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>

Pictorial Table of Contents

• Pictorial Table of Contents

Context

• Principal Governing Equations
  • Continuity Equation
  • Euler Equation
    • Rotating Reference Frame
    • Jay Call's Hybrid Scheme
  • <math>1^\mathrm{st}</math> Law of Thermodynamics
  • Poisson Equation

• Supplemental Relations
  • Total Pressure
    • Quartic Temperature Solution

• Global Energy Considerations

Applications

Spherically Symmetric Configurations

Introduction (Alternate Introduction)

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 <math>~(n_c,n_e) = (0,0)</math> … ✓ ✓          Core-Envelope Structure with <math>~(n_c,n_e) = (5,1)</math> … ✓ ✓ Limiting Masses — Summary

Stability:

Background: Sound Waves Solution Strategy Assuming Spherical Symmetry: Eulerian Perspective Lagrangian Perturbations	Virial Stability Bipolytrope Generalization
Example Solutions: Uniform-density sphere Polytropes

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
  • Cylindrical Coordinates
  • Axisymmetric Configurations

Structure:

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

Dynamics:

Three-Dimensional Configurations

• Introduction
  • Properties of Homogeneous Ellipsoids
  • Fission Hypothesis of Binary Star Formation

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

Stability:

• Lou & Bai (2011, MNRAS, 415, 925) — 3D perturbations in an isothermal self-similar flow

Related Projects Underway

• A Template for Gravitational-Wave Signals from Core-Collapse Supernovae

Appendices

• Equations
• Variables
• References
• Ramblings

See Also

• NIST Digital Library of Mathematical Functions; see also the related CUP Publication

© 2014 - 2021 by Joel E. Tohline |   H_Book Home   |   YouTube   | Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS | Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation