Appendix/References

Journal Articles

Explanation

Three or four templates are available for each individual journal-article reference. For example, for the Dyson(1893) publication:

1. Dyson1893
2. Dyson1893full
3. Dyson1893figure     $\Leftarrow$     This is the template highlighted below.
4. BAC84hereafter

If you want to see which of our MediaWiki chapters includes a link to — and, therefore, likely discusses — a particular journal article, step through the following options:

1. Under the left-hand column, click on Tools/Special_pages;
2. Click on Page_tools/What_links_here;
3. In the input-box provided next to "Page," type the desired "Template" name. For example, type in:   Template:Dyson1893full
4. Note that when a figure from a particular journal article is displayed in one or more of our MediaWiki chapters, it will usually be accompanied by a figure heading that cites the article. Hence, typing in, for example, Template:Dyson1893figure should identify all of the MediaWiki chapters that display a figure from Dyson (1893).

19^th Century

Clausius1870

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

R. J. E. Clausius (1870)
On a Mechanical Theorem Applicable to Heat
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Ser. 4, Vol. 40, issue 265, pp. 122 - 127

Dyson1893

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?
📚 F. W. Dyson (1893, Phil. Trans. Royal Soc. London. A., Vol. 184, pp. 43 - 95)
📚 Dyson (1893a)

F. W. Dyson (1893)
The Potential of an Anchor Ring
Philosophical Transactions of the Royal Society of London. A., Vol. 184, pp. 43 - 95

20^th Century

Decade1

Eddington18

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

A. S. Eddington (1918)
On the Pulsations of a Gaseous Star and the Problem of the Cepheid Variables.   Part I.
Monthly Notices of the Royal Astronomical Society, Vol. 79, pp. 2 - 22

Decade2

Miller29

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

J. C. P. Miller (1929)
The Effect of Distribution of Density on the Period of Pulsation of a Star
Monthly Notices of the Royal Astronomical Society, Vol. 90, pp. 59 - 64

Acknowledgements (p. 64): "I am greatly indebted to Professor Eddington for his valuable suggestions and help."

Decade3

Milne30

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

E. A. Milne (1930)
The Analysis of Stellar Structure
Monthly Notices of the Royal Astronomical Society, Vol. 91, pp. 4 - 55

Decade4

LP41

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

P. Ledoux & C. L. Pekeris (1941)
Radial Pulsations of Stars
The Astrophysical Journal, Vol. 94, pp. 124 - 135

Schwarzschild41

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

M. Schwarzschild (1941)
Overtone Pulsations for the Standard [Stellar] Model
The Astrophysical Journal, Vol. 94, pp. 245 - 252

Acknowledgements (p. 252): "I am indebted to Miss Lillian Feinstein for her most helpful co-operation in the work with the punched-card machines."

Cowling41

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

T. G. Cowling (1941)
The Non-radial Oscillations of Polytropic Stars
Monthly Notices of the Royal Astronomical Society, Vol. 101, pp. 367 - 375

Decade5

Chatterji51

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

L. D. Chatterji (1951)
Radial Oscillations of a Gaseous Star of Polytropic Index I
Publication of the Indian National Science Academy, Vol. 17, No. 6, pp. 467 - 470

Chatterji52

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

L. D. Chatterji (1952)
Anharmonic Pulsations of a Polytropic Model of Index Unity
Publication of the Indian National Science Academy, Vol. 18, No. 3, pp. 187 - 191

CF53

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

S. Chandrasekhar & E. Fermi (1953)
Problems of Gravitational Stability in the Presence of a Magnetic Field
The Astrophysical Journal, Vol. 118, pp. 116 - 141

MS56

What chapter(s) cite this article?
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L. Mestel & L. Spitzer, Jr. (1956)
Star Formation in Magnetic Dust Clouds
Monthly Notices of the Royal Astronomical Society, Vol. 116, pp. 503 - 514

Acknowledgements (p. 513): "One of us (L. M.) wishes to record with thanks the generous financial aid of the Commonwealth Fund of New York, and the warm Hospitality of the Princeton University Observatory."

Decade6

PG61

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

C. Prasad & H. S. Gurm (1961)
Radial Pulsations of the Polytrope $n=2$
Monthly Notices of the Royal Astronomical Society, Vol. 122, pp. 409 - 411

Hunter62

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

C. Hunter (1962)
The Instability of the Collapse of a Self-Gravitating Gas Cloud
The Astrophysical Journal, Vol. 136, pp. 594 - 608

Acknowledgements (p. 608): "I am very grateful to Dr. L. Mestel for introducing me to this problem and for his interest and advice throughout." "This research was supported by the U.S. Air Force under contract AF 49(638)-708, monitored by the Air Force Office of Scientific Research of the Air Research and Development Command."

LB62

What chapter(s) cite this article?
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D. Lynden-Bell (1962)
On the Gravitational Collapse of a Cold Rotating Gas Cloud
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue 4, pp. 709 - 711

LMS65

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

C. C. Lin, L. Mestel, & F. H. Shu (1965)
The Gravitational Collapse of a Uniform Spheroid
The Astrophysical Journal, Vol. 142, pp. 1431 - 1446

Acknowledgements (p. 1446): "One of us (L. M.) wishes to thank Professor C. C. Lin for arranging a visit to the Department of Mathematics, Massachusetts Institute of Technology as research associate during July and August, 1964. The cosmogonical importance of the present problem first arose during discussions with Professor E. E. Salpeter during his visit to Cambridge, England, in 1961. The authors are grateful to the Computation Center at Massachusetts Institute of Technology for the use of its facilities." "This work is supported in part by the National Aeronautics and space Administration through the Center for Space Research at Massachusetts Institute of Technology."

Mestel65

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L. Mestel (1965)
Problems of Star Formation — I
Quarterly Journal of the Royal Astronomical Society, Vol. 6, pp. 161 - 198

HRW66

What chapter(s) cite this article?
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M. Hurley, P. H. Roberts, & K. Wright (1966)
The Oscillations of Gas Spheres
The Astrophysical Journal, Vol. 143, pp. 535 - 551

Decade7

Horedt70

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

Gp. Horedt (1970)
Gravitational Instability of Polytropic Gas Spheres Under External Pressure
Monthly Notices of the Royal Astronomical Society, Vol. 151, pp. 81 - 86

VH74

📚 Y. P. Viala & Gp. Horedt (1974, Astron. & Ap., Vol. 33, pp. 195 - 202)
📚 Viala & Horedt (1974)
VH74

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Y. P. Viala & Gp. Horedt (1974)
Polytropic Sheets, Cylinders and Spheres with Negative Index
Astronomy & Astrophysics, Vol. 33, pp. 195 - 202

Weber76

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

S. V. Weber (1976)
Oscillation and Collapse of Interstellar Clouds
The Astrophysical Journal, Vol. 208, pp. 113 - 126

Collins78

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

George W. Collins, II (1978)
The Virial Theorem in Stellar Astrophysics
© Pachart Publishing House

Decade8

GW80

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

P. Goldreich & S. V. Weber (1980)
Homologously Collapsing Stellar Cores
The Astrophysical Journal, Vol. 238, pp. 991 - 997

Kimura81b

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

H. Kimura (1981)
A Study of Simple Polytropes.   II.  Stability against Homologous Contraction
Publication of the Astronomical Society of Japan, Vol. 33, pp. 299 - 312

Whitworth81

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

A. Whitworth (1981)
Global Gravitational Stability for One-Dimensional Polytropes
Monthly Notices of the Royal Astronomical Society, Vol. 195, pp. 967 - 977

Tohline81

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J. E. Tohline (1981)
The Collapse to Equilibrium of Rotating, Adiabatic Spheroids.  I. Protostars
The Astrophysical Journal, Vol. 248, pp. 717 - 726

Stahler83

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S. W. Stahler (1983)
The Equilibria of Rotating Isothermal Clouds.
II. Structure and Dynamical Stability
The Astrophysical Journal, Vol. 268, pp. 165 - 184

BAC84

📚 J. R. Bond, W. D. Arnett, & B. J. Carr (1984, ApJ, Vol. 280, pp. 825 - 847)
📚 Bond, Arnett, & Carr (1984)
BAC84

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

J. R. Bond, W. D. Arnett, & B. J. Carr (1984)
The Evolution and Fate of Very Massive Objects
The Astrophysical Journal, Vol. 280, May 15, pp. 825 - 847

MF85b

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

J. O. Murphy & R. Fiedler (1985)
Radial Pulsations and Vibrational Stability of a Sequence of Two Zone Polytropic Stellar Models
Proceedings of the Astronomical Society of Australia, Vol. 6, no. 2, pp. 222 - 226

Tohline85

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In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

J. E. Tohline (1985)
Star Formation: Phase Transition Not Jeans Instability
The Astrophysical Journal, Vol. 292, pp. 181 - 187

FWW86

What chapter(s) cite this article?
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G. M. Fuller, S. E. Woosley, & T. A. Weaver (1986)
The Evolution of Radiation-Dominated Stars.   I. Nonrotating Supermassive Stars
The Astrophysical Journal, Vol. 307, pp. 675 - 686

Horedt86

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G. P. Horedt (1986)
Seven-Digit Tables of Lane-Emden Functions
Astrophysics and Space Science, Vol. 126, Issue 2, pp. 357 - 408

Decade9

LRS93b

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

D. Lai, F. A. Rasio, & S. L. Shapiro (1993)
Ellipsoidal Figures of Equilibrium:  Compressible Models
The Astrophysical Journal Supplement, Vol. 88, pp. 205 - 252

21^st Century

MTF2002

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

P. M. Motl, J. E. Tohline, & J. Frank (2002)
Numerical Methods for the Simulation of Dynamical Mass Transfer in Binaries
The Astrophysical Journal Supplement, Vol 138, Issue 1, pp. 121 - 148

ZEUS-MP2006

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

J. C. Hayes, et al. (2006, ZEUS-MP)
Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS-MP
The Astrophysical Journal Supplement, Vol. 165, Issue 1, pp. 188 - 228

PK2007

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

A. Y. Poludnenko & A. M. Khokhlov (2007)
Computation of Fluid Flows in Non-inertial Contracting, Expanding, and Rotating Reference Frames
Journal of Computational Physics, Vol. 220, Issue 2, pp. 678 - 711

MT2012

What chapter(s) cite this article?
In what chapter(s), if any, does a digital image (e.g., a figure or table) from this article appear?

D. C. Marcello & J. E. Tohline (2012)
A Numerical Method for Studying Super-Eddington Mass Transfer in Double White Dwarf Binaries
The Astrophysical Journal Supplement, Vol. 199, Issue 2, article id. 35, 29 pp.

Books

Key Parallel References

The following seven references serve as excellent supplemental printed texts to this Wiki-based H_Book because the fundamental physics and astrophysics concepts that are covered in these texts have significant overlap with the concepts we are discussing. The degree to which these references provide discussions that are parallel to ours is illustrated in our accompanying key equations appendix.

• [BT87] Binney, J. & Tremaine, S. 1987, Galactic Dynamics (Princeton, NJ: Princeton University Press)

• [BLRY07] Bodenheimer, P., Laughlin, G. P., Różyczka, M. & Yorke, H. W. 2007, Numerical Methods in Astrophysics An Introduction (New York: Taylor & Francis)

• [C67] Chandrasekhar, S. 1967 (originally, 1939), An Introduction to the Study of Stellar Structure (New York: Dover)

• [H87] Huang, K. 1987 (originally 1963), Statistical Mechanics (New York: John Wiley & Sons)

• [KW94] Kippenhahn, R. & Weigert, A. 1994, Stellar Structure and Evolution (New York: Springer-Verlag)

• [LL75] Laundau, L. D. & Lifshitz, E. M. 1975 (originally, 1959), Fluid Mechanics (New York: Pergamon Press)

• [P00] Padmanabhan, T. 2000, Theoretical Astrophysics. Volume I: Astrophysical Processes (Cambridge: Cambridge University Press); and Padmanabhan, T. 2001, Theoretical Astrophysics. Volume II: Stars and Stellar Systems (Cambridge: Cambridge University Press)

• [ST83] Shapiro, S. L. & Teukolsky, S. A. 1983, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (New York: John Wiley & Sons); republished in 2004 by WILEY-VCH Verlag GmbH & Co. KGaA

Other References (Listed Chronologically)

• [Lamb32] Lamb, Horace 1932 (originally, 1879; we're referencing a 1945 reprint of), 6^th Edition, Hydrodynamics (New York: Dover)

• [MF53] Morse, Philip M. & Feshbach, H. 1953, Methods of Theoretical Physics: Parts I and II (New York: McGraw-Hill Book Company)

• [Clayton68] Clayton, Donald D. 1968, Principles of Stellar Evolution and Nucleosynthesis (New York: McGraw-Hill Book Company)

• [EFE] Chandrasekhar, S. 1987 (originally, 1969), Ellipsoidal Figures of Equilibrium (New York: Dover)

• [CRC] Selby, Samuel M. 1971 (19^th edition), CRC Standard Mathematical Tables (Cleveland, Ohio: The Chemical Rubber Co.)

• [T78] Tassoul, Jean-Louis 1978, Theory of Rotating Stars (Princeton, NJ: Princeton Univ. Press)

• [Shu92] Shu, Frank H. 1992, The Physics of Astrophysics, Volume I: Radiation & Volume II: Gas Dynamics (Mill Valey, California: University Science Books)

• [HK94] Hansen, C. J. & Kawaler, S. D. 1994, Stellar Interiors: Physical Principles, Structure, and Evolution (New York: Springer-Verlag)

• [Maeder09] Maeder, André 2009, Physics, Formation and Evolution of Rotating Stars (Berlin: Springer)

• [Choudhuri10] Choudhuri, Arnab Rai 2010, Astrophysics for Physicists (Cambridge: Cambridge University Press)

Appendix of EFE

The presentation of the subject in this book (Ellipsoidal Figures of Equilibrium) is based on the following papers:

Setup

• [Publication I] S. Chandrasekhar (1960), J. Mathematical Analysis and Applications, 1, 240: The virial theorem in hydromagnetics
• [Publication II] N. R. Lebovitz (1961), ApJ, 134, 500: The virial tensor and its application to self-gravitating fluids
• [Publication III] S. Chandrasekhar (1961), ApJ, 134, 662: A Theorem on rotating polytropes

• [Publication IV] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 135, 238: On super-potentials in the theory of Newtonian gravitation
• [Publication VII] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1032: On the superpotentials in the theory of Newtonian gravitation. II. Tensors of higher rank
• [Publication VIII] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1037: The potentials and the superpotentials of homogeneous ellipsoids
• [Publication XXXV] S. Chandrasekhar (1968), ApJ, 152, 293: The virial equations of the fourth order

Spheroidal & Ellipsoidal Sequences

• [Publication V] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 135, 248: On the oscillations and the stability of rotating gaseous masses
• [Publication IX] S. Chandrasekhar (1962), ApJ, 136, 1048: On the point of bifurcation along the sequence of the Jacobi ellipsoids
• [Publication X] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1069: On the oscillations and the stability of rotating gaseous masses. II. The homogeneous, compressible model
• [Publication XI] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1082: On the oscillations and the stability of rotating gaseous masses. III. The distorted polytropes
• [Publication XIII] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 137, 1142: On the stability of the Jacobi ellipsoids
• [Publication XIV] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 137, 1162: On the oscillations of the Maclaurin spheroid belonging to the third harmonics
• [Publication XV] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 137, 1172: The equilibrium and the stability of the Jeans spheroids
• [Publication XVI] S. Chandrasekhar (1963), ApJ, 137, 1185: The points of bifurcation along the Maclaurin, the Jacobi, and the Jeans sequences
• [Publication XXIII] Chandrasekhar & N. R. Lebovitz (1964), Astrophysica Norvegica, 9, 323: On the ellipsoidal figures of equilibrium of homogeneous masses
• [Publication XXIV] S. Chandrasekhar (1965), ApJ, 141, 1043: The equilibrium and the stability of the Dedekind ellipsoids
• [Publication XXV] S. Chandrasekhar (1965), ApJ, 142, 890: The equilibrium and the stability of the Riemann ellipsoids. I
• [Publication XXVIII] S. Chandrasekhar (1966), ApJ, 145, 842: The equilibrium and the stability of the Riemann ellipsoids. II
• [Publication XXIX] N. R. Lebovitz (1966), ApJ, 145, 878: On Riemann's criterion for the stability of liquid ellipsoids
• [Publication XXXVII] C. E. Rosenkilde (1967), ApJ, 148, 825: The tensor virial-theorem including viscous stress and the oscillations of a Maclaurin spheroid
• [Publication XXXVIII] L. F. Rossner (1967), ApJ, 149, 145: The finite-amplitude oscillations of the Maclaurin spheroids

Binary Systems

• [Publication XIX] S. Chandrasekhar (1963), ApJ, 138, 1182: The equilibrium and stability of the Roche ellipsoids
• [Publication XX] N. R. Lebovitz (1963), ApJ, 138, 1214: On the principle of the exchange of stabilities. I. The Roche ellipsoids
• [Publication XXI] S. Chandrasekhar (1964), ApJ, 140, 599: The equilibrium and the stability of the Darwin ellipsoids
• [Publication XXXI] S. Chandrasekhar (1969), Publications of the Ramanujan Institute, 1, 213 - 222: The effect of viscous dissipation on the stability of the Roche ellipsoid
• [Publication XXXIX] M. L. Aizenman (1968), ApJ, 153, 511: The equilibrium and the stability of the Roche-Riemann ellipsoids
• [Publication XL] S. Chandrasekhar (1969), ApJ, 157, 1419: The stability of the congruent Darwin ellipsoids

Effects of General Relativity

• [Publication XXVI] S. Chandrasekhar (1965), ApJ, 142, 1513: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. I. The Maclaurin spheroids and the virial theorem
• [Publication XXX] S. Chandrasekhar (1967), ApJ, 147, 334: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. II. The deformed figures of the Maclaurin spheroids
• [Publication XXXI] S. Chandrasekhar (1967), ApJ, 147, 383: Virial relations for uniformly rotating fluid masses in general relativity
• [Publication XXXII] S. Chandrasekhar (1967), ApJ, 148, 621: The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. III. The deformed figures of the Jacobi ellipsoids

Other

• [Publication VI] S. Chandrasekhar (1962), Proc. 4th U. S. Nat. Congress of Applied Mechanics, pp. 9 - 14: An approach to the theory of the equilibrium and the stability of rotating masses via the virial theorem and its extensions
• [Publication XII] S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1105: On the occurrence of multiple frequencies and beats in the β Canis Majoris stars
• [Publication XVII] S. Chandrasekhar & N. R. Lebovitz (1963), ApJ, 138, 185: Non-radial oscillations and the convective instability of gaseous masses
• [Publication XVIII] S. Chandrasekhar & P. H. Roberts (1963), ApJ, 138, 801: The ellipticity of a slowly rotating configuration
• [Publication XXII] S. Chandrasekhar (1964), Lectures in Theoretical Physics, Vol. VI, Boulder 1963 (Boulder: University of Colorado Press), pp. 1 - 72: The higher order virial equations and their applications to the equilibrium and stability of rotating configurations
• [Publication XXVII] N. R. Lebovitz (1965), lecture notes. Inst. Ap., Cointe-Sclessin, Belgium, p. 29: The Riemann ellipsoids
• [Publication XXXIII] S. Chandrasekhar (1967), Communications on Pure and Applied Mathematics, 20, 251: Ellipsoidal figures of equilibrium — an historical account
• [Publication XXXIV] N. R. Lebovitz (1967), Annual Review of Astronomy and Astrophysics, 5, 465: Rotating fluid masses

See Also

• Guide to the Subrahmanyan Chandrasekhar Papers 1913 - 2011 (University of Chicago Library)