# User:Tohline/H Book

Preface from the original version of this HyperText Book (H_Book):

November 18, 1994

Much of our present, basic understanding of the structure, stability, and dynamical evolution of individual stars, short-period binary star systems, and the gaseous disks that are associated with numerous types of stellar systems (including galaxies) is derived from an examination of the behavior of a specific set of coupled, partial differential equations. These equations — most of which also are heavily utilized in studies of continuum flows in terrestrial environments — are thought to govern the underlying physics of all macroscopic "fluid" systems in astronomy. Although relatively simple in form, they prove to be very rich in nature... <more>

# Applications

## Spherically Symmetric Configurations

### Structure:

Solution Strategies:

Detailed Force-Balance
(Introduction)

Virial Equilibrium
(Introduction)

 Example Solutions: Uniform-density sphere Isolated … ✓ ✓ Embedded in an External Medium … ✓ ✓ Polytropes Isolated … ✓ ✓ Embedded in an External Medium … ✓ ✓ Isothermal sphere Isolated … ✓ ✓ Embedded in an External Medium (Bonnor-Ebert Sphere) … ✓ ✓ Zero-temperature White Dwarf — Overview Power-law density distribution — Overview BiPolytropes (also referred to as Composite Polytropes) Overview Overview Core-Envelope Structure with $~(n_c,n_e) = (0,0)$ … ✓ ✓ Core-Envelope Structure with $~(n_c,n_e) = (5,1)$ … ✓ ✓ Limiting Masses — Summary

### Stability:

 Solution Strategy Assuming Spherical Symmetry: Example Solutions:

### Dynamics:

 Spherical Collapse: Free Fall Homologous Collapse Collapse of Stellar Cores with n = 3 — investigation by Goldreich & Weber (1980, ApJ, 238, 991) Generalization to Arbitrary Polytropic Index

## Two-Dimensional Configurations

• Introduction

### Structure:

 Solution Strategies Axisymmetric Configurations Example Solutions: Maclaurin Spheroids Rotationally Flattened, Isothermal Structures Polytropic Tori: Papaloizou-Pringle (massless) Tori Self-gravitating Tori Infinitesimally Thin, Nonaxisymmetric Disk

## Three-Dimensional Configurations

• Introduction

### Structure:

 Solution Strategies Example Solutions: Ellipsoidal Figures of Equilibrium Compressible Analogs of Riemann Ellipsoids; see also Note to Hirschmann & Neilsen and Suggested Strategy by Joel