Joel2 at 16:39, 9 January 2024

2024-01-09T16:39:52Z

← Older revision		Revision as of 12:39, 9 January 2024
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	<td align="left">Relevant Chapters:		<td align="left">Relevant Chapters:
	<ul>		<ul>
	<li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize#Isolated_n_=_1_Polytrope\|Isolated n = 1 Polytrope]]</li>		<li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2#Isolated_n_=_1_Polytrope\|Isolated n = 1 Polytrope]]</li>
	<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Polytropes\|Origin of Planetary Nebulae]]</li>		<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Polytropes\|Origin of Planetary Nebulae]]</li>
	</ul>		</ul>

Joel2: Created page with "

Isolated n = 1 Polytrope

$\gamma_g = (n+1)/n = 2$

n = 1 Eigenvectors
$\gamma_g = \tfrac{5}{3}$
n = 1 Eigenvectors Key Reference(s):
{{ Chatterj..."
2024-01-09T15:46:56Z

Created page with "<table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"><b>Isolated n = 1 Polytrope</b></td> </tr> <tr> <td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = 2</math><br /><p><br /><p><br />250px|n = 1 Eigenvectors</td> <td align="center" rowspan="2"><math>\gamma_g = \tfrac{5}{3}</math><br />250px|n = 1 Eigenvectors</td> <td align="left">Key Reference(s): <ul><li>{{ Chatterj..."

New page
<table border="1" align="center" cellpadding="5">

<tr>
<td align="center" colspan="3"><b>Isolated n = 1 Polytrope</b></td>
</tr>

<tr>
<td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = 2</math><br /><p><br /><p><br />[[File:N1osc06.gif|250px|n = 1 Eigenvectors]]</td>
<td align="center" rowspan="2"><math>\gamma_g = \tfrac{5}{3}</math><br />[[File:OurImprovedSummary2.png|250px|n = 1 Eigenvectors]]</td>
<td align="left">Key Reference(s):
<ul><li>{{ Chatterji51 }}</li></ul></td>
</tr>

<tr>
<td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize#Isolated_n_=_1_Polytrope|Isolated n = 1 Polytrope]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Polytropes|Origin of Planetary Nebulae]]</li>
</ul>
</td>

</tr>
</table>

<table border="1" align="center" cellpadding="5">

<tr>
<td align="center" colspan="2"><b>Isolated n = 3 Polytrope</b></td>
</tr>

<tr>
<td align="center" rowspan="2"><math>\gamma_g = \tfrac{20}{13}</math><br />[[File:Schwarzschild1941movie.gif|250px|n = 3 Eigenvectors]]</td>
<td align="left">Key Reference(s):
<ul><li>{{ Schwarzschild41 }}</li></ul></td>
</tr>

<tr>
<td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/n3PolytropeLAWE#Radial_Oscillations_of_n_.3D_3_Polytropic_Spheres|Radial Oscillations of n = 3 Polytropic Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Isolated_n_=_3_Polytrope_with_γg_=_20/13|Origin of Planetary Nebulae]]</li>
</ul></td>
</tr>
</table>

<table border="1" align="center" cellpadding="5">

<tr>
<td align="center" colspan="2"><b>Pressure-Truncated n = 5 Polytrope</b></td>
</tr>

<tr>
<td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = \tfrac{6}{5}</math><br />[[File:N5Truncated2.gif|250px|Truncated n = 5 Polytrope]]</td>
<td align="left">Key Reference(s):
<ul><li>n/a</li></ul></td>
</tr>

<tr>
<td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/n5PolytropeLAWE#Numerical_Integration_of_LAWE|Radial Oscillations of n = 5 Polytropic Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Pressure-Truncated_n_=_5_Polytrope_with_γg_=_6/5|Origin of Planetary Nebulae]]</li>
</ul></td>
</tr>
</table>

<table border="1" align="center" cellpadding="5">

<tr>
<td align="center" colspan="2"><b>Pressure-Truncated Isothermal (n = ∞) Sphere</b></td>
</tr>

<tr>
<td align="center" rowspan="2"><math>\gamma_g = 1</math><br />[[File:TaffVanHorn1974Harmonic.gif|250px|Truncated n = 5 Polytrope]]</td>
<td align="left">Key Reference(s):
<ul>
<li>{{ Yabushita68 }}</li>
<li>{{ TVH74 }}</li></ul>
</td>
</tr>

<tr>
<td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/Isothermal#Previously_Published_Eigenvalues_and_Eigenfunctions|Radial Oscillations of Isothermal Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Pressure-Truncated_n_=_5_Polytrope_with_γg_=_6/5|Origin of Planetary Nebulae]]</li>
</ul>
</td>
</tr>
</table>