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(→‎Detailed Force-Balanced (DFB) Models: Finished chapter reviewing Milne's first bipolytrope)
 
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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}}
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==Generated by Tohline or an Immediate Collaborator==
*SECTION:  Spherically Symmetric Configurations
** CHAPTER:  [[User:Tohline/SSC/Structure/LimitingMasses#Mass_Upper_Limits|Mass Upper Limits]]
*** Image:MassRadiusVirialLabeled.png
*** File:Stahler1983Comparison.png
*** Image:PlotSequencesBest02.png
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|BipolytropeDFB00]]
*** Image:BipolytropeDynamicalStability2.png
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|BipolytropeDFB51]]
*** 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
**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; Preamble, Contents, etc.==
==SECTION:&nbsp; Preamble, Contents, etc.==
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE#Principal_Governing_Equations|Principle Governing Equations]]</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>
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  <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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity Equation]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/Euler#Euler_Equation|Euler Equation]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <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]]</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>
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  <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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/Hybrid_Scheme_Preface#Hybrid_Advection_Scheme_.28Preface.29|Hybrid Advection Scheme (Preface)]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <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)]]</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>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/PGE/Hybrid_Scheme#Hybrid_Advection_Scheme|Jay Call's Hybrid Scheme]]</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="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SR#Supplemental_Relations|Supplemental Relations]]</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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   <td align="left" colspan="1" width="5%">&nbsp;</td>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SR/PressureCombinations#Total_Pressure|Total Pressure]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SR/Ptot_QuarticSolution#Determining_Temperature_from_Density_and_Pressure|Quartic Temperature Solution]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|Simple Rotation Profiles]]</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>
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   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/VE#Global_Energy_Considerations|Global Energy Considerations]]</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>
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  <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>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations_.28Part_I.29|Introduction]]
   <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>
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   <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|One-Dimensional PGEs]] : TILED MENU icon(s)</td>
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations#Spherically_Symmetric_Configurations|Alternate Introduction]]
   <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>
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===Detailed Force-Balanced (DFB) Models===
===Detailed Force-Balanced (DFB) Models===
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/IntroductorySummary#Applications|DFB Introductory Summary]]
   <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>
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  <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];  
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/PGE#Spherically_Symmetric_Configurations_.28Part_I.29|DFB Introduction (Part I)]]
   <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>)
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  <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies#Spherically_Symmetric_Configurations_.28Part_II.29|DFB Introduction (Part II)]]
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   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/UniformDensity#Isolated_Uniform-Density_Sphere|Uniform-Density Sphere &hellip; Isolated (DFB)]]
   <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>
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   <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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   <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)]]
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====Chapter Group Isolated====


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   <td align="left" colspan="3">WIKI CHAPTER: [[User:Tohline/SSC/Structure/Polytropes#Polytropic_Spheres|Polytropes &hellip; Isolated (DFB)]]</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>
[http://www.vistrails.org/index.php/File:PlotTheta5F.png Image:PlotTheta5F.png] (Shrivastava's n = 5 Lane-Emden Function)
   <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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  <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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[http://www.vistrails.org/index.php/File:Murphy1983Extremum02.png Eqns:Murphy1983Extremum02.png]
[http://www.vistrails.org/index.php/File:EmdenBookCover1907.jpg Title:EmdenBookCover1907.jpg];
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[http://www.vistrails.org/index.php/File:EmdenIsothermalDerivation.jpg Eqns:EmdenIsothermalDerivation.jpg];
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[https://www.vistrails.org/index.php/File:EmdenTable14.jpg Table:EmdenTable14.jpg]
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   <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">Robert Emden</td>
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   <td align="right">Title:</td>
   <td align="right">Book 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">[https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover&hl=en#v=onepage&q&f=true ''Gaskugeln'']</td>
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  <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>
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   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">Astronomical Society of Australia</td>
   <td align="left">None active; originally 1907</td>
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<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">Digitized by Google (books.google.com); originally, Druck und Verlag von B. G. Teubner: Berlin</td>
</tr>
<tr>
  <td align="right">Permission:</td>
  <td align="left">&#8212;</td>
</tr>
</tr>
</table>
</table>
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<!--  
<!--  
               MACH 2012
               H_BOOK
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:Mach2012Eqs.png Eqns:Mach2012Eqs.png]
[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>
   </td>
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   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
<table border="1" align="left" width="90%" cellpadding="3">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <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>
  <td align="left">P. Mach</td>
</tr>
</table>
  </td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left">''All Solutions of the n = 5 Lane-Emden Equation''</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>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
  <td align="left">[http://adsabs.harvard.edu/abs/2012JMP....53f2503M 2012, '''Journal of Mathematical Physics''', 53, 062503-062503-6]</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left">American Institute of Physics</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>
<tr>
<tr>
   <td align="right">Publisher:</td>
   <td align="right" colspan="2" width="10%">&nbsp;</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" colspan="2">  
</tr>
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
<tr>
  <td align="right">Permission:</td>
   <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>
   <td align="left">&#8212;</td>
</tr>
</tr>
</table>
</table>
   </td>
   </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/PolytropesEmbedded#Overlap_with_Whitworth.27s_Presentation|Polytropes &hellip; Pressure-Truncated (DFB)]]</td>
</tr>
</tr>
<!--  
<!--  
               HOREDT 1970
               MURPHY 1983
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:Horedt_PRdiagram0.png Image:Horedt_PRdiagram0.png];
[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.]
&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>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">Gp. Horedt</td>
   <td align="left">J. O. Murphy</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''Gravitational Instability of Polytropic Gas Spheres Under External Pressure''</td>
   <td align="left">''Composite and Analytical Solutions of the Lane-Emden Equation with Polytropic Indices N=1 and N=5''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
   <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>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">Royal Astronomical Society</td>
   <td align="left">Astronomical Society of Australia</td>
</tr>
</tr>
<tr>
<tr>
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</tr>
</tr>
<!--  
<!--  
               WHITWORTH 1981
               MACH 2012
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:WhitworthFig1bCopy.jpg Image:WhitworthFig1bCopy.jpg];
[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.]
&nbsp;
[http://www.vistrails.org/index.php/File:Whitworth1981TitlePage0.png Title:Whitworth1981TitlePage0.png]
   </td>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">A. Whitworth</td>
   <td align="left">P. Mach</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
   <td align="left">''All Solutions of the n = 5 Lane-Emden Equation''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
   <td align="left">[http://adsabs.harvard.edu/abs/2012JMP....53f2503M 2012, '''Journal of Mathematical Physics''', 53, 062503-062503-6]</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">Royal Astronomical Society</td>
   <td align="left">American Institute of Physics</td>
</tr>
</tr>
<tr>
<tr>
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</tr>
</tr>
<!--  
<!--  
               KIMURA 1981
               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>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">      
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:KimuraEq00.png Eqns:KimuraEq00.png];
[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;
&nbsp;
[http://www.vistrails.org/index.php/File:KimuraEq01.png Eqns:KimuraEq01.png]
[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>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">H. Kimura</td>
   <td align="left">S. L. Shapiro &amp; S. A. Teukolsky</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Book Title:</td>
   <td align="left">''A Study of Simple Polytropes &#8212; Part Two &#8212; Stability Against Homologous Constraction''</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>
<tr>
<tr>
  <td align="right">Reference:</td>
   <td align="right">Copyright:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981PASJ...33..299K 1981, '''Publications of the Astronomical Society of Japan''', 33, 299-312]</td>
   <td align="left">1983</td>
</tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="left">Astronomical Society of Japan</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">New York: John Wiley &amp; Sons</td>
</tr>
</tr>
<tr>
<tr>
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   </td>
   </td>
</tr>
</tr>
<!--
              STAHLER 1983
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/PowerLawDensity#Power-Law_Density_Distributions|Power-law Density Distribution &hellip;Overview]]
[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]
   </td>
   </td>
</tr>
</tr>
<tr>
<tr>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="2">
   <td align="left" colspan="3">WIKI CHAPTER:   [[User:Tohline/SSC/Structure/Other_Analytic_Models|Other Analytically Definable Models]]
<table border="1" align="left" width="90%" cellpadding="3">
   </td>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">S. W. Stahler</td>
</tr>
</tr>
</table>
====Chapter Group Pressure-Truncated====
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left">''The Equilibria of Rotating Isotherma Clouds &#8212; Part Two &#8212; Structure and Dynamical Stability''</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>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="right">Reference:</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left">[http://adsabs.harvard.edu/abs/1983ApJ...268..165S 1983, '''The Astrophysical Journal''', 268, 165-184]</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>
</tr>
<!--
              EBERT 1955
-->
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left">American Astronomical Society</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>
<tr>
<tr>
   <td align="right">Publisher:</td>
  <td align="right" colspan="2" width="10%">&nbsp;</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" 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>
<tr>
<tr>
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</tr>
<!--  
<!--  
               H_BOOK
               BONNOR 1956
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:HoredtPlot2.png Image:HoredtPlot2.png];
[http://www.vistrails.org/index.php/File:BonnorDerivation01.jpg Eqns:BonnorDerivation01.jpg];
&nbsp;
[http://www.vistrails.org/index.php/File:WhitworthPlot2.png Image:WhitworthPlot2.png];
&nbsp;
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png]
[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>
   </td>
</tr>
</tr>
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   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
<table border="1" align="left" width="90%" cellpadding="5">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
<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>
  <td align="right" width="15%">Author(s):</td>
   <td align="left">W. B. Bonnor</td>
</tr>
</tr>
</table>
<tr>
   </td>
  <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>
</tr>
</table>
</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/IsothermalSphere#Isothermal_Sphere|Isothermal Sphere &hellip; Isolated (DFB)]]
   </td>
   </td>
</tr>
</tr>
<!--  
<!--  
               EMDEN 1907
               WHITWORTH 1981
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:EmdenBookCover1907.jpg Title:EmdenBookCover1907.jpg];
[http://www.vistrails.org/index.php/File:WhitworthFig1bCopy.jpg Image:WhitworthFig1bCopy.jpg];
&nbsp;
&nbsp;
[http://www.vistrails.org/index.php/File:EmdenIsothermalDerivation.jpg Eqns:EmdenIsothermalDerivation.jpg];
[http://www.vistrails.org/index.php/File:WhitworthFig1bFlippedClipped.png Image:WhitworthFig1bFlippedClipped.png]
&nbsp;
[https://www.vistrails.org/index.php/File:EmdenTable14.jpg Table:EmdenTable14.jpg]
   </td>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">Robert Emden</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>
<tr>
<tr>
   <td align="right">Book Title:</td>
   <td align="right">Reference:</td>
   <td align="left">[https://books.google.com/books?id=MiDQAAAAMAAJ&printsec=frontcover&hl=en#v=onepage&q&f=true ''Gaskugeln'']</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>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">None active; originally 1907</td>
   <td align="left">Royal Astronomical Society</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Publisher:</td>
   <td align="right">Publisher:</td>
   <td align="left">Digitized by Google (books.google.com); originally, Druck und Verlag von B. G. Teubner: Berlin</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>
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   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[https://www.vistrails.org/index.php/File:IsothermalDensityPlot.jpg Image:IsothermalDensityPlot.jpg];
[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;
&nbsp;
[https://www.vistrails.org/index.php/File:EmdenMassProfile.jpg Image:EmdenMassProfile.jpg];
[https://www.vistrails.org/index.php/File:Bonnor1956DPDVplot.jpg Image:Bonnor1956DPDVplot.jpg];
&nbsp;
&nbsp;
[http://www.vistrails.org/index.php/File:PlotMeanToLocalDensity.jpg Image:PlotMeanToLocalDensity.jpg]
[http://www.vistrails.org/index.php/File:WhitworthFig1bUsingEmdenData.png Image:WhitworthFig1bUsingEmdenData.png]
   </td>
   </td>
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   </td>
   </td>
</tr>
</tr>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">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 align="left" colspan="2">WIKI CHAPTER: [[User:Tohline/SSC/Structure/PolytropesEmbedded#Overlap_with_Whitworth.27s_Presentation|Polytropes &hellip; Pressure-Truncated (DFB)]]</td>
  </td>
  <td align="right" colspan="1">[[User:Tohline/H_BookTiledMenu#Spherically_Symmetric_Configurations|Polytropes]] : TILED MENU icon(s)</td>
</tr>
</tr>
<!--  
<!--  
               EBERT 1955
               HOREDT 1970
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:EbertDerivation01.jpg Eqns:EbertDerivation01.jpg];  
[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;
&nbsp;
[http://www.vistrails.org/index.php/File:EbertFig2Title.jpg Image:EbertFig2Title.jpg];
[http://www.vistrails.org/index.php/File:HoredtEq01.png Eqns:HoredtEq01.png]
   </td>
   </td>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">R. Ebert</td>
   <td align="left">Gp. Horedt</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''&Uuml;ber die Verdichtung von HI-Gebieten''</td>
   <td align="left">''Gravitational Instability of Polytropic Gas Spheres Under External Pressure''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
   <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>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">&#8212;</td>
   <td align="left">Royal Astronomical Society</td>
</tr>
</tr>
<tr>
<tr>
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</tr>
</tr>
<!--  
<!--  
               BONNOR 1956
               WHITWORTH 1981
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:BonnorDerivation01.jpg Eqns:BonnorDerivation01.jpg];
[http://www.vistrails.org/index.php/File:WhitworthFig1bCopy.jpg Image:WhitworthFig1bCopy.jpg];
&nbsp;
&nbsp;
[http://www.vistrails.org/index.php/File:Bonnor1956Fig1reproduced.jpg Image:Bonnor1956Fig1reproduced.jpg]
[http://www.vistrails.org/index.php/File:Whitworth1981TitlePage0.png Title:Whitworth1981TitlePage0.png]
   </td>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">W. B. Bonnor</td>
   <td align="left">A. Whitworth</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''Boyle's Law and Gravitational Instability''</td>
   <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
   <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>
<tr>
<tr>
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</tr>
</tr>
<!--  
<!--  
               WHITWORTH 1981  
               KIMURA 1981  
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">      
[http://www.vistrails.org/index.php/File:WhitworthFig1bFlipped.jpg Image:WhitworthFig1bFlipped.jpg]
[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>
   </td>
</tr>
</tr>
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<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
   <td align="left">A. Whitworth</td>
   <td align="left">H. Kimura</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right">Title:</td>
   <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</td>
   <td align="left">''A Study of Simple Polytropes &#8212; Part Two &#8212; Stability Against Homologous Constraction''</td>
</tr>
</tr>
<tr>
<tr>
   <td align="right">Reference:</td>
   <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>
   <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>
<tr>
<tr>
   <td align="right">Copyright:</td>
   <td align="right">Copyright:</td>
   <td align="left">Royal Astronomical Society</td>
   <td align="left">Astronomical Society of Japan</td>
</tr>
</tr>
<tr>
<tr>
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</tr>
</tr>
<!--  
<!--  
               H_BOOK
               STAHLER 1983
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[https://www.vistrails.org/index.php/File:BonnorFig1usingEmdenData.jpg Image:BonnorFig1usingEmdenData.jpg];
[http://www.vistrails.org/index.php/File:Stahler1983TitlePage0.png Title:Stahler1983TitlePage0.png];
&nbsp;
[https://www.vistrails.org/index.php/File:EbertFig2UsingEmdenData2.jpg Image:EbertFig2UsingEmdenData2.jpg];
&nbsp;
&nbsp;
[https://www.vistrails.org/index.php/File:Bonnor1956DPDVplot.jpg Image:Bonnor1956DPDVplot.jpg]
[http://www.vistrails.org/index.php/File:Stahler_MRdiagram1.png Image:Stahler_MRdiagram1.png] <font color="red">'''SCHEMATIC''' (appears twice)</font>
   </td>
   </td>
</tr>
</tr>
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   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
<table border="1" align="left" width="90%" cellpadding="5">
<table border="1" align="left" width="90%" cellpadding="3">
<tr>
<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>
  <td align="right" width="15%">Author(s):</td>
   <td align="left">S. W. Stahler</td>
</tr>
</tr>
</table>
<tr>
   </td>
  <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>
</table>
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="right">Permission:</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Structure/WhiteDwarfs#White_Dwarfs|Zero-temperature White Dwarf &hellip;Overview]]
   <td align="left">&#8212;</td>
</tr>
</table>
   </td>
   </td>
</tr>
</tr>
<!--  
<!--  
               SHAPIRO & TEUKOLSKY 1983
               H_BOOK
-->
-->
<tr>
<tr>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:ST83Eq3_3_11.png Eqn:ST83Eq3_3_11.png];
[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;
&nbsp;
[http://www.vistrails.org/index.php/File:ST83Eq3_3_12.png Eqn:ST83Eq3_3_12.png];
[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png];
&nbsp;
&nbsp;
[http://www.vistrails.org/index.php/File:ST83Eq2_3_23.png Eqn:ST83Eq2_3_23.png];
[http://www.vistrails.org/index.php/File:DFBsequenceB.png Image:DFBsequenceB.png]
   </td>
   </td>
</tr>
</tr>
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   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
<table border="1" align="left" width="90%" cellpadding="3">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <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>
  <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>
</table>
</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>
   </td>
</tr>
</tr>
</table>
</table>


 
<!--
              Category:  Marginally Unstable Pressure-Truncated Gas Clouds 
-->
<table border="0" cellpadding="2" align="left" width="100%">
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <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 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>
  <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>
</tr>
<!--  
<!--  
               COWLING 1931
               H_BOOK
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   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f535;</font></td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
[http://www.vistrails.org/index.php/File:CowlingRE_Milne1931.jpg Text:CowlingRE_Milne1931.jpg]
[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];
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   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
   <td align="left" colspan="2">  
   <td align="left" colspan="2">  
<table border="1" align="left" width="90%" cellpadding="3">
<table border="1" align="left" width="90%" cellpadding="5">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <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>
  <td align="left">T. G. Cowling</td>
</tr>
</tr>
<tr>
</table>
  <td align="right">Title:</td>
   </td>
   <td align="left">''Note on the Fitting of Polytropic Models in the Theory of Stellar Structure''</td>
</tr>
</tr>
</table>
====Chapter Group Bipolytropes====
<table border="0" cellpadding="2" align="left" width="100%">
<tr>
<tr>
   <td align="right">Reference:</td>
  <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left">[http://adsabs.harvard.edu/abs/1931MNRAS..91..472C 1931, '''Monthly Notices of the Royal Astronomical Society''', 91, 472-478]</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>
<tr>
<tr>
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<tr>
<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <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|Three-halves-Three Bipolytrope (DFB)]]
   <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>
   </td>
</tr>
</tr>
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<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SphericallySymmetricConfigurations/Virial#Energy_Extrema|Introduction]]</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>
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<tr>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left" colspan="3">WIKI CHAPTER:  [[User:Tohline/SSC/Virial/FormFactors|Structural Form Factors]]</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>
</tr>
<!--  
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<table border="0" cellpadding="2" align="left" width="100%">
 
 
** CHAPTER:  [[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|Isolated Isothermal Sphere (DFB)]]
*** File:EmdenBookCover1907.jpg
*** File:EmdenIsothermalDerivation.jpg
*** File:EmdenTable14.jpg
** CHAPTER:  [[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|Pressure-Truncated Isothermal Sphere (DFB)]]
*** File:BonnorDerivation01.jpg
*** File:EbertDerivation01.jpg
*** File:Bonnor1956Fig1reproduced.jpg
*** File:EbertFig2Title.jpg
*** File:WhitworthFig1bFlipped.jpg
** CHAPTER:  [[User:Tohline/SSC/Structure/LimitingMasses#Mass_Upper_Limits|Mass Upper Limits]]
*** Image:SC42excerpt.jpg
*** File:Stahler1983TitlePage0.png
*** File:Stahler_MRdiagram1.png
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|BipolytropesDFB (Overview)]]
*** Image:CowlingRE_Milne1931.jpg
*** Image:SchonbergChandra1942.jpg
** CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|BipolytropeDFB51]]
*** Image:SC42_Fig1.jpg
*** Image:HenrichChandra41b.jpg
*** Image:HenrichChandra41a.jpg
*** Image:EagletonFaulknerCannon98.jpg
*** File:Buchdahl1978.png
**CHAPTER:  [[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#BiPolytrope_with_nc_.3D_1_and_ne_.3D_5|BipolytropeDFB15]]
*** File:Table3CompleteCol1.png
*** File:Table3CompleteCol2.png
*** File:Table3CompleteCol3.png
*** File:Table3CompleteCol4.png
*** File:Table3CompleteCol5.png
*** File:Table3CompleteCol6.png
*** File:MF85Table1.png
** CHAPTER:  [[User:Tohline/SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|Isolated Polytropes (Virial)]]
*** File:Whitworth1981Eq5.jpg  [used in another chapter as well]
<table border="0" align="center" width="90%" cellpadding="3">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="left" colspan="1" width="5%">&nbsp;</td>
   <td align="left">A. Whitworth</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>
</tr>
<!--
              WHITWORTH 1981
-->
<tr>
<tr>
   <td align="right">Title:</td>
   <td align="right" colspan="2" width="10%"><font size="-1">&#x1f534;</font></td>
   <td align="left">''Global Gravitational Stability for One-dimensional Polytropes''</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>
<tr>
<tr>
   <td align="right">Reference:</td>
   <td align="right" colspan="2" width="10%">&nbsp;</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1981MNRAS.195..967W 1981, '''Monthly Notices of the Royal Astronomical Society''', 195, 967-977]</td>
   <td align="left" colspan="2">  
</tr>
<table border="1" align="left" width="90%" cellpadding="3">
<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>
</table>
** CHAPTER:  [[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|Embedded Polytropes (Virial)]]
*** File:Whitworth1981Eq10.jpg
*** File:Whitworth1981Eq5.jpg [used in another chapter as well]
*** File:EnergyRadiusViewCombined5.png (1/4 of this image extracted from Whitworth's work)
<table border="0" align="center" width="90%" cellpadding="3">
<tr>
<tr>
   <td align="right" width="15%">Author(s):</td>
   <td align="right" width="15%">Author(s):</td>
Line 1,683: Line 1,699:
   <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>
** CHAPTER:  [[User:Tohline/SSC/Virial/Isothermal|Isothermal (Virial)]]
  </td>
*** File:Bonnor1951Eq1.2.jpg
</tr>
*** File:WhitworthFig1aCopy.jpg
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              H_BOOK
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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:AdabaticBoundedSpheres_Virial.jpg Image:AdabaticBoundedSpheres_Virial.jpg];
  </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">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>
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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>
  <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>
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              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>
</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:MassRadiusVirialLabeled.png Image:MassRadiusVirialLabeled.png];
&nbsp;
[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png] <font color="red">(repeat)</font>;
&nbsp;
[http://www.vistrails.org/index.php/File:PlotSequencesBest02.png Image:PlotSequencesBest02.png] <font color="red">(repeat)</font>
  </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">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/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>
</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:EbertFig2Title.jpg Image:EbertFig2Title.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">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">&#x1f534;</font></td>
  <td align="left" colspan="2">
[http://www.vistrails.org/index.php/File:Bonnor1956Fig1reproduced.jpg Image:Bonnor1956Fig1reproduced.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">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>
<!--
              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: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>
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<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>
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<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>
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  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
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  <td align="left">[http://adsabs.harvard.edu/abs/1941ApJ....94..525H 1941, '''The Astrophysical Journal''', 94, 525-536]</td>
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==Books==
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=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:
🔵

Image:AdabaticBoundedSpheres_Virial.jpg;

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


  WIKI CHAPTER: Virial Equilibrium of Isothermal Spheres
🔴

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
Permission:
🔴

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
Permission:
🔵

Image:Bonnor1956Fig1.jpg;   Image:WhitworthLogFig1a_norm.jpg;

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Virial Equilibrium of Embedded Polytropic Spheres FreeNRGpressureRadiusIsothermal.png : TILED MENU icon(s)
🔴

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
Permission:
🔵

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;

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


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

Image:SSC_SynopsisImage2.png

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

Summaries

  WIKI CHAPTER: Limiting Masses … Summary
🔴

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
Permission:
🔴

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
Permission:
🔵

Image:MassRadiusVirialLabeled.png;   Image:Stahler1983Comparison.png (repeat);   Image:PlotSequencesBest02.png (repeat)

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


  WIKI CHAPTER: Turning Points Turning-Points (Broader Context) : TILED MENU icon(s)
🔴

Image:EbertFig2Title.jpg (repeat)

 
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:
🔴

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
Permission:
🔴

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:
🔴

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
Permission:
🔴

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
Permission:
🔴

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
Permission:
🔴

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
Permission:
🔴

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
Publisher: Provided by the NASA Astrophysics Data System
Permission:
🔴

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
Permission:
🔵

Image:EvolutionArrows01.png;   Image:CaseMcompareTogether.png;   Image:MimicStahlerPlot3.png;   Image:TruncatedPolytropeMvsR2.png;
Image:SC_42EvolutionArrows.png;   Image:Qvsnu51b2.png;   Image:BinarySimpleModel02.png;   Image:DarwinP1compare.png;   Image:P0Diagram.png;

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

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  • Journal of Mathematical Physics (AIP)
  • Zeitschrift für Astrophysik

Books

  • Shapiro & Teukolsky

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation