H BookTiledMenu

Tiled Menu

ATTENTION:   You may need to alter your browser's magnification (zoom out and/or widen its window, for example) in order to view the most orderly layout of the "menu tiles" on this page.

Context

Global Energy Considerations

Principal Governing Equations (PGEs)		Continuity		Euler		1st Law of Thermodynamics		Poisson

 

Equation of State (EOS)		Ideal Gas		Total Pressure   Bond, Arnett, & Carr (1984)

Spherically Symmetric Configurations

(Initially) Spherically Symmetric Configurations

 

		Structural Form Factors		Free-Energy of Spherical Systems

One-Dimensional PGEs

Equilibrium Structures

1D STRUCTURE

 

		Scalar Virial Theorem

Hydrostatic Balance Equation		$\frac{dP}{dr}=-\frac{G{M}_r\rho }{r^2}$		Solution Strategies

Uniform-Density Sphere

 

Isothermal Sphere		$\frac{1}{{\xi }^2}\frac{d}{d\xi }\left({\xi }^2\frac{d\psi }{d\xi }\right)=e^{-\psi }$		via Direct Numerical Integration

Isolated Polytropes		Lane (1870)		$\frac{1}{{\xi }^2}\frac{d}{d\xi }\left({\xi }^2\frac{d{\mathrm{\Theta }}_H}{d\xi }\right)=-{\mathrm{\Theta }}_H^n$		Known Analytic Solutions		via Direct Numerical Integration		via Self-Consistent Field (SCF) Technique

 

Zero-Temperature White Dwarf		Chandrasekhar Limiting Mass (1935)

Virial Equilibrium of Pressure-Truncated Polytropes

Pressure-Truncated Configurations		Bonnor-Ebert (Isothermal) Spheres (1955 - 56)		Embedded Polytropes		Equilibrium Sequence Turning-Points ♥				Turning-Points (Broader Context)

Free Energy of Bipolytropes (nc, ne) = (5, 1)

Composite Polytropes (Bipolytropes)		Milne (1930)		Schönberg- Chandrasekhar Mass (1942)		Murphy (1983) Analytic (nc, ne) = (1, 5)		Eggleton, Faulkner & Cannon (1998) Analytic (nc, ne) = (5, 1)

See Also