User:Tohline/SSC/Stability/Isothermal
Radial Oscillations of Pressure-Truncated Isothermal Spheres
Here we draw primarily from the following three sources:
- §5.3.8 (p. 372) of Horedt's (2004) treatise on Polytropes: Applications in Astrophysics and Related Fields
- S. Yabushita (1968, MNRAS, 140, 109) — Jeans's Type Gravitational Instability of Finite Isothermal Gas Spheres
- L. G. Taff & H. M. Horn (1974, MNRAS, 168, 427-432) — Radial Pulsations of Finite Isothermal Gas Spheres
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Groundwork
Linearized Wave Equation
In an accompanying discussion, we derived the so-called,
Adiabatic Wave (or Radial Pulsation) Equation
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<math>~ \frac{d^2x}{dr_0^2} + \biggl[\frac{4}{r_0} - \biggl(\frac{g_0 \rho_0}{P_0}\biggr) \biggr] \frac{dx}{dr_0} + \biggl(\frac{\rho_0}{\gamma_\mathrm{g} P_0} \biggr)\biggl[\omega^2 + (4 - 3\gamma_\mathrm{g})\frac{g_0}{r_0} \biggr] x = 0 </math> |
whose solution gives eigenfunctions that describe various radial modes of oscillation in spherically symmetric, self-gravitating fluid configurations.
See Also
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© 2014 - 2021 by Joel E. Tohline |