臺灣博碩士論文加值系統

Abstract

In this thesis we calculate the effect of finite disk thickness on the structure and stability of a differentially rotating three-dimensional disk galaxy with stars and gas on the basis of the self-consistent theory of density waves. In this theory, if the matter density is perturbed by some cause, then this initial density perturbation must necessarily generate induced gravitational potential perturbations via the governing three-dimensional Poission equation for the galactic disk with finite thickness whereas the induced gravitational potential response will in turn produce the induced matter density perturbations via the stellar dynamical Jean’s equations for the stars and the continuum fluid dynamical equations for the gas. If this induced matter density perturbation is equal to the initial input density perturbation in amplitude, then such density waves are said to be self-consistent. However, the induced matter density perturbations are computed from the two-dimensional stellar dynamical equations for the stars and the continuum fluid dynamical equations for the gas since it is generally believed that observed majestic sweep of spiral arms across the face of a galaxy is confined entirely in the galactic plane with zero thickness.

In order to bring out the physical significance of the effect of finite thickness clearly we concentrate in this thesis on the axially symmetric modes with azimuthal symmetry. In this way we avoid the WKB approximation generally adopted for the spiral modes. In the limit of an infinitely thin disk, our result naturally reduces to Toomre’s criterion for a stellar disk and to Kalnajs’s result for a gaseous disk. In addition, the effect of finite disk thickness on the stability and spatial structure of genuine three dimensional spiral galaxies is investigated and application of our theory to the Milky Way Galaxy yields good results in general agreement with recent observations.

Contents


Abstract ……………………………………………………………i
Contents …………………………………………………………iii
Figure Captions ……………………………………………………………iv
Chapter 1 Introduction ………………………………………………………1
Chapter 2 Mathematical Formulation for 3D Spiral Galaxies
2-1 Mathematical Formulation for 3D Spiral Galaxies …………11
2-2 The Mathematical Problem ……………………………14
2-3 The Response in Stars to the Spiral Gravitational Potential …………17
2-4 The Response in the Gas to the Spiral Gravitational Potential …………24
Chapter 3 The Local Stability of the Axisymmetric Galactic Disk with Finite Thickness
3-1 The Reduction Factors …………………28
3-2 The Axisymmetric Stellar Disk Models ………………35
Chapter 4 The Local Stability of Spiral Galaxies with Finite Thickness
4-1 Reduction Factors and the Toomre parameter ………………………………… 48
4-2 Stability of 3D Spiral Galaxies ………………63
4-3 The Role of Radial Velocity Dispersion ……………65
4-4 Spiral Structure in 3D Galactic Disks ………………72
Chapter 5 Summary & Conclusion …………………………………………76
Bibliography ……………………………………………………………82
Appendix A The Radial Self-Gravity of the Galactic Disk and the Estimate of the Halo Mass…86
Appendix B The Perturbed Gravitational Potential ………………………95
Appendix C Derivation the Perturbed Gravitational Potential for a Genuine 3D Disk…99

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