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

Supplemental Relations

Virial Equations

Applications

Spherically Symmetric Configurations

If the self-gravitating configuration that we wish to construct is spherically symmetric, then the coupled set of multidimensional, partial differential equations that serve as our principal governing equations can be simplified to a coupled set of one-dimensional, ordinary differential equations. This is accomplished by expressing each of the multidimensional spatial operators — gradient (<math>\nabla</math>), divergence (<math>\nabla\cdot</math>), and Laplacian (<math>\nabla^2</math>) — in spherical coordinates (<math>r, \theta, \varphi</math>) (see, for example, the Wikipedia discussion of integration and differentiation in spherical coordinates) then setting to zero all derivatives that are taken with respect to the angular coordinates <math>\theta</math> and <math>\varphi</math>. After making this simplification, our governing equations become... <more>

Structure:

• Solution Strategies
• Example Solutions:
  • Uniform-density sphere
  • Polytropes
  • Zero-temperature White Dwarf
  • Isothermal sphere

Stability:

• Solution Strategy
• Example Solutions:
  • Uniform-density sphere
  • Polytropes

Appendices

© 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