Difference between revisions of "User:Tohline/Appendix/Images"

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=Images (to be) Displayed in this H_Book=
=Images (to be) Displayed in this H_Book=
This replaces an earlier [[User:Tohline/Appendix/Images2016Layout|''Appendix/Images2016Layout'']] wiki page.
{{LSU_HBook_header}}
{{LSU_HBook_header}}


==Generated by Tohline or an Immediate Collaborator==
==SECTION:&nbsp; Preamble, Contents, etc.==
* CHAPTER:  [[User:Tohline/H_Book/ImageContent01#TitleImage|Pictorial Table of Contents]]
** Image:Graphical_Content_SSC.jpg


*SECTION:  Spherically Symmetric Configurations
<table border="0" cellpadding="2" align="left" width="100%">
** CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations#Spherically_Symmetric_Configurations|Alternate Introduction]]
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*** Image:LSU_Stable.animated.gif
  <td align="left" colspan="1" width="5%">&nbsp;</td>
*** Image:Minitorus.animated.gif
  <td align="left" colspan="3">WIKI CHAPTER:   [[User:Tohline/Preface#Preface|Preface]]</td>
** CHAPTER: [[User:Tohline/SphericallySymmetricConfigurations/Virial#Visual_Representation|Virial Equilibrium Structures (Introduction)]]
</tr>
*** File:3DFreeEnergy.jpg
<tr>
** CHAPTER: [[User:Tohline/SSC/Structure/Polytropes#Example_Interval|Isolated Polytropes (DFB)]]
  <td align="left" colspan="1" width="5%">&nbsp;</td>
*** File:PlotTheta5F.png (Shrivastava's n = 5 Lane-Emden Function)
  <td align="left" colspan="3">WIKI CHAPTER:   [[User:Tohline/H_Book/ImageContent01#TitleImage|Pictorial Table of Contents]]</td>
** CHAPTER: [[User:Tohline/SSC/Structure/PolytropesEmbedded#Overlap_with_Whitworth.27s_Presentation|Embedded Polytropes (DFB)]]
</tr>
*** File:HoredtPlot2.png
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** CHAPTER:  [[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Isolated Isothermal Sphere (DFB)]]
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*** File:IsothermalDensityPlot.jpg
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
*** File:EmdenMassProfile.jpg
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*** File:PlotMeanToLocalDensity.jpg
[http://www.vistrails.org/index.php/Image:Graphical_Content_SSC.jpg Image:Graphical_Content_SSC.jpg]
** CHAPTER:  [[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Pressure-Truncated Isothermal Sphere (DFB)]]
  </td>
*** File:BonnorFig1usingEmdenData.jpg
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*** File:EbertFig2UsingEmdenData2.jpg
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*** File:Bonnor1956DPDVplot.jpg
  <td align="right" colspan="2" width="10%">&nbsp;</td>
** CHAPTER:  [[User:Tohline/SSC/Structure/LimitingMasses#Mass_Upper_Limits|Mass Upper Limits]]
  <td align="left" colspan="2">
*** Image:MassRadiusVirialLabeled.png
<table border="1" align="left" width="90%" cellpadding="5">
*** File:Stahler1983Comparison.png
<tr>
*** Image:PlotSequencesBest02.png
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|BipolytropeDFB00]]
</tr>
*** Image:BipolytropeDynamicalStability2.png
</table>
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|BipolytropeDFB51]]
  </td>
*** Image:DenXi05.jpg
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*** Image:DenXi10.jpg
</table>
*** Image:DenXi30.jpg
<div align="center">&nbsp;</div>
*** Image:PresXi05.jpg
*** Image:PresXi10.jpg
*** Image:PresXi30.jpg
*** Image:MassXi05.jpg
*** Image:MassXi10.jpg
*** Image:MassXi30.jpg
*** Image:PlotSequencesBest02.png
*** Image:SC_42Comparison.jpg
*** Image:PlotStabilityBest02.png
**CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|BipolytropeDFB15]]
*** File:MurphyF2roots05.png
*** File:InterfaceMap02.png
*** File:MurphyPhysicallyViableTable3d.png
*** File:MF85Table1byTohline02.png
** CHAPTER:  [[User:Tohline/SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|Isolated Polytropes (Virial)]]
*** File:AdabaticBoundedSpheres_Virial.jpg
** CHAPTER:  [[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|Embedded Polytropes (Virial)]]
*** File:FreeNRGmassRadiusN5.png
*** File:FreeNRGpressureRadiusIsothermal.png
*** File:EnergyRadiusViewCombined5.png (3/4 of this image constructed for this H_Book)
** CHAPTER:  [[User:Tohline/SSC/Virial/Isothermal|Isothermal (Virial)]]
*** File:Bonnor1956Fig1.jpg
*** File:WhitworthLogFig1a_norm.jpg


==SECTION:&nbsp; Governing Physics==


==Extracted from Other Sources==
<table border="0" cellpadding="2" align="left" width="100%">
* CHAPTER:  [[User:Tohline/PGE/Hybrid_Scheme#Focus_on_Tracking_Angular_Momentum|Jay Call's Hybrid Scheme]]
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/PGE#Principal_Governing_Equations|Principal Governing Equations]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000a.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Principal Governing Equations (PGEs)]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity Equation]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000b.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Continuity]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/PGE/Euler#Euler_Equation|Euler Equation]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000c.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Euler]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/PGE/FirstLawOfThermodynamics#First_Law_of_Thermodynamics|First Law of Thermodynamics]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000d.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|1<sup>st</sup> Law of Thermodynamics]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SR/PoissonOrigin#Origin_of_the_Poisson_Equation|Origin of the Poisson Equation]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000e.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Poisson]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/RotatingFrame#Rotating_Reference_Frame|Rotating Reference Frame]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">C000c.txt</font></td>
</tr>
</table>


** File:NormanWilson78C.png  
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  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/Hybrid_Scheme_Preface#Hybrid_Advection_Scheme_.28Preface.29|Hybrid Advection Scheme (Preface)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">E000b.txt</font></td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/AStarScheme#Hybrid_Advection_Scheme_.28Background.29|Hybrid Advection Scheme (Background ''circa'' 2000)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">E000a.txt</font></td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/Hybrid_Scheme#Hybrid_Advection_Scheme|Jay Call's Hybrid Scheme]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">B000t.txt</font></td>
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:NormanWilson78D.png Eqns:NormanWilson78D.png] &#8212; (embedded in wiki chapter [[User:Tohline/PGE/Hybrid_Scheme#NormanWilson78|here]])
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
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   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
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   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
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  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
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** File:NewTohline97B.png
  </td>
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/Image:NewTohline97C.png Eqns:NewTohline97C.png] &#8212; (embedded in wiki chapter  [[User:Tohline/PGE/Hybrid_Scheme#NewTohline97|here]])
  </td>
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  <td align="left" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
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   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
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   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">[http://ioppublishing.org/copyright Institute of Physics Publishing]</td>
   <td align="left">[http://ioppublishing.org/copyright Institute of Physics Publishing]</td>
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  <td align="right">Permission:</td>
  <td align="left">Granted by J.E.Tohline, who is one of the authors</td>
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  </td>
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</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SR#Supplemental_Relations|Supplemental Relations]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000g.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Equation of State (EOS)]] : TILED MENU icon(s)</td>
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<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SR/IdealGas#Ideal_Gas_Equation_of_State|Ideal Gas Equation of State]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000h.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Ideal Gas]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SR/PressureCombinations#Total_Pressure|Total Pressure]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000i.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Total Pressure]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SR/Ptot_QuarticSolution#Determining_Temperature_from_Density_and_Pressure|Quartic Temperature Solution]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">B001m.txt</font></td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|Simple Rotation Profiles]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A004d.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Axisymmetric_Equilibrium_Structures|''Simple'' Rotation Profiles]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/VE#Global_Energy_Considerations|Global Energy Considerations]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000f.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Context|Global Energy Considerations]] : TILED MENU icon(s)</td>
</tr>
</table>
<div align="center">&nbsp;</div>
==SECTION:&nbsp; Spherically Symmetric Configurations==
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations_.28Part_I.29|Introduction]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000j.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|One-Dimensional PGEs]] : TILED MENU icon(s)</td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations#Spherically_Symmetric_Configurations|Alternate Introduction]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">C001a.txt</font>
  </td>
</tr>
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  <td align="right" colspan="2" width="10%"><font size="+1">&#x1F3A6;</font></td>
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[http://www.vistrails.org/index.php/Image:LSU_Stable.animated.gif Animation:LSU_Stable.animated.gif]; &nbsp; see, also, [http://www.phys.lsu.edu/astro/movie_captions/equalmass.binary.html an associated description]
  </td>
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<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Animated gif created by the LSU astrophysics group in support of Figure 10 in the following publication:</td>
</tr>
</table>
  </td>
</tr>
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  <td align="left" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">K. C. B. New &amp; J. E. Tohline</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''The Relative Stability Against Merger of Close, Compact Binaries''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://iopscience.iop.org/0004-637X/490/1/311/ 1997, '''The Astrophysical Journal''', 490, 311-327]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">The American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">[http://ioppublishing.org/copyright Institute of Physics Publishing]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">Granted by J.E.Tohline, one of the authors</td>
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</table>
  </td>
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[http://www.vistrails.org/index.php/Image:Minitorus.animated.gif Animation:Minitorus.animated.gif]
  </td>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
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  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
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  </td>
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<div align="left">&nbsp;</div>
===Detailed Force-Balanced (DFB) Models===
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/IntroductorySummary#Applications|DFB Introductory Summary]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">C001c.txt</font>
  </td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Hydrodynamic Balance Equation]] : TILED MENU icon(s)</td>
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[https://www.vistrails.org/index.php/File:FreeNRGpressureRadiusIsothermal.png Image:FreeNRGpressureRadiusIsothermal.png];
&nbsp;
[https://www.vistrails.org/index.php/File:MassRadiusVirialLabeled.png Image:MassRadiusVirialLabeled.png];
&nbsp;
[https://www.vistrails.org/index.php/File:PlotSequencesBest02.png Image:PlotSequencesBest02.png]
  </td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|Image:FreeNRGpressureRadiusIsothermal.png]] : TILED MENU icon(s)</td>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
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  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations_.28Part_I.29|DFB Introduction (Part I)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Same as ''SECTION'' Introduction (''i.e.,'' archived file <font color="darkgreen">A000j.txt</font>)
  </td>
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  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|DFB Introduction (Part II)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000n.txt</font></td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Hydrostatic Balance Equation]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Solution Strategies]] : TILED MENU icon(s)</td>
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====Chapter Group Isolated====
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  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/UniformDensity#Isolated_Uniform-Density_Sphere|Uniform-Density Sphere &hellip; Isolated (DFB)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">C001d.txt</font></td>
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  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Isothermal Sphere &hellip; Isolated (DFB)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A000r.txt</font> </td>
  <td align="right" colspan="1" width="40%">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Isothermal Sphere]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|via Direct Numerical Integration]] : TILED MENU icon(s)</td>
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<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:EmdenBookCover1907.jpg Title:EmdenBookCover1907.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:EmdenIsothermalDerivation.jpg Eqns:EmdenIsothermalDerivation.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:EmdenTable14.jpg Table:EmdenTable14.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">Robert Emden</td>
</tr>
<tr>
  <td align="right">Book Title:</td>
  <td align="left">[https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover&hl=en#v=onepage&q&f=true ''Gaskugeln'']</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">None active; originally 1907</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Digitized by Google (books.google.com); originally, Druck und Verlag von B. G. Teubner: Berlin</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[https://www.vistrails.org/index.php/File:IsothermalDensityPlot.jpg Image:IsothermalDensityPlot.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:EmdenMassProfile.jpg Image:EmdenMassProfile.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:PlotMeanToLocalDensity.jpg Image:PlotMeanToLocalDensity.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/Polytropes#Polytropic_Spheres|Polytropes &hellip; Isolated (DFB)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A001a.txt</font></td>
</tr>
<tr>
  <td align="right" colspan="4">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Isolated Polytropes]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Known Analytic Solutions]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|via Direct Numerical Integration]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|via Self-Consistent Field (SCF) Technique]] : TILED MENU icon(s)</td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:PlotTheta5F.png Image:PlotTheta5F.png] (Shrivastava's n = 5 Lane-Emden Function)
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<!--
              MURPHY 1983
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Murphy1983Extremum02.png Eqns:Murphy1983Extremum02.png];  [This pair of equations appear in an "equation table", retyped as LaTeX equations.]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">J. O. Murphy</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983PASAu...5..175M 1983, '''Proceedings of the Astronomical Society of Australia''', 5, 175-179]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Astronomical Society of Australia</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              MACH 2012
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Mach2012Eqs.png Eqns:Mach2012Eqs.png];  [This pair of equations appear in an "equation table", retyped as LaTeX equations.]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">P. Mach</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''All Solutions of the n = 5 Lane-Emden Equation''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/2012JMP....53f2503M 2012, '''Journal of Mathematical Physics''', 53, 062503-062503-6]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Institute of Physics</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">TILED CHAPTER:  [[User:Tohline/SSC/Structure/Lane1870#Lane.27s_1870_Work|Lane (1870)]] &nbsp; &nbsp; &hellip; &nbsp; &nbsp; Archived on MacHD2 on 2020/01/31 as: <font color="darkgreen">A001b.txt</font> </td>
  <td align="right" colspan="1" width="40%">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Lane (1870)]] : TILED MENU icon(s)</td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/WhiteDwarfs#White_Dwarfs|Zero-temperature White Dwarf &hellip;Overview]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Zero-Temperature White Dwarf]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Chandrasekhar Limiting Mass (1935)]] : TILED MENU icon(s)</td>
</tr>
<!--
              SHAPIRO & TEUKOLSKY 1983
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:ST83Eq3_3_11.png Eqn:ST83Eq3_3_11.png];
&nbsp;
[http://www.vistrails.org/index.php/File:ST83Eq3_3_12.png Eqn:ST83Eq3_3_12.png];
&nbsp;
[http://www.vistrails.org/index.php/File:ST83Eq2_3_23.png Eqn:ST83Eq2_3_23.png]; [All 3 appear in an "equation table", retyped as LaTeX equations.]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">S. L. Shapiro &amp; S. A. Teukolsky</td>
</tr>
<tr>
  <td align="right">Book Title:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983bhwd.book.....S ''Black Holes, White Dwarfs, and Neutron Stars:  The Physics of Compact Objects'']</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">1983</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">New York:  John Wiley &amp; Sons</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/PowerLawDensity#Power-Law_Density_Distributions|Power-law Density Distribution &hellip;Overview]]
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/Other_Analytic_Models|Other Analytically Definable Models]]
  </td>
</tr>
</table>
====Chapter Group Pressure-Truncated====
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/UniformDensity#Uniform-Density_Sphere_Embedded_in_an_External_Medium|Uniform-Density Sphere  &hellip; Pressure-Truncated (DFB)]]
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Isothermal Sphere &hellip; Pressure-Truncated (DFB)]]; &nbsp; Familiarly, a <font color="red"><b>Bonnor-Ebert Sphere</b></font></td>
  <td align="right" colspan="1" width="40%">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Bonnor-Ebert (Isothermal) Spheres (1955 - 56)]] : TILED MENU icon(s)</td>
</tr>
<!--
              EBERT 1955
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:EbertDerivation01.jpg Eqns:EbertDerivation01.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:EbertFig2Title.jpg Image:EbertFig2Title.jpg]; [The first of these images appears in an "equation table", retyped as text &amp; LaTeX equations.]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">R. Ebert</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''&Uuml;ber die Verdichtung von HI-Gebieten''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1955ZA.....37..217E 1955, '''Zeitschrift f&uuml;r Astrophysik''', 37, 217-232]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">&#8212;</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              BONNOR 1956
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:BonnorDerivation01.jpg Eqns:BonnorDerivation01.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:Bonnor1956Fig1reproduced.jpg Image:Bonnor1956Fig1reproduced.jpg]; [The first of these images appears in an "equation table", retyped as text &amp; LaTeX equations.]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">W. B. Bonnor</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Boyle's Law and Gravitational Instability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1956MNRAS.116..351B 1956, '''Monthly Notices of the Royal Astronomical Society''', 116, 351-359]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:WhitworthFig1bCopy.jpg Image:WhitworthFig1bCopy.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:WhitworthFig1bFlippedClipped.png Image:WhitworthFig1bFlippedClipped.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">A. Whitworth</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[https://www.vistrails.org/index.php/File:Bonnor1956Fig1EmdenDataCleaner.png Image:Bonnor1956Fig1EmdenDataCleaner.png];
&nbsp;
[https://www.vistrails.org/index.php/File:EbertFig2UsingEmdenData2.jpg Image:EbertFig2UsingEmdenData2.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:Bonnor1956DPDVplot.jpg Image:Bonnor1956DPDVplot.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:WhitworthFig1bUsingEmdenData.png Image:WhitworthFig1bUsingEmdenData.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/PolytropesEmbedded#Overlap_with_Whitworth.27s_Presentation|Polytropes &hellip; Pressure-Truncated (DFB)]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|Polytropes]] : TILED MENU icon(s)</td>
</tr>
<!--
              HOREDT 1970
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Horedt_PRdiagram0.png Image:Horedt_PRdiagram0.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Horedt_EmbeddedPolytrope.png Title:Horedt_EmbeddedPolytrope.png];
&nbsp;
[http://www.vistrails.org/index.php/File:HoredtEq00.png Eqns:HoredtEq00.png];
&nbsp;
[http://www.vistrails.org/index.php/File:HoredtEq01.png Eqns:HoredtEq01.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">Gp. Horedt</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Gravitational Instability of Polytropic Gas Spheres Under External Pressure''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1970MNRAS.151...81H 1970, '''Monthly Notices of the Royal Astronomical Society''', 151, 81-86]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:WhitworthFig1bCopy.jpg Image:WhitworthFig1bCopy.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:Whitworth1981TitlePage0.png Title:Whitworth1981TitlePage0.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">A. Whitworth</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              KIMURA 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">     
[http://www.vistrails.org/index.php/File:KimuraEq00.png Eqns:KimuraEq00.png];
&nbsp;
[http://www.vistrails.org/index.php/File:KimuraEq01.png Eqns:KimuraEq01.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">H. Kimura</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''A Study of Simple Polytropes &#8212; Part Two &#8212; Stability Against Homologous Constraction''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981PASJ...33..299K 1981, '''Publications of the Astronomical Society of Japan''', 33, 299-312]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Astronomical Society of Japan</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              STAHLER 1983
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:Stahler1983TitlePage0.png Title:Stahler1983TitlePage0.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler_MRdiagram1.png Image:Stahler_MRdiagram1.png] <font color="red">'''SCHEMATIC''' (appears twice)</font>
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">S. W. Stahler</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''The Equilibria of Rotating Isotherma Clouds &#8212; Part Two &#8212; Structure and Dynamical Stability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983ApJ...268..165S 1983, '''The Astrophysical Journal''', 268, 165-184]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:HoredtPlot2.png Image:HoredtPlot2.png];
&nbsp;
[http://www.vistrails.org/index.php/File:WhitworthPlot2.png Image:WhitworthPlot2.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png];
&nbsp;
[http://www.vistrails.org/index.php/File:DFBsequenceB.png Image:DFBsequenceB.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
<!--
              Category:  Marginally Unstable Pressure-Truncated Gas Clouds 
-->
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Marginally_Unstable_Pressure-Truncated_Gas_Clouds|Marginally Unstable Pressure-Truncated Gas Clouds]]</td>
  <td align="right" colspan="1" width="40%"><font color="green" size="+2">&hearts;</font>&nbsp;[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Equilibrium Sequence Turning-Points]] : TILED MENU icon(s)</td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:IsothermalTrunc4.png Image:IsothermalTrunc4.png];
&nbsp;
[http://www.vistrails.org/index.php/File:IsothermalTrunc12.png Image:IsothermalTrunc12.png];
&nbsp;
[http://www.vistrails.org/index.php/File:IsothermalTrunc11.png Image:IsothermalTrunc11.png];
<br />
[http://www.vistrails.org/index.php/File:Yabushita1975Combined.png Image:Yabushita1975Combined.png];
&nbsp;
[http://www.vistrails.org/index.php/File:MassVsRadiusCombined02.png Image:MassVsRadiusCombined02.png];
&nbsp;
[http://www.vistrails.org/index.php/File:YabushitaMontageB.png Image:YabushitaMontageB.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
====Chapter Group Bipolytropes====
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|BiPolytropes (also referred to as ''Composite Polytropes'') &hellip; Overview]]
  </td>
</tr>
<!--
              COWLING 1931
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:CowlingRE_Milne1931.jpg Text:CowlingRE_Milne1931.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">T. G. Cowling</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Note on the Fitting of Polytropic Models in the Theory of Stellar Structure''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1931MNRAS..91..472C 1931, '''Monthly Notices of the Royal Astronomical Society''', 91, 472-478]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              SCHONBERG & CHANDRASEKHAR 1942
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:SchonbergChandra1942.jpg Text:SchonbergChandra1942.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">M. Sch&ouml;nberg &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''On the Evolution of the Main-Sequence Stars''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1942ApJ....96..161S 1942, '''The Astrophysical Journal''', 96, 161-172]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|Zero-Zero Bipolytrope (DFB)]]
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[https://www.vistrails.org/index.php/File:BipolytropeDynamicalStability2.png Image:BipolytropeDynamicalStability2.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|Five-One Bipolytrope (DFB)]]
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[https://www.vistrails.org/index.php/File:DenXi05.jpg Image:DenXi05.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:DenXi10.jpg Image:DenXi10.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:DenXi30.jpg Image:DenXi30.jpg]; <br />
[https://www.vistrails.org/index.php/File:PresXi05.jpg Image:PresXi05.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:PresXi10.jpg Image:PresXi10.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:PresXi30.jpg Image:PresXi30.jpg]; <br />
[https://www.vistrails.org/index.php/File:MassXi05.jpg Image:MassXi05.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:MassXi10.jpg Image:MassXi10.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:MassXi30.jpg Image:MassXi30.jpg]; <br />
[https://www.vistrails.org/index.php/File:PlotSequencesBest02.png Image:PlotSequencesBest02.png];
&nbsp;
[https://www.vistrails.org/index.php/File:SC_42Comparison.jpg Image:SC_42Comparison.jpg];
&nbsp;
[https://www.vistrails.org/index.php/File:PlotStabilityBest02.png Image:PlotStabilityBest02.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<!--
              SCHONBERG & CHANDRASEKHAR 1942
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:SC42_Fig1.jpg Image:SC42_Fig1.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">M. Sch&ouml;nberg &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''On the Evolution of the Main-Sequence Stars''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1942ApJ....96..161S 1942, '''The Astrophysical Journal''', 96, 161-172]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              HENRICH & CHANDRASEKHAR 1941
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:HenrichChandra41b.jpg Image:HenrichChandra41b.jpg]
&nbsp;
[http://www.vistrails.org/index.php/File:HenrichChandra41a.jpg Text:HenrichChandra41a.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">L. R. Henrich &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Stellar Models with Isothermal Cores''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1941ApJ....94..525H 1941, '''The Astrophysical Journal''', 94, 525-536]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              EGGLETON, FAULKNER & CANNON 1998
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:EagletonFaulknerCannon98.jpg Text:EagletonFaulknerCannon98.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">P. P. Eggleton, J. Faulkner, &amp; R. C. Cannon</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''A Small Contribution to the Giant Problem''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1998MNRAS.298..831E 1998, '''Monthly Notices of the Royal Astronomical Society''', 298, 831-834]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              BUCHDAHL 1978
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Buchdahl1978.png Eqn:Buchdahl1978.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">H. A. BUCHDAHL</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Remark on the Polytrope of Index 5''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1978AuJPh..31..115B 1978, '''Australian Journal of Physics''', 31, 115-116]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">[http://www.publish.csiro.au/journals/copyright CSIRO Publishing]</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|One-Five Bipolytrope (DFB)]]</td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:MurphyF2roots05.png Image:MurphyF2roots05.png];
&nbsp;
[http://www.vistrails.org/index.php/File:InterfaceMap02.png Image:InterfaceMap02.png];
&nbsp;
[http://www.vistrails.org/index.php/File:MurphyPhysicallyViableTable3d.png Image:MurphyPhysicallyViableTable3d.png];<br />
[http://www.vistrails.org/index.php/File:DenXi05.jpg Image:DenXi05.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:DenXi10.jpg Image:DenXi10.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:DenXi30.jpg Image:DenXi30.jpg];<br />
[http://www.vistrails.org/index.php/File:PresXi05.jpg Image:PresXi05.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:PresXi10.jpg Image:PresXi10.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:PresXi30.jpg Image:PresXi30.jpg];<br />
[http://www.vistrails.org/index.php/File:MassXi05.jpg Image:MassXi05.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:MassXi10.jpg Image:MassXi10.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:MassXi30.jpg Image:MassXi30.jpg];
<br />
[http://www.vistrails.org/index.php/File:MF85Table1byTohline02.png Table:MF85Table1byTohline02.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</tr>
</table>
</table>
*SECTION: Spherically Symmetric Configurations
  </td>
** CHAPTER: [[User:Tohline/SphericallySymmetricConfigurations/Virial#Energy_Extrema|Virial Equilibrium Structures (Introduction)]]
</tr>
*** Image:Tohline1985_Eq9.png
<!--
<table border="0" align="center" width="90%" cellpadding="3">
              MURPHY 1983
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Table3CompleteCol1.png TableColumn:Table3CompleteCol1.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Table3CompleteCol2.png TableColumn:Table3CompleteCol2.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Table3CompleteCol3.png TableColumn:Table3CompleteCol3.png];<br />
[http://www.vistrails.org/index.php/File:Table3CompleteCol4.png TableColumn:Table3CompleteCol4.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Table3CompleteCol5.png TableColumn:Table3CompleteCol5.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Table3CompleteCol6.png TableColumn:Table3CompleteCol6.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">J. O. Murphy</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983PASAu...5..175M 1983, '''Proceedings of the Astronomical Society of Australia''', 5, 175-179]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Astronomical Society of Australia</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              MURPHY & FIEDLER 1985
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:MF85Table1.png Table:MF85Table1.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">J. O. Murphy &amp; R. Fiedler</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Physical Structure of a Sequence of Two Zone Polytropic Stellar Models''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1985PASAu...6..219M 1985, '''Proceedings of the Astronomical Society of Australia''', 6, 219-222]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Astronomical Society of Australia</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1.5_3#BiPolytrope_with__and_ne_.3D_3|The ''Milne'' Bipolytrope (DFB)]]
  </td>
</tr>
<!--
              COWLING 1931
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:CoreRelations01.png Eqns:CoreRelations01.png];
&nbsp;
[http://www.vistrails.org/index.php/File:EnvelopeRelations01.png Eqns:EnvelopeRelations01.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">E. A. Milne</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''The Analysis of Stellar Structure''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1930MNRAS..91....4M 1930, '''Monthly Notices of the Royal Astronomical Society''', 91, 4-55]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
</table>
 
 
<div align="left">&nbsp;</div>
 
===Virial Equilibrium Configurations===
 
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER: [[User:Tohline/SphericallySymmetricConfigurations/Virial#Energy_Extrema|Introduction]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|Free-Energy of Spherical Systems]] || [[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Scalar Virial Theorem]] : TILED MENU icon(s)</td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:3DFreeEnergy.jpg Image:3DFreeEnergy.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
<!--
              TOHLINE 1985
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Tohline1985_Eq9.png Eqns:Tohline1985_Eq9.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
Line 135: Line 1,562:
   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">Granted by J.E.Tohline, who is the sole author</td>
</tr>
</tr>
</table>
</table>
*** Image:Weber1976_EqB3.png
  </td>
<table border="0" align="center" width="90%" cellpadding="3">
</tr>
<!--
              WEBER 1976
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Weber1976_EqB3.png Eqns:Weber1976_EqB3.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
Line 158: Line 1,602:
   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Virial/FormFactors|Structural Form Factors]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|Structural Form Factors]] : TILED MENU icon(s)</td>
</tr>
<!--
              VIALA & HOREDT 1974
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:VialaHoredt1974.png Eqns:VialaHoredt1974.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">Y. P. Viala &amp; Gp. Horedt</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Polytropic Sheets, Cylinders and Spheres with Negative Index''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1974A%26A....33..195V 1974, '''Astronomy and Astrophysics''', 33, 195-202]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">European Southern Observatory</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Virial/Polytropes#Virial_Equilibrium_of_Adiabatic_Spheres|Virial Equilibrium of Isolated Polytropic Spheres]]</td>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Whitworth1981Eq5.jpg Eqns:Whitworth1981Eq5.jpg] <font color="red">(repeat)</font>
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">A. Whitworth</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:AdabaticBoundedSpheres_Virial.jpg Image:AdabaticBoundedSpheres_Virial.jpg];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Virial/Isothermal|Virial Equilibrium of Isothermal Spheres]]</td>
</tr>
<!--
              BONNOR 1956
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Bonnor1951Eq1.2.jpg TxtEqns:Bonnor1951Eq1.2.jpg];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">W. B. Bonnor</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Boyle's Law and Gravitational Instability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1956MNRAS.116..351B 1956, '''Monthly Notices of the Royal Astronomical Society''', 116, 351-]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:WhitworthFig1aCopy.jpg Image:WhitworthFig1aCopy.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">A. Whitworth</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Bonnor1956Fig1.jpg Image:Bonnor1956Fig1.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:WhitworthLogFig1a_norm.jpg Image:WhitworthLogFig1a_norm.jpg];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|Virial Equilibrium of Embedded Polytropic Spheres]]</td>
  <td align="right" colspan="1" width="40%">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|FreeNRGpressureRadiusIsothermal.png]] : TILED MENU icon(s)</td>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Whitworth1981Eq10.jpg Eqns:Whitworth1981Eq10.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:Whitworth1981Eq5.jpg Eqns:Whitworth1981Eq5.jpg] <font color="red">(repeat)</font>
&nbsp;
[http://www.vistrails.org/index.php/File:EnergyRadiusViewBottom6.png Image:EnergyRadiusViewBottom6.png] <font color="red">(half of this image is Whitworth figure)</font>;
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">A. Whitworth</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:FreeNRGmassRadiusN5.png Image:FreeNRGmassRadiusN5.png];
&nbsp;
[http://www.vistrails.org/index.php/File:FreeNRGpressureRadiusIsothermal.png Image:FreeNRGpressureRadiusIsothermal.png];
<br />
[http://www.vistrails.org/index.php/File:EnergyRadiusViewTop5.png Image:EnergyRadiusViewTop5.png];
&nbsp;
[http://www.vistrails.org/index.php/File:FEmovie02.gif Animation:FEmovie02.gif];
&nbsp;
[http://www.vistrails.org/index.php/File:EnergyRadiusViewBottom6.png Image:EnergyRadiusViewBottom6.png] <font color="red">(half of this image is Whitworth figure)</font>;
<br />&hellip; or &hellip; &nbsp; &nbsp;
[http://www.vistrails.org/index.php/File:EnergyRadiusViewCombined5.png Image:EnergyRadiusViewCombined5.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/SSC/Synopsis_StyleSheet#Spherically_Symmetric_Configurations_Synopsis_.28Using_Style_Sheet.29|Style-Sheet Synopsis]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Style-Sheet Synopsis]] : TILED MENU icon(s)</td>
</tr>
<!--
              H_BOOK
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:SSC_SynopsisImage2.png Image:SSC_SynopsisImage2.png]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
</table>
===Summaries===
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/LimitingMasses#Mass_Upper_Limits|Limiting Masses &hellip; Summary]]
  </td>
</tr>
<!--
              SCHONBERG & CHANDRASEKHAR 1942
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:SC42excerpt.jpg Text:SC42excerpt.jpg]
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">M. Sch&ouml;nberg &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''On the Evolution of the Main-Sequence Stars''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1942ApJ....96..161S 1942, '''The Astrophysical Journal''', 96, 161-172]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              STAHLER 1983 
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:Stahler1983TitlePage0.png Title:Stahler1983TitlePage0.png] <font color="red">(repeat)</font>;
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler_MRdiagram1.png Image:Stahler_MRdiagram1.png] <font color="red">'''SCHEMATIC''' (repeat)</font>
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">S. W. Stahler</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''The Equilibria of Rotating Isotherma Clouds &#8212; Part Two &#8212; Structure and Dynamical Stability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983ApJ...268..165S 1983, '''The Astrophysical Journal''', 268, 165-184]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
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</table>
  </td>
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<!--
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:MassRadiusVirialLabeled.png Image:MassRadiusVirialLabeled.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png] <font color="red">(repeat)</font>;
&nbsp;
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
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  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
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<table border="0" cellpadding="2" align="left" width="100%">
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  <td align="left" colspan="1" width="5%">&nbsp;</td>
  <td align="left" colspan="2">WIKI CHAPTER:  [[User:Tohline/Appendix/Ramblings/Turning_Points#Turning_Points|Turning Points]]</td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Equilibrium_Structures|Turning-Points (Broader Context)]] : TILED MENU icon(s)</td>
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<!--
              EBERT 1955
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[http://www.vistrails.org/index.php/File:EbertFig2Title.jpg Image:EbertFig2Title.jpg] <font color="red">(repeat)</font>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">R. Ebert</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''&Uuml;ber die Verdichtung von HI-Gebieten''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1955ZA.....37..217E 1955, '''Zeitschrift f&uuml;r Astrophysik''', 37, 217-232]</td>
</tr>
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  <td align="right">Copyright:</td>
  <td align="left">&#8212;</td>
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  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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<!--
              BONNOR 1956
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
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[http://www.vistrails.org/index.php/File:Bonnor1956Fig1reproduced.jpg Image:Bonnor1956Fig1reproduced.jpg] <font color="red">(repeat)</font>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">W. B. Bonnor</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Boyle's Law and Gravitational Instability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1956MNRAS.116..351B 1956, '''Monthly Notices of the Royal Astronomical Society''', 116, 351-]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Astronomical Society</td>
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<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
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</table>
  </td>
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<!--
              STAHLER 1983 
-->
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:Stahler_MRdiagram1.png Image:Stahler_MRdiagram1.png] <font color="red">'''SCHEMATIC''' (repeat)</font>;
  </td>
</tr>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">S. W. Stahler</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''The Equilibria of Rotating Isotherma Clouds &#8212; Part Two &#8212; Structure and Dynamical Stability''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1983ApJ...268..165S 1983, '''The Astrophysical Journal''', 268, 165-184]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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</table>
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<!--
              HENRICH & CHANDRASEKHAR 1941
-->
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
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[http://www.vistrails.org/index.php/File:HenrichChandra41b.jpg Image:HenrichChandra41b.jpg] <font color="red">(repeat)</font>
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  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">L. R. Henrich &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Stellar Models with Isothermal Cores''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1941ApJ....94..525H 1941, '''The Astrophysical Journal''', 94, 525-536]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</table>
  </td>
</tr>
<!--
              SCHONBERG & CHANDRASEKHAR 1942
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:SC42_Fig1.jpg Image:SC42_Fig1.jpg] <font color="red">(repeat)</font>
&nbsp;
[http://www.vistrails.org/index.php/File:SC42excerpt.jpg Text:SC42excerpt.jpg] <font color="red">(repeat)</font>
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">M. Sch&ouml;nberg &amp; S. Chandrasekhar</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''On the Evolution of the Main-Sequence Stars''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1942ApJ....96..161S 1942, '''The Astrophysical Journal''', 96, 161-172]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
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</table>
  </td>
</tr>
<!--
              DARWIN 1906 
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:DarwinPreface.png Text:DarwinPreface.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Darwin1906Eq1b.png Eqns:Darwin1906Eq1b.png];
&nbsp;
[http://www.vistrails.org/index.php/File:DarwinText01.png Text:DarwinText01.png];
&nbsp;
[http://www.vistrails.org/index.php/File:DarwinText02.png Text:DarwinText02.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">G. H. Darwin</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''IV. &nbsp;On the Figure and Stability of a Liquid Satellite''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[https://royalsocietypublishing.org/doi/abs/10.1098/rsta.1906.0018 1906, '''Philosophical Transactions of the Royal Society A''', 268, 165-184]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">Royal Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">The Royal Society Publishing</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
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</table>
  </td>
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<!--
              LRS-Supplement 1993 
-->
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  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
  <td align="left" colspan="2">   
[http://www.vistrails.org/index.php/File:LRS93SFig10.png Image:LRS93SFig10.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
  <td align="right" width="15%">Author(s):</td>
  <td align="left">D. Lai, F. A. Rasio &amp; S. L. Shapiro</td>
</tr>
<tr>
  <td align="right">Title:</td>
  <td align="left">''Ellipsoidal Figures of Equilibrium &#8212; Compressible Models''</td>
</tr>
<tr>
  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1993ApJS...88..205L 1993, '''The Astrophysical Journal Supplement Series''', 88, 205-252]</td>
</tr>
<tr>
  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
</tr>
<tr>
  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
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** CHAPTER: [[User:Tohline/SSC/Structure/Polytropes#Example_Interval|Isolated Polytropes (DFB)]]
  </td>
*** File:Murphy1983Extremum02.png
</tr>
<table border="0" align="center" width="90%" cellpadding="3">
<!--
              LRS-Letters 1993 
-->
<tr>
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
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[http://www.vistrails.org/index.php/File:LRS93BinarySequence.png Image:LRS93BinarySequence.png];
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<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">J. O. Murphy</td>
   <td align="left">D. Lai, F. A. Rasio &amp; S. L. Shapiro</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5''</td>
   <td align="left">''Hydrodynamic Instability and Coalescence of Close Binary Systems''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <td align="right">Reference:</td>
   <td align="left">[http://adsabs.harvard.edu/abs/1983PASAu...5..175M 1983, '''Proceedings of the Astronomical Society of Australia''', 5, 175-179]</td>
   <td align="left">[http://adsabs.harvard.edu/abs/1993ApJ...406L..63L 1993, '''Astrophysical Journal Letters''', 406, L63-L66]</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">American Society of Australia</td>
   <td align="left">American Astronomical Society</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
   <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</tr>
</table>
</table>
*** File:Mach2012Eqs.png
  </td>
** CHAPTER: [[User:Tohline/SSC/Structure/PolytropesEmbedded#Overlap_with_Whitworth.27s_Presentation|Embedded Polytropes (DFB)]]
</tr>
*** File:Horedt_EmbeddedPolytrope.png
<!--
*** File:WhitworthFig1bCopy.jpg
              New & Tohline 1997 
*** File:Horedt_EmbeddedPolytrope.png
-->
*** File:Whitworth1981TitlePage0.png
<tr>
*** File:Stahler1983TitlePage0.png
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
*** File:Stahler_MRdiagram1.png
  <td align="left" colspan="2">   
*** File:HoredtEq00.png
[http://www.vistrails.org/index.php/File:NewTohline97Fig1c.png Image:NewTohline97Fig1c.png];
*** File:HoredtEq01.png
  </td>
*** File:KimuraEq00.png
</tr>
*** File:KimuraEq01.png
<tr>
** CHAPTER:  [[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Isolated Isothermal Sphere (DFB)]]
  <td align="right" colspan="2" width="10%">&nbsp;</td>
*** File:EmdenBookCover1907.jpg
  <td align="left" colspan="2">
*** File:EmdenIsothermalDerivation.jpg
<table border="1" align="left" width="90%" cellpadding="3">
*** File:EmdenTable14.jpg
<tr>
** CHAPTER:  [[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Pressure-Truncated Isothermal Sphere (DFB)]]
  <td align="right" width="15%">Author(s):</td>
*** File:BonnorDerivation01.jpg
  <td align="left">K. C. B. New &amp; J. E. Tohline</td>
*** File:EbertDerivation01.jpg
</tr>
*** File:Bonnor1956Fig1reproduced.jpg
<tr>
*** File:EbertFig2Title.jpg
  <td align="right">Title:</td>
*** File:WhitworthFig1bFlipped.jpg
  <td align="left">''The Relative Stability Against Merger of Clos, compact Binaries''</td>
** CHAPTER: [[User:Tohline/SSC/Structure/LimitingMasses#Mass_Upper_Limits|Mass Upper Limits]]
</tr>
*** Image:SC42excerpt.jpg
<tr>
*** File:Stahler1983TitlePage0.png
  <td align="right">Reference:</td>
*** File:Stahler_MRdiagram1.png
  <td align="left">[http://adsabs.harvard.edu/abs/1997ApJ...490..311N 1997, '''The Astrophysical Journal''', 490, 311-327]</td>
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|BipolytropesDFB (Overview)]]
</tr>
*** Image:CowlingRE_Milne1931.jpg
<tr>
*** Image:SchonbergChandra1942.jpg
  <td align="right">Copyright:</td>
** CHAPTER: [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|BipolytropeDFB51]]
  <td align="left">American Astronomical Society</td>
*** Image:SC42_Fig1.jpg
</tr>
*** Image:HenrichChandra41b.jpg
<tr>
*** Image:HenrichChandra41a.jpg
  <td align="right">Publisher:</td>
*** Image:EagletonFaulknerCannon98.jpg
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
*** File:Buchdahl1978.png
</tr>
**CHAPTER: [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|BipolytropeDFB15]]
<tr>
*** File:Table3CompleteCol1.png
  <td align="right">Permission:</td>
*** File:Table3CompleteCol2.png
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*** File:Table3CompleteCol3.png
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*** File:Table3CompleteCol4.png
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*** File:Table3CompleteCol5.png
  </td>
*** File:Table3CompleteCol6.png
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*** File:MF85Table1.png
<!--
** CHAPTER: [[User:Tohline/SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|Isolated Polytropes (Virial)]]
              H_BOOK
*** File:Whitworth1981Eq5.jpg
-->
** CHAPTER:  [[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|Embedded Polytropes (Virial)]]
<tr>
*** File:Whitworth1981Eq10.jpg
  <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
*** File:Whitworth1981Eq5.jpg
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*** File:EnergyRadiusViewCombined5.png (1/4 of this image extracted from Whitworth's work)
[http://www.vistrails.org/index.php/File:EvolutionArrows01.png Image:EvolutionArrows01.png];
** CHAPTER: [[User:Tohline/SSC/Virial/Isothermal|Isothermal (Virial)]]
&nbsp;
*** File:Bonnor1951Eq1.2.jpg
[http://www.vistrails.org/index.php/File:CaseMcompareTogether.png Image:CaseMcompareTogether.png];
*** File:WhitworthFig1aCopy.jpg
&nbsp;
[http://www.vistrails.org/index.php/File:MimicStahlerPlot3.png Image:MimicStahlerPlot3.png];
&nbsp;
[http://www.vistrails.org/index.php/File:TruncatedPolytropeMvsR2.png Image:TruncatedPolytropeMvsR2.png];
<br />
[http://www.vistrails.org/index.php/File:SC_42EvolutionArrows.png Image:SC_42EvolutionArrows.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Qvsnu51b2.png Image:Qvsnu51b2.png];
&nbsp;
[http://www.vistrails.org/index.php/File:BinarySimpleModel02.png Image:BinarySimpleModel02.png];
&nbsp;
[http://www.vistrails.org/index.php/File:DarwinP1compare.png Image:DarwinP1compare.png];
&nbsp;
[http://www.vistrails.org/index.php/File:P0Diagram.png Image:P0Diagram.png];
  </td>
</tr>
<tr>
  <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left" colspan="2">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
  <td align="left">Created by the author (J. E. Tohline) for inclusion in this H_Book, ''The Structure, Stability &amp; Dynamics of Self-Gravitating Fluids''.</td>
</tr>
</table>
  </td>
</tr>
 
</table>
 
=Copyright Policies=
 
==Journals==
 
 
<div id="ApJ">
* The Astrophysical Journal (AAS)
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Excerpts from Online Instructions (verbatim text printed in dark green):
 
<font color="darkgreen">Permission to reproduce material from articles published in ''The Astronomical Journal'' or ''The Astrophysical Journal'' or ''The Astrophysical Journal Letters'' or ''The Astrophysical Journal Supplement'' or ''Research Notes of the American Astronomical Society'' is managed on behalf of the AAS by IOP Publishing. In order to gain permission to reproduce material under AAS copyright, you should do the following:
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* Philosophical Transactions of the Royal Society A
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* Journal of Mathematical Physics (AIP)
* Zeitschrift f&uuml;r Astrophysik
 
==Books==
* Shapiro & Teukolsky


=See Also=
=See Also=

Latest revision as of 17:22, 19 July 2020

Images (to be) Displayed in this H_Book

This replaces an earlier Appendix/Images2016Layout wiki page.

Whitworth's (1981) Isothermal Free-Energy Surface
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |

SECTION:  Preamble, Contents, etc.

  WIKI CHAPTER: Preface
  WIKI CHAPTER: Pictorial Table of Contents
🔵

Image:Graphical_Content_SSC.jpg

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
 

SECTION:  Governing Physics

  WIKI CHAPTER: Principal Governing Equations     …     Archived on MacHD2 on 2020/01/31 as: A000a.txt Principal Governing Equations (PGEs) : TILED MENU icon(s)
  WIKI CHAPTER: Continuity Equation     …     Archived on MacHD2 on 2020/01/31 as: A000b.txt Continuity : TILED MENU icon(s)
  WIKI CHAPTER: Euler Equation     …     Archived on MacHD2 on 2020/01/31 as: A000c.txt Euler : TILED MENU icon(s)
  WIKI CHAPTER: First Law of Thermodynamics     …     Archived on MacHD2 on 2020/01/31 as: A000d.txt 1st Law of Thermodynamics : TILED MENU icon(s)
  WIKI CHAPTER: Origin of the Poisson Equation     …     Archived on MacHD2 on 2020/01/31 as: A000e.txt Poisson : TILED MENU icon(s)
  WIKI CHAPTER: Rotating Reference Frame     …     Archived on MacHD2 on 2020/01/31 as: C000c.txt
  WIKI CHAPTER: Hybrid Advection Scheme (Preface)     …     Archived on MacHD2 on 2020/01/31 as: E000b.txt
  WIKI CHAPTER: Hybrid Advection Scheme (Background circa 2000)     …     Archived on MacHD2 on 2020/01/31 as: E000a.txt
  WIKI CHAPTER: Jay Call's Hybrid Scheme     …     Archived on MacHD2 on 2020/01/31 as: B000t.txt
🔴

Eqns:NormanWilson78D.png — (embedded in wiki chapter here)

 
Author(s): M. L. Norman & J. R. Wilson
Title: The Fragmentation of Isothermal Rings and Star Formation
Reference: 1978, The Astrophysical Journal, 224, 497-511
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵

Eqns:NewTohline97C.png — (embedded in wiki chapter here)

 
Author(s): K. C. B. New & J. E. Tohline
Title: The Relative Stability Against Merger of Close, Compact Binaries
Reference: 1997, The Astrophysical Journal, 490, 311-327
Copyright: The American Astronomical Society
Publisher: Institute of Physics Publishing
Permission: Granted by J.E.Tohline, who is one of the authors
  WIKI CHAPTER: Supplemental Relations     …     Archived on MacHD2 on 2020/01/31 as: A000g.txt Equation of State (EOS) : TILED MENU icon(s)
  WIKI CHAPTER: Ideal Gas Equation of State     …     Archived on MacHD2 on 2020/01/31 as: A000h.txt Ideal Gas : TILED MENU icon(s)
  WIKI CHAPTER: Total Pressure     …     Archived on MacHD2 on 2020/01/31 as: A000i.txt Total Pressure : TILED MENU icon(s)
  WIKI CHAPTER: Quartic Temperature Solution     …     Archived on MacHD2 on 2020/01/31 as: B001m.txt
  WIKI CHAPTER: Simple Rotation Profiles     …     Archived on MacHD2 on 2020/01/31 as: A004d.txt Simple Rotation Profiles : TILED MENU icon(s)
  WIKI CHAPTER: Global Energy Considerations     …     Archived on MacHD2 on 2020/01/31 as: A000f.txt Global Energy Considerations : TILED MENU icon(s)
 

SECTION:  Spherically Symmetric Configurations

  WIKI CHAPTER: Introduction     …     Archived on MacHD2 on 2020/01/31 as: A000j.txt One-Dimensional PGEs : TILED MENU icon(s)
  WIKI CHAPTER: Alternate Introduction     …     Archived on MacHD2 on 2020/01/31 as: C001a.txt
🎦

Animation:LSU_Stable.animated.gif;   see, also, an associated description

 
Animated gif created by the LSU astrophysics group in support of Figure 10 in the following publication:
 
Author(s): K. C. B. New & J. E. Tohline
Title: The Relative Stability Against Merger of Close, Compact Binaries
Reference: 1997, The Astrophysical Journal, 490, 311-327
Copyright: The American Astronomical Society
Publisher: Institute of Physics Publishing
Permission: Granted by J.E.Tohline, one of the authors
🎦

Animation:Minitorus.animated.gif

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
 

Detailed Force-Balanced (DFB) Models

  WIKI CHAPTER: DFB Introductory Summary     …     Archived on MacHD2 on 2020/01/31 as: C001c.txt Hydrodynamic Balance Equation : TILED MENU icon(s)
🔵

Image:FreeNRGpressureRadiusIsothermal.png;   Image:MassRadiusVirialLabeled.png;   Image:PlotSequencesBest02.png

Image:FreeNRGpressureRadiusIsothermal.png : TILED MENU icon(s)
 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: DFB Introduction (Part I)     …     Same as SECTION Introduction (i.e., archived file A000j.txt)
  WIKI CHAPTER: DFB Introduction (Part II)     …     Archived on MacHD2 on 2020/01/31 as: A000n.txt Hydrostatic Balance Equation || Solution Strategies : TILED MENU icon(s)

Chapter Group Isolated

  WIKI CHAPTER: Uniform-Density Sphere … Isolated (DFB)     …     Archived on MacHD2 on 2020/01/31 as: C001d.txt
  WIKI CHAPTER: Isothermal Sphere … Isolated (DFB)     …     Archived on MacHD2 on 2020/01/31 as: A000r.txt Isothermal Sphere || via Direct Numerical Integration : TILED MENU icon(s)
🔵

Title:EmdenBookCover1907.jpg;   Eqns:EmdenIsothermalDerivation.jpg;   Table:EmdenTable14.jpg

 
Author(s): Robert Emden
Book Title: Gaskugeln
Copyright: None active; originally 1907
Publisher: Digitized by Google (books.google.com); originally, Druck und Verlag von B. G. Teubner: Berlin
🔵

Image:IsothermalDensityPlot.jpg;   Image:EmdenMassProfile.jpg;   Image:PlotMeanToLocalDensity.jpg

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Polytropes … Isolated (DFB)     …     Archived on MacHD2 on 2020/01/31 as: A001a.txt
Isolated Polytropes || Known Analytic Solutions || via Direct Numerical Integration || via Self-Consistent Field (SCF) Technique : TILED MENU icon(s)
🔵

Image:PlotTheta5F.png (Shrivastava's n = 5 Lane-Emden Function)

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
🔵

Eqns:Murphy1983Extremum02.png; [This pair of equations appear in an "equation table", retyped as LaTeX equations.]

 
Author(s): J. O. Murphy
Title: Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5
Reference: 1983, Proceedings of the Astronomical Society of Australia, 5, 175-179
Copyright: Astronomical Society of Australia
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵;

Eqns:Mach2012Eqs.png; [This pair of equations appear in an "equation table", retyped as LaTeX equations.]

 
Author(s): P. Mach
Title: All Solutions of the n = 5 Lane-Emden Equation
Reference: 2012, Journal of Mathematical Physics, 53, 062503-062503-6
Copyright: American Institute of Physics
Publisher: Provided by the NASA Astrophysics Data System
Permission:
  TILED CHAPTER: Lane (1870)     …     Archived on MacHD2 on 2020/01/31 as: A001b.txt Lane (1870) : TILED MENU icon(s)


  WIKI CHAPTER: Zero-temperature White Dwarf …Overview Zero-Temperature White Dwarf || Chandrasekhar Limiting Mass (1935) : TILED MENU icon(s)
🔵

Eqn:ST83Eq3_3_11.png;   Eqn:ST83Eq3_3_12.png;   Eqn:ST83Eq2_3_23.png; [All 3 appear in an "equation table", retyped as LaTeX equations.]

 
Author(s): S. L. Shapiro & S. A. Teukolsky
Book Title: Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects
Copyright: 1983
Publisher: New York: John Wiley & Sons
Permission:
  WIKI CHAPTER: Power-law Density Distribution …Overview
  WIKI CHAPTER: Other Analytically Definable Models

Chapter Group Pressure-Truncated

  WIKI CHAPTER: Uniform-Density Sphere … Pressure-Truncated (DFB)
  WIKI CHAPTER: Isothermal Sphere … Pressure-Truncated (DFB);   Familiarly, a Bonnor-Ebert Sphere Bonnor-Ebert (Isothermal) Spheres (1955 - 56) : TILED MENU icon(s)
🔴

Eqns:EbertDerivation01.jpg;   Image:EbertFig2Title.jpg; [The first of these images appears in an "equation table", retyped as text & LaTeX equations.]

 
Author(s): R. Ebert
Title: Über die Verdichtung von HI-Gebieten
Reference: 1955, Zeitschrift für Astrophysik, 37, 217-232
Copyright:
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵

Eqns:BonnorDerivation01.jpg;   Image:Bonnor1956Fig1reproduced.jpg; [The first of these images appears in an "equation table", retyped as text & LaTeX equations.]

 
Author(s): W. B. Bonnor
Title: Boyle's Law and Gravitational Instability
Reference: 1956, Monthly Notices of the Royal Astronomical Society, 116, 351-359
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵

Image:WhitworthFig1bCopy.jpg;   Image:WhitworthFig1bFlippedClipped.png

 
Author(s): A. Whitworth
Title: Global Gravitational Stability for One-dimensional Polytropes
Reference: 1981, Monthly Notices of the Royal Astronomical Society, 195, 967-977
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵

Image:Bonnor1956Fig1EmdenDataCleaner.png;   Image:EbertFig2UsingEmdenData2.jpg;   Image:Bonnor1956DPDVplot.jpg;   Image:WhitworthFig1bUsingEmdenData.png

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Polytropes … Pressure-Truncated (DFB) Polytropes : TILED MENU icon(s)
🔴

Image:Horedt_PRdiagram0.png;   Title:Horedt_EmbeddedPolytrope.png;   Eqns:HoredtEq00.png;   Eqns:HoredtEq01.png

 
Author(s): Gp. Horedt
Title: Gravitational Instability of Polytropic Gas Spheres Under External Pressure
Reference: 1970, Monthly Notices of the Royal Astronomical Society, 151, 81-86
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Image:WhitworthFig1bCopy.jpg;   Title:Whitworth1981TitlePage0.png

 
Author(s): A. Whitworth
Title: Global Gravitational Stability for One-dimensional Polytropes
Reference: 1981, Monthly Notices of the Royal Astronomical Society, 195, 967-977
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Eqns:KimuraEq00.png;   Eqns:KimuraEq01.png

 
Author(s): H. Kimura
Title: A Study of Simple Polytropes — Part Two — Stability Against Homologous Constraction
Reference: 1981, Publications of the Astronomical Society of Japan, 33, 299-312
Copyright: Astronomical Society of Japan
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Title:Stahler1983TitlePage0.png;   Image:Stahler_MRdiagram1.png SCHEMATIC (appears twice)

 
Author(s): S. W. Stahler
Title: The Equilibria of Rotating Isotherma Clouds — Part Two — Structure and Dynamical Stability
Reference: 1983, The Astrophysical Journal, 268, 165-184
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔵

Image:HoredtPlot2.png;   Image:WhitworthPlot2.png;   Image:Stahler1983Comparison.png;   Image:DFBsequenceB.png

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Marginally Unstable Pressure-Truncated Gas Clouds  Equilibrium Sequence Turning-Points : TILED MENU icon(s)
🔵

Image:IsothermalTrunc4.png;   Image:IsothermalTrunc12.png;   Image:IsothermalTrunc11.png;
Image:Yabushita1975Combined.png;   Image:MassVsRadiusCombined02.png;   Image:YabushitaMontageB.png;

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.

Chapter Group Bipolytropes

  WIKI CHAPTER: BiPolytropes (also referred to as Composite Polytropes) … Overview
🔴

Text:CowlingRE_Milne1931.jpg

 
Author(s): T. G. Cowling
Title: Note on the Fitting of Polytropic Models in the Theory of Stellar Structure
Reference: 1931, Monthly Notices of the Royal Astronomical Society, 91, 472-478
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Text:SchonbergChandra1942.jpg

 
Author(s): M. Schönberg & S. Chandrasekhar
Title: On the Evolution of the Main-Sequence Stars
Reference: 1942, The Astrophysical Journal, 96, 161-172
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
  WIKI CHAPTER: Zero-Zero Bipolytrope (DFB)
🔵

Image:BipolytropeDynamicalStability2.png;

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Five-One Bipolytrope (DFB)
🔵

Image:DenXi05.jpg;   Image:DenXi10.jpg;   Image:DenXi30.jpg;
Image:PresXi05.jpg;   Image:PresXi10.jpg;   Image:PresXi30.jpg;
Image:MassXi05.jpg;   Image:MassXi10.jpg;   Image:MassXi30.jpg;
Image:PlotSequencesBest02.png;   Image:SC_42Comparison.jpg;   Image:PlotStabilityBest02.png

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
🔴

Image:SC42_Fig1.jpg

 
Author(s): M. Schönberg & S. Chandrasekhar
Title: On the Evolution of the Main-Sequence Stars
Reference: 1942, The Astrophysical Journal, 96, 161-172
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Image:HenrichChandra41b.jpg   Text:HenrichChandra41a.jpg

 
Author(s): L. R. Henrich & S. Chandrasekhar
Title: Stellar Models with Isothermal Cores
Reference: 1941, The Astrophysical Journal, 94, 525-536
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Text:EagletonFaulknerCannon98.jpg

 
Author(s): P. P. Eggleton, J. Faulkner, & R. C. Cannon
Title: A Small Contribution to the Giant Problem
Reference: 1998, Monthly Notices of the Royal Astronomical Society, 298, 831-834
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Eqn:Buchdahl1978.png

 
Author(s): H. A. BUCHDAHL
Title: Remark on the Polytrope of Index 5
Reference: 1978, Australian Journal of Physics, 31, 115-116
Copyright: CSIRO Publishing
Publisher: Provided by the NASA Astrophysics Data System
Permission:
  WIKI CHAPTER: One-Five Bipolytrope (DFB)
🔵

Image:MurphyF2roots05.png;   Image:InterfaceMap02.png;   Image:MurphyPhysicallyViableTable3d.png;
Image:DenXi05.jpg;   Image:DenXi10.jpg;   Image:DenXi30.jpg;
Image:PresXi05.jpg;   Image:PresXi10.jpg;   Image:PresXi30.jpg;
Image:MassXi05.jpg;   Image:MassXi10.jpg;   Image:MassXi30.jpg;
Table:MF85Table1byTohline02.png;

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
🔴

TableColumn:Table3CompleteCol1.png;   TableColumn:Table3CompleteCol2.png;   TableColumn:Table3CompleteCol3.png;
TableColumn:Table3CompleteCol4.png;   TableColumn:Table3CompleteCol5.png;   TableColumn:Table3CompleteCol6.png

 
Author(s): J. O. Murphy
Title: Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5
Reference: 1983, Proceedings of the Astronomical Society of Australia, 5, 175-179
Copyright: Astronomical Society of Australia
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

Table:MF85Table1.png

 
Author(s): J. O. Murphy & R. Fiedler
Title: Physical Structure of a Sequence of Two Zone Polytropic Stellar Models
Reference: 1985, Proceedings of the Astronomical Society of Australia, 6, 219-222
Copyright: Astronomical Society of Australia
Publisher: Provided by the NASA Astrophysics Data System
Permission:
  WIKI CHAPTER: The Milne Bipolytrope (DFB)
🔴

Eqns:CoreRelations01.png;   Eqns:EnvelopeRelations01.png

 
Author(s): E. A. Milne
Title: The Analysis of Stellar Structure
Reference: 1930, Monthly Notices of the Royal Astronomical Society, 91, 4-55
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:


 

Virial Equilibrium Configurations

  WIKI CHAPTER: Introduction Free-Energy of Spherical Systems || Scalar Virial Theorem : TILED MENU icon(s)
🔵

Image:3DFreeEnergy.jpg

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
🔵

Eqns:Tohline1985_Eq9.png

 
Author(s): J. E. Tohline
Title: Star Formation: Phase Transition, not Jeans Instability
Reference: 1985, The Astrophysical Journal, 292, 181-187
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission: Granted by J.E.Tohline, who is the sole author
🔴

Eqns:Weber1976_EqB3.png

 
Author(s): S. V. Weber
Title: Oscillation and Collapse of Interstellar Clouds
Reference: 1976, The Astrophysical Journal, 208, 113-126
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:


  WIKI CHAPTER: Structural Form Factors Structural Form Factors : TILED MENU icon(s)
🔴

Eqns:VialaHoredt1974.png

 
Author(s): Y. P. Viala & Gp. Horedt
Title: Polytropic Sheets, Cylinders and Spheres with Negative Index
Reference: 1974, Astronomy and Astrophysics, 33, 195-202
Copyright: European Southern Observatory
Publisher: Provided by the NASA Astrophysics Data System
Permission:


  WIKI CHAPTER: Virial Equilibrium of Isolated Polytropic Spheres
🔴

Eqns:Whitworth1981Eq5.jpg (repeat)

 
Author(s): A. Whitworth
Title: Global Gravitational Stability for One-dimensional Polytropes
Reference: 1981, Monthly Notices of the Royal Astronomical Society, 195, 967-977
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
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  WIKI CHAPTER: Virial Equilibrium of Isothermal Spheres
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TxtEqns:Bonnor1951Eq1.2.jpg;

 
Author(s): W. B. Bonnor
Title: Boyle's Law and Gravitational Instability
Reference: 1956, Monthly Notices of the Royal Astronomical Society, 116, 351-
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:WhitworthFig1aCopy.jpg

 
Author(s): A. Whitworth
Title: Global Gravitational Stability for One-dimensional Polytropes
Reference: 1981, Monthly Notices of the Royal Astronomical Society, 195, 967-977
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:Bonnor1956Fig1.jpg;   Image:WhitworthLogFig1a_norm.jpg;

 
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  WIKI CHAPTER: Virial Equilibrium of Embedded Polytropic Spheres FreeNRGpressureRadiusIsothermal.png : TILED MENU icon(s)
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Eqns:Whitworth1981Eq10.jpg;   Eqns:Whitworth1981Eq5.jpg (repeat)   Image:EnergyRadiusViewBottom6.png (half of this image is Whitworth figure);

 
Author(s): A. Whitworth
Title: Global Gravitational Stability for One-dimensional Polytropes
Reference: 1981, Monthly Notices of the Royal Astronomical Society, 195, 967-977
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:FreeNRGmassRadiusN5.png;   Image:FreeNRGpressureRadiusIsothermal.png;
Image:EnergyRadiusViewTop5.png;   Animation:FEmovie02.gif;   Image:EnergyRadiusViewBottom6.png (half of this image is Whitworth figure);
… or …     Image:EnergyRadiusViewCombined5.png;

 
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  WIKI CHAPTER: Style-Sheet Synopsis Style-Sheet Synopsis : TILED MENU icon(s)
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Summaries

  WIKI CHAPTER: Limiting Masses … Summary
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Text:SC42excerpt.jpg

 
Author(s): M. Schönberg & S. Chandrasekhar
Title: On the Evolution of the Main-Sequence Stars
Reference: 1942, The Astrophysical Journal, 96, 161-172
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Title:Stahler1983TitlePage0.png (repeat);   Image:Stahler_MRdiagram1.png SCHEMATIC (repeat)

 
Author(s): S. W. Stahler
Title: The Equilibria of Rotating Isotherma Clouds — Part Two — Structure and Dynamical Stability
Reference: 1983, The Astrophysical Journal, 268, 165-184
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:MassRadiusVirialLabeled.png;   Image:Stahler1983Comparison.png (repeat);   Image:PlotSequencesBest02.png (repeat)

 
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  WIKI CHAPTER: Turning Points Turning-Points (Broader Context) : TILED MENU icon(s)
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Image:EbertFig2Title.jpg (repeat)

 
Author(s): R. Ebert
Title: Über die Verdichtung von HI-Gebieten
Reference: 1955, Zeitschrift für Astrophysik, 37, 217-232
Copyright:
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Image:Bonnor1956Fig1reproduced.jpg (repeat)

 
Author(s): W. B. Bonnor
Title: Boyle's Law and Gravitational Instability
Reference: 1956, Monthly Notices of the Royal Astronomical Society, 116, 351-
Copyright: Royal Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:Stahler_MRdiagram1.png SCHEMATIC (repeat);

 
Author(s): S. W. Stahler
Title: The Equilibria of Rotating Isotherma Clouds — Part Two — Structure and Dynamical Stability
Reference: 1983, The Astrophysical Journal, 268, 165-184
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
Permission:
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Image:HenrichChandra41b.jpg (repeat)

 
Author(s): L. R. Henrich & S. Chandrasekhar
Title: Stellar Models with Isothermal Cores
Reference: 1941, The Astrophysical Journal, 94, 525-536
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:SC42_Fig1.jpg (repeat)   Text:SC42excerpt.jpg (repeat)

 
Author(s): M. Schönberg & S. Chandrasekhar
Title: On the Evolution of the Main-Sequence Stars
Reference: 1942, The Astrophysical Journal, 96, 161-172
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Text:DarwinPreface.png;   Eqns:Darwin1906Eq1b.png;   Text:DarwinText01.png;   Text:DarwinText02.png;

 
Author(s): G. H. Darwin
Title: IV.  On the Figure and Stability of a Liquid Satellite
Reference: 1906, Philosophical Transactions of the Royal Society A, 268, 165-184
Copyright: Royal Society
Publisher: The Royal Society Publishing
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Image:LRS93SFig10.png;

 
Author(s): D. Lai, F. A. Rasio & S. L. Shapiro
Title: Ellipsoidal Figures of Equilibrium — Compressible Models
Reference: 1993, The Astrophysical Journal Supplement Series, 88, 205-252
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:LRS93BinarySequence.png;

 
Author(s): D. Lai, F. A. Rasio & S. L. Shapiro
Title: Hydrodynamic Instability and Coalescence of Close Binary Systems
Reference: 1993, Astrophysical Journal Letters, 406, L63-L66
Copyright: American Astronomical Society
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Image:NewTohline97Fig1c.png;

 
Author(s): K. C. B. New & J. E. Tohline
Title: The Relative Stability Against Merger of Clos, compact Binaries
Reference: 1997, The Astrophysical Journal, 490, 311-327
Copyright: American Astronomical Society
Publisher: Provided by the NASA Astrophysics Data System
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Image:EvolutionArrows01.png;   Image:CaseMcompareTogether.png;   Image:MimicStahlerPlot3.png;   Image:TruncatedPolytropeMvsR2.png;
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See Also

Whitworth's (1981) Isothermal Free-Energy Surface

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