and Booth, R. 1976,
Astr. & Astrophys., 52, 467.

Roberts, M.S. 1972, in IAU Symposium #44: External Galaxies and Quasi-
Stellar Objects, ed. D.S. Evans (Dordrecht, Holland: D. Reidel
Publishing Co.J, 12.

Rotts, A.H. 1975, Astr. & Atrophys., 45, 43.

Rotts, A.H. and Shane, W.W. 1975, Astr. & Astrophys., 45, 25.

Sandage, A. 1961, The Hubble Atlas of Galaxies (Washington, D.C.:
Carnegie Institution of Washington).

Sandage, A. and Visvanathan, N. 1969, Ap. J., 157, 1065.

Sanders, R.H. and Balamore, D.S. 1971, Ap. J., 166, 7.

Schmidt, G.D., Angel, J.R.P., and Cromwell, R.H. 1976, Ap. J., 206, 888.

Seyfert, C.K. 1943, Ap. J., 97, 28.

Smart, W.M. 1965, spherical Astronomy (Cambridge: Cambridge University
Press).

Solinger, A.B. 1969, Ap. J., 155, 403.

Solinger, A.B. and Markert, T. 1975, Ap. J., 197, 309.

Solinger, A.B., Morrison, P., and Markert, T. 1977, Ap J., 211, 707.








Szebehely, V. 1967, Theory of Orbits: The Restricted Problem of Three
Bodies (New York: Academic Press, Inc.).

Tammann, G.A. and Sandage, A. 1968, Ap. J., 151, 825.

Tashpulatov, N. 1970a, Soviet AJ, 13, 968.

Tashpulatov, N. 1970b, Soviet AJ, 14, 227.

Toomre, A. 1974, in IAU Symposium #58: The Formation and Dynamics of
Galaxies, ed. J.R. Shakeshaft (Boston: D. Reidel Publishing Co.),
347.

Toomre, A. and Toomre, J. 1972, Ap. J., 178, 623.

Van den Bergh, S. 1971, Astr. and Astrophys., 12, 474.

Van den Bergh, S. 1976, Ap. J., 206, 883.

Van der Hulst, J.M. 1977, doctoral thesis, Rijksuniversiteit te Groningen.

Van der Kruit, P.C. 1971, Astr. & Astrophys., 15, 110.

Van der Kruit, P.C. 1973, Astr. & Astrophys., 29, 231.

Visvanathan, N. and Sandage, A.R. 1972, Ap. J., 176, 57.

Volders, L. and Hogbom, J.A. 1961, Bul. Astr. Inst. Netherlands, 15, 307.

Von Kap-herr, A., Jones, B.B., and Wielebinski, R. 1975, Astr. & Astro-
phys., 41, 115.

Weliachew, L. 1974, Ap. J., 191, 639.

Wilkinson, P.N. 1971, Mon. Not. Roy. Astr. Soc., 154, 1P.

Wright, A.E. 1972, Mon. Not. Roy. Astr. Soc., 157, 309.

Yabushita, S. 1971, Mon. Not. Roy. Astr. Soc., 153, 97.

Yabushita, S. 1977, Mon. Not. Roy. Astr. Soc., 178, 289.














BIOGRAPHICAL SKETCH


David John Killian was born 19 December 1951, in Maryville, Missouri.

He is the son of Stearl Bishop Killian and Agnes Elizabeth Howington

Killian, and has one younger brother, Stephen Lynn, and one older step-

sister, Jesse Mae Borchardt.

David was raised in the small agricultural community of Maitland in

northwestern Missouri. He attended Maitland Elementary School and

Nodaway-Holt High School, from which he graduated as valedictorian of

his class in 1969. He then entered Northwest Missouri State University

at Maryville, Missouri, where be obtained a Bachelor of Science in

physics with highest honors in 1973. Also during his undergraduate

career, he attended the University of Missouri-Columbia while partici-

pating in the NSF Summer Undergraduate Research Program.

In September of 1973, David entered graduate school at the University

of Florida on an Arts and Sciences Graduate Fellowship. He served sub-

sequently as a Graduate Teaching Assistant in the University of Florida

astronomy laboratories while working toward his Ph.D. in astronomy. Con-

currently with his academic endeavors, David developed an interest in

karate and received his first degree black belt from the Cuong Nhu Karate

Association in May of 1978. Upon completion of his degree, David hopes

to pursue a course of theoretical and observational research in astronomy

and to eventually obtain a university level teaching position in

astronomy.











I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.


'T.i ,'7.. ; i>! i^. ___
Stephen T. Gottesman, Chairman
Associate Professor of Astronomy





I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.



Carol C. Williams
Associate Professor of Astronomy





I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy. -



J P. Oliver
Associate Professor of Astronomy




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