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(→‎Detailed Force-Balanced (DFB) Models: Finished chapter reviewing Milne's first bipolytrope)
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  <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]]
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[http://www.vistrails.org/index.php/File:SC42excerpt.jpg Text:SC42excerpt.jpg]
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  <td align="right" width="15%">Author(s):</td>
  <td align="left">M. Sch&ouml;nberg &amp; S. Chandrasekhar</td>
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  <td align="right">Title:</td>
  <td align="left">''On the Evolution of the Main-Sequence Stars''</td>
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  <td align="right">Reference:</td>
  <td align="left">[http://adsabs.harvard.edu/abs/1942ApJ....96..161S 1942, '''The Astrophysical Journal''', 96, 161-172]</td>
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  <td align="right">Copyright:</td>
  <td align="left">American Astronomical Society</td>
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  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
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[http://www.vistrails.org/index.php/File:Stahler_MRdiagram1.png Image:Stahler_MRdiagram1.png] <font color="red">(repeat)</font>
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  <td align="right" width="15%">Author(s):</td>
  <td align="left">S. W. Stahler</td>
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  <td align="right">Title:</td>
  <td align="left">''The Equilibria of Rotating Isotherma Clouds &#8212; Part Two &#8212; Structure and Dynamical Stability''</td>
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  <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>
</tr>
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  <td align="right">Publisher:</td>
  <td align="left">Provided by the [http://doc.adsabs.harvard.edu/abs_doc/help_pages/overview.html#use NASA Astrophysics Data System]</td>
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  <td align="right">Permission:</td>
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[http://www.vistrails.org/index.php/File:MassRadiusVirialLabeled.png Image:MassRadiusVirialLabeled.png];
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[http://www.vistrails.org/index.php/File:Stahler1983Comparison.png Image:Stahler1983Comparison.png] <font color="red">(repeat)</font>;
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[http://www.vistrails.org/index.php/File:PlotSequencesBest02.png Image:PlotSequencesBest02.png] <font color="red">(repeat)</font>
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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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Revision as of 23:25, 3 December 2016

Images (to be) Displayed in this H_Book

Whitworth's (1981) Isothermal Free-Energy Surface
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Generated by Tohline or an Immediate Collaborator

  • SECTION: Spherically Symmetric Configurations
    • CHAPTER: Mass Upper Limits
      • Image:MassRadiusVirialLabeled.png
      • File:Stahler1983Comparison.png
      • Image:PlotSequencesBest02.png
    • CHAPTER: BipolytropeDFB00
      • Image:BipolytropeDynamicalStability2.png
    • CHAPTER: 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: BipolytropeDFB15
      • File:MurphyF2roots05.png
      • File:InterfaceMap02.png
      • File:MurphyPhysicallyViableTable3d.png
      • File:MF85Table1byTohline02.png
    • CHAPTER: Isolated Polytropes (Virial)
      • File:AdabaticBoundedSpheres_Virial.jpg
    • CHAPTER: Embedded Polytropes (Virial)
      • File:FreeNRGmassRadiusN5.png
      • File:FreeNRGpressureRadiusIsothermal.png
      • File:EnergyRadiusViewCombined5.png (3/4 of this image constructed for this H_Book)
    • CHAPTER: Isothermal (Virial)
      • File:Bonnor1956Fig1.jpg
      • File:WhitworthLogFig1a_norm.jpg

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: Principle Governing Equations
  WIKI CHAPTER: Continuity Equation
  WIKI CHAPTER: Euler Equation
  WIKI CHAPTER: Rotating Reference Frame
  WIKI CHAPTER: Hybrid Advection Scheme (Preface)
  WIKI CHAPTER: Hybrid Advection Scheme (Background circa 2000)
  WIKI CHAPTER: Jay Call's Hybrid Scheme
🔴

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
  WIKI CHAPTER: Total Pressure
  WIKI CHAPTER: Quartic Temperature Solution
  WIKI CHAPTER: Simple Rotation Profiles
  WIKI CHAPTER: Global Energy Considerations
 

SECTION:  Spherically Symmetric Configurations

  WIKI CHAPTER: Introduction
  WIKI CHAPTER: Alternate Introduction
🎦

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
🔵

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

 
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)
  WIKI CHAPTER: DFB Introduction (Part II)
  WIKI CHAPTER: Uniform-Density Sphere … Isolated (DFB)
  WIKI CHAPTER: Uniform-Density Sphere … Pressure-Truncated (DFB)
  WIKI CHAPTER: Polytropes … Isolated (DFB)
🔵

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

 
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

 
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: —


  WIKI CHAPTER: Polytropes … Pressure-Truncated (DFB)
🔴

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

 
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

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

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: Isothermal Sphere … Pressure-Truncated (DFB);   Familiarly, a Bonnor-Ebert Sphere
🔴

Eqns:EbertDerivation01.jpg;   Image:EbertFig2Title.jpg;

 
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

 
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:WhitworthFig1bFlipped.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:BonnorFig1usingEmdenData.jpg;   Image:EbertFig2UsingEmdenData2.jpg;   Image:Bonnor1956DPDVplot.jpg

 
Created by the author (J. E. Tohline) for inclusion in this H_Book, The Structure, Stability & Dynamics of Self-Gravitating Fluids.
  WIKI CHAPTER: Zero-temperature White Dwarf …Overview
🔵

Eqn:ST83Eq3_3_11.png;   Eqn:ST83Eq3_3_12.png;   Eqn:ST83Eq2_3_23.png;

 
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
  WIKI CHAPTER: Power-law Density Distribution …Overview
  WIKI CHAPTER: Other Analytically Definable Models


  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: Three-halves-Three 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: —


  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 (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.


 

Virial Equilibrium Configurations

  WIKI CHAPTER: Introduction
🔵

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
🔴

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: —



    • CHAPTER: Isolated Isothermal Sphere (DFB)
      • File:EmdenBookCover1907.jpg
      • File:EmdenIsothermalDerivation.jpg
      • File:EmdenTable14.jpg
    • CHAPTER: Pressure-Truncated Isothermal Sphere (DFB)
      • File:BonnorDerivation01.jpg
      • File:EbertDerivation01.jpg
      • File:Bonnor1956Fig1reproduced.jpg
      • File:EbertFig2Title.jpg
      • File:WhitworthFig1bFlipped.jpg
    • CHAPTER: Mass Upper Limits
      • Image:SC42excerpt.jpg
      • File:Stahler1983TitlePage0.png
      • File:Stahler_MRdiagram1.png
    • CHAPTER: BipolytropesDFB (Overview)
      • Image:CowlingRE_Milne1931.jpg
      • Image:SchonbergChandra1942.jpg
    • CHAPTER: BipolytropeDFB51
      • Image:SC42_Fig1.jpg
      • Image:HenrichChandra41b.jpg
      • Image:HenrichChandra41a.jpg
      • Image:EagletonFaulknerCannon98.jpg
      • File:Buchdahl1978.png
    • CHAPTER: BipolytropeDFB15
      • File:Table3CompleteCol1.png
      • File:Table3CompleteCol2.png
      • File:Table3CompleteCol3.png
      • File:Table3CompleteCol4.png
      • File:Table3CompleteCol5.png
      • File:Table3CompleteCol6.png
      • File:MF85Table1.png
    • CHAPTER: Isolated Polytropes (Virial)
      • File:Whitworth1981Eq5.jpg [used in another chapter as well]
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
    • CHAPTER: 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)
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

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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