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Contents

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
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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 Principle Governing Equations (PGEs) : TILED MENU icon(s)
  WIKI CHAPTER: Continuity Equation Continuity : TILED MENU icon(s)
  WIKI CHAPTER: Euler Equation Euler : TILED MENU icon(s)
  WIKI CHAPTER: First Law of Thermodynamics 1st Law of Thermodynamics : TILED MENU icon(s)
  WIKI CHAPTER: Origin of the Poisson Equation Poisson : TILED MENU icon(s)
  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
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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:
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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 Equation of State (EOS) : TILED MENU icon(s)
  WIKI CHAPTER: Ideal Gas Equation of State Ideal Gas : TILED MENU icon(s)
  WIKI CHAPTER: Total Pressure Total Pressure : TILED MENU icon(s)
  WIKI CHAPTER: Quartic Temperature Solution
  WIKI CHAPTER: Simple Rotation Profiles Simple Rotation Profiles : TILED MENU icon(s)
  WIKI CHAPTER: Global Energy Considerations Global Energy Considerations : TILED MENU icon(s)
 

SECTION:  Spherically Symmetric Configurations

  WIKI CHAPTER: Introduction One-Dimensional PGEs : TILED MENU icon(s)
  WIKI CHAPTER: Alternate Introduction
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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
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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)
  WIKI CHAPTER: DFB Introduction (Part II) Hydrostatic Balance Equation || Solution Strategies : TILED MENU icon(s)

Chapter Group Isolated

  WIKI CHAPTER: Uniform-Density Sphere … Isolated (DFB)
  WIKI CHAPTER: Isothermal Sphere … Isolated (DFB) Isothermal Sphere || via Direct Numerical Integration : TILED MENU icon(s)
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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
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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)
Isolated Polytropes || Known Analytic Solutions || via Direct Numerical Integration || via Self-Consistent Field (SCF) Technique : TILED MENU icon(s)
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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:


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

Copyright Polices

Journals

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Publisher: IOPscience.iop.org
Copyright: American Astronomical Society
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INSTRUCTIONS


  • Zeitschrift für Astrophysik
Publisher: Springer
Copyright: Springer-Verlag
Rights & Permissions:

Excerpts from online instructions (verbatim text printed in dark green):

Request to use copyrighted material

Content published by Springer can be re-used in all kinds of products in different formats and distributed by third parties. Any type of use is subject to permission by Springer. Permission can be requested to use material obtained from any of the following sources:

  • Any previously published material from which a direct quotation is used of a length which totals more than 5% of the whole, or which totals more than 250 words in any single excerpt or more than 500 words in total (note: each publisher sets their own quotation lengths, so number of words can differ from publisher to publisher)
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  • Anything in its entirety (this applies particularly to holograph documents, such as postcards, etc.

Obtaining Permissions

Some publishers, such as Springer, have entrusted the Copyright Clearance Center in the USA to manage the copyright permission procedure on their behalf. Please contact RightsLink for further information. Alternatively, Springer can provide you with a template to use when requesting permissions. Please comply with the instructions stipulated in the permission(s) concerning acknowledgements or credit lines within your manuscript (e.g., reference to the copyright holder in captions) and keep the written confirmation of the permission in your possession with the copy of your manuscript. Please be aware that some publishers do not always grant right of reproduction for free. Springer will not be able to refund any costs that may have been incurred in receiving these permissions. As an alternative, material from other sources should be used.

Contact the author helpdesk for questions on rights and permissions


  • Philosophical Transactions of the Royal Society A
  • Astronomy & Astrophysics (ESO)
  • Publications of the Astronomical Society of Japan
  • Australian Journal of Physics (CSIRO Publishing)
  • Journal of Mathematical Physics (AIP)
  • Zeitschrift für Astrophysik

Books

  • Shapiro & Teukolsky

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

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