Appendix/References

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Journal Articles

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  4. BAC84hereafter

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18th Century

19th Century

Clausius1870

What chapter(s) cite this article?
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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?
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📚 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

20th Century

Decade0

Decade1

Eddington18

What chapter(s) cite this article?
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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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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?
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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?
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P. Ledoux & C. L. Pekeris (1941)
Radial Pulsations of Stars
The Astrophysical Journal, Vol. 94, pp. 124 - 135

Schwarzschild41

What chapter(s) cite this article?
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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

What chapter(s) cite this article?
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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

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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

What chapter(s) cite this article?
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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

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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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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
Acknowledgements:  n/a

Hunter62

What chapter(s) cite this article?
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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
Acknowledgements:  n/a

LMS65

What chapter(s) cite this article?
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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

What chapter(s) cite this article?
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L. Mestel (1965)
Problems of Star Formation — I
Quarterly Journal of the Royal Astronomical Society, Vol. 6, pp. 161 - 198
Acknowledgements:  n/a

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
Acknowledgements (p. 551):
"This research was partially supported by the National Science Foundation (Grant GP-975); the authors are glad to acknowledge its assistance. We are also grateful to Professor S. Chandrasekhar for helpful comments, and to Mr. Jackson, of the Yerkes Observatory, for the radii of polytropes of indices 3.0 and 3.25 (see Table 4)."

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
Acknowledgements (p. 85):
"The author is greatly indebted to Dr M. Penston for his precious support and to an anonymous referee."

VH74

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

What chapter(s) cite this article?
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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

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S. V. Weber (1976)
Oscillation and Collapse of Interstellar Clouds
The Astrophysical Journal, Vol. 208, pp. 113 - 126
Acknowledgements (p. 123):
"I am indebted to Professor Frank Shu for suggesting the problem, providing advice and encouragement, and suggesting changes in the original draft of the paper. I also wish to acknowledge the tenure of an NSF Graduate Fellowship."

Collins78

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

Decade8

GW80

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P. Goldreich & S. V. Weber (1980)
Homologously Collapsing Stellar Cores
The Astrophysical Journal, Vol. 238, pp. 991 - 997
Acknowledgements (p. 996):
"We are grateful for comments by Doug Keeley and Frank Shu. We also acknowledge Glen Hermannsfeldt for excellent assistance with the computing. Stephen V. Weber was supported by a Chaim Weizmann postdoctoral fellowship. This work was supported by NSF grants AST78-21453 and AST76-80801 A02."

Kimura81b

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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
Acknowledgements (p. 308):
"A portion of the work reported here formed part of the author's doctoral thesis, submitted to the University of Tokyo. The author is indebted to Professors W. Unno and S. Aoki for helpful discussions. Thanks are also due to Mrs. K. Sakurai for her assistance in preparing the manuscript."

Whitworth81

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

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
Acknowledgements (p. 726):
"Because Leon Mestel's (1965; Mestel65) paper has not been specifically referenced in the body of this paper, I must acknowledge its importance here. It was from Professor Mestel's work that I first gained a clear glimpse of how this problem could be attacked analytically. It is a pleasure also to acknowledge conversations with Alan Boss from which I first began to appreciate the fact that an analysis akin to the one presented in this paper was desperately needed. I thank Alan also for furnishing me with his data prior to its publication."
"This work was performed under the auspices of the USERDA."

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
Acknowledgements (p. 180):
"I wish to thank Martin Duncan, Mark Haugan, and Saul Teukolsky for useful discussions. This research was supported in part by National Science Foundation grant AST81-16370."

BAC84

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

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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
Acknowledgements (p. 844):
"We thank Willy Fowler, Lee Lindblom, Wolfgang Ober, Bob Wagoner, and Stan Woosley for useful discussions. In particular, Stan Woosley often emphasized the many ways rotation could transform simplicity into complexity. This research was supported by grants NSF AST-80-22876 at Chicago, NSF AST 79-23243 at Berkeley, and NSF PHY 81-19387 at Stanford, and by the SERC at Cambridge."

MF85b

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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
Acknowledgements:  n/a

Tohline85

What chapter(s) cite this article?
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J. E. Tohline (1985)
Star Formation: Phase Transition Not Jeans Instability
The Astrophysical Journal, Vol. 292, pp. 181 - 187
Acknowledgements (p. 187):
"Frank Shu and Hugh Van Horn have made extremely enlightening comments to me in the course of this investigation. I thank them for their interest and support. I am indebted to Mort Roberts for allowing me to pull my thoughts together in the friendly, invigorating environment of NRAO, Charlottesville, and to E. F. Zganjar, A. U. Landolt, and C. L. Perry for doing all the dirty work at LSU while I was gone for the summer. This work was supported by the National Science Foundation through grant AST-8217744."

FWW86

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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
Acknowledgements (p. 685):
"The authors gratefully acknowledge many stimulating and informative conversations with Willy Fowler on the subject of supermassive stars. This research has been supported by the National Science Foundation under grants AST81-08509 A01 and AST 84-18185 and, at Livermore, by the Department of Energy under W-7405-EN6-48 [probably should be ENG, rather than EN6]."

Horedt86

What chapter(s) cite this article?
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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
Acknowledgements:  n/a

Decade9

LRS93b

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

21st Century

MTF2002

What chapter(s) cite this article?
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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?
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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?
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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?
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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), 6th 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 (19th 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


Spheroidal & Ellipsoidal Sequences

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

 

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