User:Tohline/SSC/Structure/Polytropes

Radial Oscillations of Polytropic Spheres

Overview

The eigenvector associated with radial oscillations in isolated polytropes has been determined numerically and the results have been presented in a variety of key publications:

• P. LeDoux & Th. Walraven (1958, Handbuch der Physik, 51, 353) —
• M. Hurley, P. H. Roberts, & K. Wright (1966, ApJ, 143, 535) — The Oscillations of Gas Spheres
• J. P. Cox (1974, Reports on Progress in Physics, 37, 563) — Pulsating Stars

Tables

Quantitative Information Regarding Eigenvectors of Oscillating Polytropes <math>~(\Gamma_1 = 5/3)</math>
<math>~n</math>	<math>~\frac{\rho_c}{\bar\rho}</math>	Excerpts from Table 1 of Hurley, Roberts, & Wright (1966) <math>~s^2 (n+1)/(4\pi G\rho_c)</math>	Excerpts from Table 3 of J. P. Cox (1974) <math>~\sigma_0^2 R^3/(GM)</math>	<math>\frac{(n+1) *\mathrm{Cox74}}{3 *\mathrm{HRW66}} \cdot \frac{\bar\rho}{\rho_c}</math>
<math>~0</math>	<math>~1</math>	<math>~1/3</math>	<math>~1</math>	<math>~1</math>
<math>~1</math>	<math>~3.30</math>	<math>~0.38331</math>	<math>~1.892</math>	<math>~0.997</math>
<math>~1.5</math>	<math>~5.99</math>	<math>~0.37640</math>	<math>~2.712</math>	<math>~1.002</math>
<math>~2</math>	<math>~11.4</math>	<math>~0.35087</math>	<math>~4.00</math>	<math>~1.000</math>
<math>~3</math>	<math>~54.2</math>	<math>~0.22774</math>	<math>~9.261</math>	<math>~1.000</math>
<math>~3.5</math>	<math>~153</math>	<math>~0.12404</math>	<math>~12.69</math>	<math>~1.003</math>
<math>~4.0</math>	<math>~632</math>	<math>~0.04056</math>	<math>~15.38</math>	<math>~1.000</math>

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