SELF-CONSISTENT MODELS OF BARRED SPIRAL GALAXIES DAVID EUGENE KAUFMANN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1993 To Mom, Dad, Greg, Eric, Elizabeth, and Carol ACKNOWLEDGMENTS With this dissertation my education has, in two very different senses, both drawn to a close and started anew. Although there will be no more classes, exams, or theses, I have just begun to learn. Many special people have helped to bring me this far. Dr. George Contopoulos, the de facto advisor ofmy thesis, not only has taught me essentially all that I know about the fascinating topics ofnonlinear dynamics and chaos, he has also provided an unmatched role model for this young scientist. I personally know of no other person who strives harder to find truth. To this goal I also dedicate myself. Drs. James Hunter and Stephen Gottesman helped me greatly during the course of my research, especially during the periods of Dr. Contopoulos’ absence. Dr. Hunter, who served as chairman for thisdissertation, instilledin me the valueofbalancingpurely computational results with the underlying theory. He taught me that one is of limited value without the other. Dr. Gottesman, who acted as cochairman for the dissertation, impressed upon me the need for theoretical results to address the observations and kept me from getting absorbed in the purely abstract. After all, there is the real world. Dr. Neil Sullivan, the final member of my committee, and Dr. James Fry, a member until the Fall of 1992, allowed me the freedom to conduct this research as I deemed fit. For that I thank them. 111 I would also like to thank several colleagues whose technical assistance was invalu- able. Dr. Nikos Hiotelis generously loaned me his smoothed particle hydrodynamics code and very ably instructed me in the basics of its proper use. Drs. Martin England and Elizabeth Moore provided essential information concerning the neutral hydrogen NGC NGC observations of 1073 and 1398, respectively. Also, Dr. Preben Grosbpl helped me understand some of the more subtle details of his original codes. Dr. Robert Leacock, Jeanne Kerrick, Darlene Jeremiah, Debra Hunter, and Ann Elton have my deepest gratitude for leading me around the pitfalls of academic bureaucracy. Many others have provided me with steadfast friendship and moral support during the course of my graduate study. Dr. Jim Webb and Tom Barnello thankfully showed me that quality basketball does indeed exist outside the state of North Carolina! Dr. Gregory Fitzgibbons kept me laughing instead of crying while I studied for the written qualifying exams. Dirk Terrell and Dan Durda finally persuaded me, to my benefit, to stick my head underwater and learn scuba diving. I enjoyed many exciting games of backgammon with Jer-Chyi Liou and Damo Nair, even though they defy the laws of probability with their dice-rolling skills! Chuck Higgins put up with me for one year as a roommate and kindly slowed down to allow me to keep up during our cycling excursions. Bryan Feigenbaum, whojust may be able to beat me (occasionally) in one- on-one basketball, tolerated me as a roommate for three years and made some trying times bearable with his humor. My good friends Jaydeep Mukherjee and Billy Cooke have always been there for me through the good times and the bad. Thanks guys! And to all those whom I have not explicitly mentioned here, please accept my apologies and my sincerest gratitude. IV Finally and most importantly, I would like to thank my mother Betty, my father John, my brothers Greg and Eric, and their respective wives Elizabeth and Carol. They have always stood behind me with unwavering support and encouragement. To them I dedicate this dissertation. TABLE OF CONTENTS ACKNOWLEDGMENTS Ill LIST OF TABLES Vlll LIST OF FIGURES X . ABSTRACT xvii CHAPTERS INTRODUCTION 1. . . . 1 MODELING TECHNIQUES 2. 11 . . The Method of Contopoulos and Grosb0l (CG Method) 11 . . The CG Method Modified for the Case of Barred Spiral Galaxies 31 . . Gas Response Using Smoothed Particle Hydrodynamics (SPH) 43 . . . PROGRAM GALAXIES 3. 50 . . NGC 3992 57 . . Observations 57 . . Best Model 61 . . NGC 1073 72 . . Observations 72 . . Best Model 77 . . NGC 1398 82 . . Observations 82 . . Best Model 86 . . VARIATION OF PARAMETERS 4. 94 . . A Variation of 94 . . Variation of Ar 96 . . Variation of io 97 . . Variation of es 97 . . Variation of Hp 98 . . A Variation of ’ 102 . Variation of ^2 103 . Variation of ri, r2, ki, k2, and A4 . 105 Variation of the Bar Semiaxes a, b, and c 108 . Mg Variation of the Bar Mass 108 . Variation of cq and eo 109 . VI Variation of <ro and or 112 Interpretation of Results 113 5. STOCHASTIC ORBITS 118 Surfaces of Section 123 Individual Stochastic Orbits 136 Proportions of Ordered and Stochastic Orbits in the Models 141 6. GAS RESPONSE 145 SUMMARY 7. 171 Self-Consistent Models of Barred Spirals 171 The Role of Stochastic Orbits 173 The Gas Response 174 Directions for Future Research 175 APPENDIX: MODEL BAR QUANTITIES 177 BIBLIOGRAPHY 180 BIOGRAPHICAL SKETCH 186 Vll LIST OF TABLES 2- 2-1 Initial conditions of the periodic orbit and the eight nonperiodic orbits used to 3- calculate the effect of the velocity dispersion 24 2-2 The values of the Xj and wvi of Table 2-1 24 3 Adjustable parameters in the axisymmetric rotation curve fitting procedure. 39 . 1 HI rotation velocity data for NGC 3992 58 3-2 Selected global and disk parameter values adopted for NGC 3992. The errors given are simply the formal errors of a least-squares analysis of the observed velocity field and do not imply that these quantities have been determined to this level of precision 60 NGC 3-3 Photometrically derived parameter values for 3992 62 NGC 3-4 Parameter values for the best self-consistent model of 3992 63 NGC 3-5 Resonance locations of the best model of 3992 66 3-6 Parameters used to calculate the surface density response for the best model of NGC 3992 67 3-7 HI rotation velocity data for NGC 1073 73 NGC 3-8 Selected global and disk parameter values adopted for 1073. Here again, the errors listed are simply the formal errors of a least-squares analysis of the velocity field 75 3-9 Photometrically derived parameter values for NGC 1073 76 NGC 3-10 Parameter values for the best self-consistent model of 1073 77 NGC 3-11 Resonance locations of the best model of 1073 79 3-12 Parameters used to calculate the surface density response for the best model NGC of 1073 79 3-13 HI rotation velocity data for NGC 1398 84 NGC 3-14 Selected global and disk parameter values adopted for 1398 85 NGC 3-15 Photometrically derived parameter values for 1398 87 NGC 3-16 Parameter values for the best self-consistent model of 1398 87 NGC 3-17 Resonance locations of the best model of 1398 89 3-18 Parameters used to calculate the surface density response for the best model of NGC 1398 90 5-1 Summary of basic stochastic orbit types and their behaviors 137 5-2 Estimated breakdown of the mass-weighted orbit populations comprising the models of Chapter 3 according to type (trapped versus stochastic) and location (bar, disk, or both). The errors in the cited figures are somewhat uncertain, but are estimated to be of the order of 5% 143 IX LIST OF FIGURES 2-1 The effect of varying Sb on the shape of the model rotation curve given by Eq. (2-1): (1) £b = (2) £b = (3) £b = 2£di (4) £b = £d- In all cases fj, = 1. 13 2-2 The effect of varying fj, on the shape of the model rotation curve given by Eq. 2- (2-1): (1) ff, = 0; (2) f^ = 0.5; (3) fb = 1; (4) f,, = 2. In all cases £b = 5ed- 14 23--3 Rotation curves of the exponential disk (solid curve) and a point with the same total mass (dotted curve) 33 2-4 Rotation curves of the Plummer sphere (solid curve) and a point with the same total mass (dotted curve) 35 5 Three normalized “axisymmetric” bar rotation curves for cases where a = 1 and c = 0.1: (1) b = 0.15, (2) b = 0.3, and (3) b = 0.6. The dotted line Mg represents the Keplerian rotation curve for a point mass equal to 37 1 NGC 3992 (NASA Atlas of Galaxies Useful for Measuring the Cosmological Distance Scale 1988) 52 3-2 NGC 1073 (NASA Atlas of Galaxies Useful for Measuring the Cosmological Distance Scale 1988) 54 3-3 NGC 1398 (Sandage 1961, The Hubble Atlas of Galaxies) 56 3-4 Comparison of observed and theoretical rotation curves for NGC 3992. The NGC theoretical curve is derived from our most successful model of 3992. Also shown are the contributions of the separate components of this model to the total theoretical rotation curve 59 3-5 Characteristics of the orbit families included in the model. Each characteristic plots X, where a given orbit crosses the minor bar axis b, as a function of Jacobi constant, as parameterized by rc 63 3-6 The 2/1 family of periodic orbits in the model of NGC 3992. The darker circle represents corotation at 5.5 kpc 65