MASS DISTRIBUTIONS and STELLAR POPULATIONS in SPIRAL GALAXIES By
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RICE UNIVERSITY MASS DISTRIBUTIONS AND STELLAR POPULATIONS IN SPIRAL GALAXIES by Joseph C. Davis, Jr. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE THESIS DIRECTOR'S SIGNATURE: March 1977 MASS DISTRIBUTIONS AND STELLAR POPULATIONS IN SPIRAL GALAXIES by Joseph C. Davis, Jr. ABSTRACT The techniques of obtaining mass models for spiral galaxies from their observed rotation curves are reviewed. A fast method for fitting the Toomre type disk mass model together with a simple prescription for the distribution of central bulge material is developed based on observed rotation curves. Several well observed galaxies are then modeled in this fashion. These mass models of real galaxies are then used as in¬ put to an extension of an ongoing program of galactic evolu¬ tion modeling. Multizone galactic models are constructed assuming each radial zone evolves independently with a rate of star formation proportional to the frequency of spiral arm passage as derived from density wave theory. The pro¬ portionality factor, called the efficiency of star formation, is the only free parameter of the model. An initial era of star formation is assumed to deplete an amount of gas into stars equal to: the amount of bulge mass at each radius. A constant initial mass function equal to the Salpeter IMF is employed throughout. An evolutionary model of the near¬ by spiral galaxy M33 shows that a variable efficiency factor is required to reproduce both the observed integrated colors and luminosities. i It is also shown that this model for the star forma¬ tion rate coupled with the initial mass function determined from the stars in the local solar neighborhood will not produce model galaxies as blue as the bluest real galaxies. Therefore, either the IMF cannot be a universal constant or the star formation rate is a more complex function of time. ii ACKNOWLEDGEMENTS I would like to thank Dr. Raymond J. Talbot, Jr. for introducing me to the study of galaxies and for patiently helping me at every stage of this work. And I should also add that all of my successes in life and none of my failures are due to my parents and to the loving family which revolves around them. TABLE OF CONTENTS Page CHAPTER I - INTRODUCTION 1 LA — General Properties of Spiral Galaxies 1 Primary Types of Mass Distributions........ 2 The Toomre Local Gravitational Instability. 3 The Large Scale Instabilities of Numerical Treatments 4 I.B — Stellar Populations and Mass Distri¬ butions 5 CHAPTER II - THE DEVELOPMENT OF MASS MODELS II.A — Toomre Disk Models 11 II.B — The Shu, Stachnik, and Yost Spheroid 22 II.C — Future Proposals for Mass Models 29 CHAPTER III - MODELS OF SPECIFIC GALAXIES 34 III.A — Available Data on Well Observed Galaxies 34 III.B — Fitting Procedures 37 III.C — Mass Models for Some Specific Galaxies 44 NGC 224 = M31 = The Andromeda Galaxy 44 NGC 598 = M33 46 NGC 5457 = M101 47 CHAPTER IV - ELEMENTS OF GALACTIC EVOLUTION MODELING 55 IV.A — Multizone Galactic Models The Initial Collapse of the Proto-galactic Cloud 55 Initial Conditions 56 Matter Flow in the Gaseous Disk 58 Constructing Model Galaxies From a Set of "One Zone" Models 59 The Birthrate Prescription 60 The Initial Mass Function 61 Necessary Elements of Stellar Evolution... 61 Comparison With Observational Data 62 IV. B — The Initial Mass Function 63 Page CHAPTER V - MODEL GALAXIES WITH A BIRTHRATE PRESCRIPTION BASED ON DENSITY WAVE THEORY 72 V.A — A Two Phase Birthrate Prescription Based on Spiral Density Wave Passage 72 V.B — Initial Modeling of M33 78 V.C — Conclusions 86 REFERENCES 90 1 CHAPTER I INTRODUCTION The motivation for this paper was provided by Talbot and Arnett (1975). In developing simple models for the evolution of highly flattened disk galaxies, they pro¬ posed that to model specific galaxies it is necessary to use mass models which reproduce the observed rotation curve of the galaxy under consideration. Chapters II and III of this paper describe the details of the mass models we have chosen and the methods of fitting them to actual galaxies. Chapter IV introduces the elements of multizone galactic modeling and Chapter V presents the results of using specific mass models for observed galaxies in con¬ junction with theoretical models for the evolution of the gas and stars in these systems. This is part of an ongoing effort, under the direction of Dr. Talbot here at Rice University, to explain the general observed features of these galaxies and the interrelated physics. The present chapter is an introduction to several features of spiral galaxies which must be explained in any successful theoretical model for the structure and evolu¬ tion of galaxies. I. A — General Properties of Spiral Galaxies Spiral galaxies may be characterized as self-gravitat¬ ing bodies composed of mass in the form of gas, dust, and stars. The total mass of one of these galaxies ranges 2 6 12 from 10 flU© to 10 M©_. However, most well observed spiral 10 galaxies have masses between 1 and 20 x 10 MQ, with the total number of stars on the order of ten to one hundred billion. The fraction of mass in the form of gas can vary from a few percent to upwards of fifty percent. Primary Types of Mass Distributions The most evident shape of a typical spiral galaxy is a rather flattened disk when viewed edge-on, and a prominent, though often erratic and hard-to-define, multi-arm spiral when viewed face on. It is now fairly well established that the spiral features are simply indicative of intrinsically bright features, especially the young 0 and B stars and the H H regions they illuminate, and represents only a minor enhancement to the density of mass. To a good approximation, the primary mass distribution is disk-like, with the outer¬ most radial extent ill determined and with the surface mass density depending almost solely on the radial coordinate. Asymmetries are observed in specific cases, but in many cases these may be explained by gravitational distortions produced by the passage of nearby galaxies. These distor¬ tions undoubtedly produce many interesting features inex¬ plicable by simple axisymmetric disks, but we will not attempt to incorporate this complication in our present work. Another type of mass distribution superimposed on the disk distribution is often evident in photographic plates of spiral galaxies: these are the central bulges which 3 resemble oblate spheroids whose axis of revolution is coincident with the axis of rotation of the disk. While many researchers have incorporated such spheriodal mass bulges into their mass models in order to adequately fit rotation curves, they have generally not been included in models for the evolution of gas into stars by other re¬ searchers. However, the nuclear bulges often have a large effect on the mass distribution in the inner parts of galaxies, and since the inner parts are often the best observed, it is necessary to include their effects. Another possible component of the total galactic mass distribution is the proposed galactic halo which generally is pictured as having a similar shape as the central bulge but with much greater size and mass. Numerical simulations of two dimensional disks of stars, such as done by Ostriker and Peebles (1973) and by Hohl (1971 and 1976) seem to indicate that gross instabilities exist in disks alone. The halo population is hypothesized to stabilize the disk. The Toomre Local Gravitational Instability Toomre (1964) showed that instabilities causing fast growing clumping of mass on a local scale will occur in any disk initially in equilibrium between gravitational and centrifugal forces unless the random motion within the disk is greater than a certain value. This minimum value of the root-mean-squared velocity dispersion in the radial direction, in essence defining a minimum temperature 4 of the disk, was expressed by Toomre in terms of the local surface density, a, and K, the epicycle frequency of the disk. The value of this minimum velocity in the radial direction was found to be i / <v2> • 2 =3.36 GO/K I.A-1 min where G is the gravitational constant. It is important to note that instabilities arising from failure to meet this criterion are estimated to manifest themselves in mere fractions of a galactic rotation period. The Large Scale Instabilities of Numerical Treatments Even though numerical N-body treatments of disks assume an initial velocity dispersion equaling or exceeding the Toomre criterion, the gross instabilities of Ostriker and Peebles, etc., appear on a time scale of one to several galactic rotation periods. These instabilities seem to lead to barlike and ringlike shapes. The numerical models reach stability when the mean kinetic energy of rotation is lowered to a value of about 14% of the total gravita¬ tional potential energy of the system. While the nature of these slower large scale instab¬ ilities has not been firmly theoretically established, their existence could possibly explain the large number of barred spirals and spirals with ring components observed in nature. It remains to explain the pure, non-barred spirals. 5 A leading hypothesis is to add a massive halo with very high thermal kinetic energy. The crucial factor is to change the relative proportions of rotational kinetic energy, K, and "thermal" kinetic energy, U. The virial theorem requires that K + ^-|v|, where V is the total gravi¬ tational potential energy. If a massive, hot halo dominates both the kinetic and potential terms, then the disk can remain relatively "cool" and stable. It is found by Ostriker and Peebles (1973) that a halo to disk ratio of 1 to 2.5 is required.