User:Tohline/SSC/Structure/Polytropes

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Radial Oscillations of Polytropic Spheres

Whitworth's (1981) Isothermal Free-Energy Surface
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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:

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>

Related Discussions

Whitworth's (1981) Isothermal Free-Energy Surface

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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