Difference between revisions of "User:Tohline/SSC/Structure/Polytropes"
(Begin summarizing what analyses exist of isolated polytropes) |
(begin developing table of numbers) |
||
| Line 12: | Line 12: | ||
<table border="1" align="center" cellpadding="5"> | <table border="1" align="center" cellpadding="5"> | ||
<tr> | <tr> | ||
<th align="center"> | <th align="center" colspan="5"> | ||
Quantitative Information Regarding Eigenvectors of Oscillating Polytropes | Quantitative Information Regarding Eigenvectors of Oscillating Polytropes | ||
<math>~(\Gamma_1 = 5/3)</math> | |||
</th> | </th> | ||
</tr> | |||
<tr> | |||
<td align="center"> | |||
{{User:Tohline/Math/MP_PolytropicIndex}} | |||
</td> | |||
<td align="center"> | |||
<math>~\frac{\rho_c}{\bar\rho}</math> | |||
</td> | |||
<td align="center"> | |||
Excerpts from Table 1 of | |||
[http://adsabs.harvard.edu/abs/1966ApJ...143..535H Hurley, Roberts, & Wright (1966)] | |||
<math>~s^2 (n+1)/(4\pi G\rho_c)</math> | |||
</td> | |||
<td align="center"> | |||
Excerpts from Table 3 of | |||
[http://adsabs.harvard.edu/abs/1974RPPh...37..563C J. P. Cox (1974)] | |||
<math>~\sigma_0^2 R^3/(GM)</math> | |||
</td> | |||
<td align="center"> | |||
<math>\frac{(n+1) *\mathrm{Cox74}}{3 *\mathrm{HRW66}}</math> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td align="center"> | |||
<math>~0</math> | |||
</td> | |||
<td align="center"> | |||
<math>~1</math> | |||
</td> | |||
<td align="center"> | |||
<math>~1/3</math> | |||
</td> | |||
<td align="center"> | |||
<math>~1</math> | |||
</td> | |||
<td align="center"> | |||
<math>~1</math> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td align="center"> | |||
<math>~1</math> | |||
</td> | |||
<td align="center"> | |||
<math>~3.30</math> | |||
</td> | |||
<td align="center"> | |||
<math>~0.38331</math> | |||
</td> | |||
<td align="center"> | |||
<math>~1.892</math> | |||
</td> | |||
<td align="center"> | |||
<math>~</math> | |||
</td> | |||
</tr> | </tr> | ||
</table> | </table> | ||
Revision as of 00:25, 31 March 2015
Radial Oscillations of Polytropic Spheres
|
|---|
| | Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
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 <math>~\sigma_0^2 R^3/(GM)</math> |
<math>\frac{(n+1) *\mathrm{Cox74}}{3 *\mathrm{HRW66}}</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>~</math> |
Related Discussions
|
|
|---|
|
© 2014 - 2021 by Joel E. Tohline |