SSC/Stability/BiPolytropes/Index

Organizational Index

This index helps organize and summarize the insight that we have gained from our broad investigation into the relative stability of spherically symmetric bipolytropic configurations. The most relevant summary chapter is named, SSC/Stability/BiPolytropes.

Motivation

Schönberg-Chandrasekhar mass limit:

• Schönberg-Chandrasekhar mass limit.
• Potential connection with Bonnor-Ebert mass limit; another pointer is contained here.
• Origin of Planetary Nebulae

Simpler Systems

Stability

Normal Fluids

• Buoyancy: For stability, need gas density to decrease outward. In bipolytropes, this reduces to the requirement that ${\mu }_e/{\mu }_c\le 1$.
• Convection: For stability, need specific entropy to increase outward; uniform specific entropy is marginally stable.

LAWE Solutions

Isolated n = 1 Polytrope
${\gamma }_g=(n+1)/n=2$	${\gamma }_g=\frac{5}{3}$	Key Reference(s): 📚 Chatterji (1951)
		Relevant Chapters: Isolated n = 1 Polytrope Origin of Planetary Nebulae

Isolated n = 3 Polytrope
${\gamma }_g=\frac{20}{13}$	Key Reference(s): 📚 Schwarzschild (1941)
	Relevant Chapters: Radial Oscillations of n = 3 Polytropic Spheres Origin of Planetary Nebulae

Pressure-Truncated n = 5 Polytrope
${\gamma }_g=(n+1)/n=\frac{6}{5}$	Key Reference(s): n/a
	Relevant Chapters: Radial Oscillations of n = 5 Polytropic Spheres Origin of Planetary Nebulae

Pressure-Truncated Isothermal (n = ∞) Sphere
${\gamma }_g=1$	Key Reference(s): 📚 Yabushita (1968) 📚 Taff, & van Horn (1974)
	Relevant Chapters: Radial Oscillations of Isothermal Spheres Origin of Planetary Nebulae

See Also