# Journal Articles

## Explanation

Three or four templates are available for each individual journal-article reference. For example, for the Dyson (1893) publication or for BAC84:

1. Dyson1893
2. Dyson1893full
3. Dyson1893figure     ${\displaystyle \Leftarrow }$     This template is 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, click the relevant question, "What chapter(s) cite this article?"

## 19th Century

### Clausius1870

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
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### Dyson1893

F. W. Dyson (1893)
The Potential of an Anchor Ring
Phil. Trans. Royal Soc. London. A., Vol. 184, pp. 43 - 95
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

## 20th Century

#### Darwin06

G. H. Darwin (1906)
IV.  On the figure and stability of a liquid satellite
Philosophical Transactions of the Royal Society A, Vol. 206, pp. 161 - 248
 Acknowledgements: n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Eddington18

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
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Miller29

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Milne30

E. A. Milne (1930)
The Analysis of Stellar Structure
Monthly Notices of the Royal Astronomical Society, Vol. 91, pp. 4 - 55
 Acknowledgements (p. 55):"It is my pleasant duty to express my thanks to those investigators who have so kindly assisted in these researches. Mr. Norman Fairclough performed a numerical integration of Emden's ${\displaystyle n=3}$ equation, working from the boundary inwards, at a crucial stage of the investigation. His results influenced much of the course of the argument from that point onwards. For Mr. Fairclough's services I am indebted to a grant from the Department of Scientific and Industrial Research. To Mr. T. G. Cowling I am indebted for theoretical considerations which indicated that it was the more luminous configurations which might be expected to possess central condensations and not the less luminous. To Mr. R. H. Fowler I am indebted for exhaustive analysis of the properties of solutions of the differential equations that arose. His work lifted my results to a level of rigour quite beyond my own powers. I am especially grateful to him for pointing out to me the existence of a type of solution of Emden's ${\displaystyle n={\tfrac {3}{2}}}$ equation which (though searching for it) I had entirely overlooked." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LP41

P. Ledoux & C. L. Pekeris (1941)
The Astrophysical Journal, Vol. 94, pp. 124 - 135
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Schwarzschild41

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### HC41

L. R. Henrich, & S. Chandrasekhar (1941)
Stellar Models with Isothermal Cores
The Astrophysical Journal, Vol. 94, pp. 525 - 536
 Acknowledgements:   n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Cowling41

T. G. Cowling (1941)
The Non-radial Oscillations of Polytropic Stars
Monthly Notices of the Royal Astronomical Society, Vol. 101, pp. 367 - 375
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### SC42

M. Schönberg & S. Chandrasekhar (1942)
On the Evolution of the Main-Sequence Stars
The Astrophysical Journal, Vol. 96, pp. 161 - 172
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Chatterji51

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
 Acknowledgements (p. 470):"My very best thanks are due to Prof. A. C. Banerji and Dr. P. L. Bhatnagar for their keen interest and valuable suggestions in the preparation of this paper." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Chatterji52

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
 Acknowledgements (p. 191):"I am indebted to Prof. A. C. Banerji for his keen interest in this paper." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### CF53

S. Chandrasekhar & E. Fermi (1953)
Problems of Gravitational Stability in the Presence of a Magnetic Field
The Astrophysical Journal, Vol. 118, pp. 116 - 141
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Ebert55

R. Ebert (1955)
Über die Verdichtung von HI-Gebieten
Zeitschrift für Astrophysik, Vol. 37, pp. 217 - 232
 Acknowledgements (p. 232):"Herrn Prof. v. Weissäcker bin ich für die Ermöglichung dieser Arbeit und für viele Diskussionen zu großem Dank verpflichtet. Dem Max-Planck-Institut für Physik danke ich für die Gewährung eines Stipendiums." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Bonnor56

W. B. Bonnor (1956)
Boyle's Law and gravitational instability
Monthly Notices of the Royal Astronomical Society
Vol. 116, pp. 351 - 359
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### MS56

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LW58

P. Ledoux & Th. Walraven (1958)
Variable Stars
Handbuch der Physik, Vol. 51, pp. 353 - 604
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Lebovitz61

N. R. Lebovitz (1961)
The Virial Tensor and Its Application to Self-Gravitating Fluids
The Astrophysical Journal, Vol. 134, pp. 500 - 536
 Acknowledgements (p. 532):"I wish to thank Professor S. Chandrasekhar for suggesting the development of the virial tensor method, as well as its application to the problem of self-gravitating fluids. His advice and encouragement while the problem was being solved were invaluable. This work was done during the tenure of a National Science Foundation Pre-doctoral Fellowship, which is gratefully acknowledged." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### PG61

C. Prasad & H. S. Gurm (1961)
Radial Pulsations of the Polytrope ${\displaystyle n=2}$
Monthly Notices of the Royal Astronomical Society, Vol. 122, pp. 409 - 411
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Hunter62

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LB62

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 Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Chandrasekhar65_XXV

S. Chandrasekhar (1965)
The Equilibrium and the Stability of the Riemann Ellipsoids. I.
The Astrophysical Journal, Vol. 142, pp. 890 - 961
 Acknowledgements (p. 921):"I am greatly indebted to Miss Donna Elbert for her patience in carrying out the extensive numerical work which was required in the preparation of this paper. I am also grateful to Dr. M. Clement for his careful scrutiny of the analysis and to Dr. N. Lebovitz for many helpful discussions." "The research reported in this paper has in part been supported by the Office of Naval Research under contract Nonr-2121(24) with the University of Chicago." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Chandrasekhar66_XXVIII

S. Chandrasekhar (1966)
The Equilibrium and the Stability of the Riemann Ellipsoids. II.
The Astrophysical Journal, Vol. 145, pp. 842 - 877
 Acknowledgements (p. 877):"I am grateful to Dr. M. Clement whose careful scrutiny of the analysis helped the elimination of a number of oversights and obscurities; he also generously programmed for machine calculations1, the characteristic equation (both in its finite and asymptotic forms) for the determination of its roots. I am equally grateful to Dr. N. R. Lebovitz for many clarifying discussions and particularly for his examination of Riemann's criterion for determining the stability of his figures and demonstration of the place where he erred. I am also indebted to Miss Donna Elbert for her continued patience in assisting with these investigations; in this particular instance it was most essential." "The research reported in this paper has in part been supported by the Office of Naval Research under contract Nonr-2121(24) with the University of Chicago." 1The machine calculations were performed with an IBM 1620 computer at the Yerkes Observatory. Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LMS65

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Mestel65

L. Mestel (1965)
Problems of Star Formation — I
Quarterly Journal of the Royal Astronomical Society, Vol. 6, pp. 161 - 198
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### HRW66

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)." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LBO67

D. Lynden-Bell & P. Ostriker (1967)
On the Stability of Differentially Rotating Bodies
Monthly Notices of the Royal Astronomical Society, Vol. 136, pp. 293 - 310
 Acknowledgements (p. 310):"D. Lynden-Bell would like to thank Professor Oort for the hospitality of the Leiden Observatory in 1964 December where this work began." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Horedt70

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### B-KB74

G. S. Bisnovatyi-Kogan & S. I. Blinnikov (1974)
Static Criteria for Stability of Arbitrarily Rotating Stars
Astronomy & Astrophysics, Vol. 31, pp. 391 - 404
 Acknowledgements (p. 402):"The authors wish to express their gratitude to Zeldovich for helpful discussions." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Lebovitz74

N. R. Lebovitz (1974)
The Fission Theory of Binary Stars,  II. Stability to Third-Harmonics Disturbances
The Astrophysical Journal, Vol. 190, pp. 121 - 130
 Acknowledgements (p. 130):"The research reported here was supported by the National Science Foundation under grant NSF GP-22584. I wish to thank Dr. Giles Auchmuty for a helpful conversation." (Note: A Google search led to a scanned NSF budget sheet identifying N. R. Lebovitz as the recipient of Grant No. GP22584 from "Mathematics" — FY '71 and 12 month duration — titled, Structural Stability of Rotating Fluid Systems.) Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### TVH74

L. G. Taff, & H. M. van Horn (1974)
Radial Pulsations of Finite Isothermal Gas Spheres
Monthly Notices of the Royal Astronomical Society,
Vol. 168, pp. 427 - 432
 Acknowledgements (p. 431):"This work was supported by the National Science Foundation (U.S.A.) under grant GP-36098." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### VH74

Y. P. Viala & Gp. Horedt (1974)
Polytropic Sheets, Cylinders and Spheres with Negative Index
Astronomy & Astrophysics, Vol. 33, pp. 195 - 202
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Weber76

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Collins78

George W. Collins, II (1978)
The Virial Theorem in Stellar Astrophysics
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### GW80

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Kimura81b

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Whitworth81

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 Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Tohline81

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Stahler83

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### BAC84

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### MF85b

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 Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Tohline85

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." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### FWW86

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]." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Horedt86

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 Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Beech88

M. Beech (1988)
The Schoenberg-Chandrasekhar Limit — a Polytropic Approximation
Astrophysics and Space Science, Vol. 147, issue 2, pp. 219 - 227
 Acknowledgements:  n/a Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Lebovitz89a

N. R. Lebovitz (1989a)
The Stability Equations for Rotating, Inviscid Fluids:   Galerkin Methods and Orthogonal Bases
Geophysical & Astrophysical Fluid Dynamics, Vol. 46:4, pp. 221 - 243
 Acknowledgements (p. 237):"I wish to thank Mr. Apurba Kar for checking the manuscript and correcting several mistakes. The research reported here was supported in part by the National Science Foundation through Grant No. DMS-8602031 with the University of Chicago. It was initiated in 1985 during the Summer Seminar in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution. I would like to thank Prof. George Veronis for his kind hospitality during my visit to Woods Hole." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### Lebovitz89b

N. R. Lebovitz (1989b)
Lagrangian Perturbations of Riemann Ellipsoids
Geophysical & Astrophysical Fluid Dynamics, Vol. 47:1, pp. 225 - 236
 Acknowledgements (p. 236):"The research reported here was supported in part by the National Science Foundation through Grant No. DMS-8602031 with the University of Chicago." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LRS93a

D. Lai, F. A. Rasio, & S. L. Shapiro (1993a)
Hydrodynamic Instability and Coalescence of Close Binary Systems
Astrophysical Journal Letters, Vol. 406, pp. L63 - L66
 Acknowledgements (p. L66):"We thank L. Bildsten, J. Goodman, K. Thorne, and C. Will for useful discussions. This work was supported in part by NSF grant AST 91-19475 and NASA Grant NAGW-2364 to Cornell University. Partial support was also provided by NASA through Grant HF-1037.01-92A awarded by the Space Telescope Science Institute which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS5-26555." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LRS93b

D. Lai, F. A. Rasio, & S. L. Shapiro (1993)
Ellipsoidal Figures of Equilibrium:  Compressible Models
The Astrophysical Journal Supplement, Vol. 88, pp. 205 - 252
 Acknowledgements (p. 248):"This work was supported by NSF grant AST 90-15451 and NASA grant NAGW-2364 to Cornell University. Partial support was also provided by NASA through grant HF-1037.01-92A awarded by the Space Telescope Science Institute which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA under contract NAS5-26555. Computations were performed on the Cornell National Supercomputer Facility, a resource of the Center for Theory and Simulation in Science and Engineering at Cornell University, which receives major funding from the NSF and from the IBM Corporation, with additional support from New York State and members of its Corporate Research Institute." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### LL96

N. R. Lebovitz & A. Lifschitz (1996)
New Global Instabilities of the Riemann ellipsoids
The Astrophysical Journal, Vol. 458, pp. 699 - 713
 Acknowledgements (p. 712):"The research reported here was supported by the National Science Foundation through grants DMS 9207808 [should be, DMS 9207080] with the University of Chicago (N. R. L.) and IRI 9924605 with the University of Illinois at Chicago (A. L.)." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### NT97

K. C. B. New & J. E. Tohline (1997)
The Relative Stability Against Merger of Close, Compact Binaries
The Astrophysical Journal, Vol. 490, pp. 311 - 327
 Acknowledgements (pp. 326 - 327):"This work has been supported, in part, by funding from the National Science Foundation through grants AST 90-08166, AST 95-28424, and PHY 92-08914, from NASA through grants NAGW-2447 and NAG 5-2777, from the Louisiana State Board of Regents through grant LEQSF(1995-1998)-115-35-4412, from the Baton Rouge, Louisiana Branch of the American Association of University Women through a Doctoral Candidate Scholarship, and by computational resources from the Pittsburgh Supercomputing Center through grant PHY 91-0018P. The great majority of the numerical simulations presented herein were carried out on computers in the Department of Physics and Astronomy's Concurrent Computing Laboratory for Materials Simulation, which was established through grants LEQSF(1990-92)-ENH-12 and LEQSF(1993-94)-ENH-TR05 from the Louisiana State Board of Regents. Several of the numerical simulations also were carried out at the Scalable Computing Laboratory of the Department of Energy Ames Laboratory at Iowa State University. We would also like to thank Joan Centrella, Dimitris Christodoulou, Greg Cook, Dong Lai, Dustin Laurence, Kip Thorne, and Horst Väth for useful conversations and assistance." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### EFC98

P. P. Eggleton, J. Faulkner, & R. C. Cannon (1998)
A Small Contribution to the Giant Problem
Monthly Notices of the Royal Astronomical Society, Vol. 298, issue 3, pp. 831 - 834
 Acknowledgements (p. 833):"JF thanks the Institute of Astronomy, Cambridge, for its hospitality during the completion of this paper. PPE and RCC are grateful to the Institute of Theoretical Physics, Santa Barbara (NSF grant PH489-04035) [should be PHY-8904035] for its hospitality at an earlier stage." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

## 21st Century

### MTF2002

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
 Acknowledgements (p. 148):"This work has been performed with support from the National Science Foundation through grants AST-9720771, AST-9528424, AST-9987344, and DGE-935507 [should be, DGE-9355007] and from the National Aeronautics and Space Administration through the Astrophysics Theory Program grant NAG5-8497. This research has been supported in part, by grants of high-performance computing time at the National Partnership for Advanced Computing Infrastructure (NPACI) facilities at the San Diego Supercomputer Center and by Louisiana State University's High Performance Computing facilities. We would also like to acknowledge the many useful comments made by the referee that led to a significant improvement in the contents of this paper." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### Ou2006

S. Ou (2006)
An Approximate Solver for Riemann and Riemann-Like Ellipsoidal Configurations
The Astrophysical Journal, Vol. 639, pp. 549 - 558
 Acknowledgements (p. 558):"I would like to thank Joel Tohline for valuable suggestions, discussions, and for carefully reading through this paper. I also thank Juhan Frank and Patrick Motl for helpful comments. It is a pleasure to thank Norman Lebovitz for drawing our attention to the particular analytical expression of the velocity field of Riemann S-type ellipsoids used in this study. I would also thank Howard Cohl for developing the Poisson solver that was an important ingredient in this work. I thank the anonymous referee for insightful suggestions on the analysis of our models. This work was partially supported by National Science foundation grants AST 04-07070 and PHY-0326311 and by the Center for Computation and Technology at LSU." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### ZEUS-MP2006

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
 Acknowledgements (p. 211):"The release of a vastly redesigned and augmented 'Version 2' of ZEUS-MP was occasioned by ZEUS-MP's adoption by the Terascale Supernova Initiative as a computational platform for simulating core-collapse supernova explosions in multidimensions. The TSI project, led by Anthony Mezzacappa, provided both the demand and much of the financial support for the effort that created this code. We are indebted to Tony Mezzacappa for his continued support, enthusiasm, and remarkable patience during the development phase of ZEUS-MP 2.0. In addition, we gratefully acknowledge the continued support and wise counsel from Frank Graziani at the Lawrence Livermore National Laboratory. This work was supported by SciDAC grants from the DOE Office of Science High-Energy, Nuclear, and Advanced Scientific Computing Research Programs, and by DOE contract W-7405-ENG-48." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### OTM2007

S. Ou, J. E. Tohline, & P. M. Motl (2007)
Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars
The Astrophysical Journal, Vol. 665, pp. 1074 - 1083)]
 Acknowledgements (p. 1083):"We would like to thank Lee Lindblom, John Friedman, Nikolaos Stergioulas, Yuk Tung Liu, and Juhan Frank for valuable discussions. This work was partially supported by NSF grants AST-0407070 and PHY-0326311. The computations were performed on the Supermike cluster and the Superhelix cluster at LSU, and on the Tungsten cluster at National Center for Supercomputing Applications (NCSA)." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### PK2007

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
 Acknowledgements (p. 710):"This work was supported in part by the US Department of Energy under contract B523820 to the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. AYP also expresses gratitude to the Institute for Pure and Applied Mathematics (IPAM), UCLA for support during the semester program 'Grand Challenge Problems in Computational Astrophysics', March-June, 2005. The authors are grateful to anonymous referees for valuable comments and criticisms." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

### MT2012

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.

 Acknowledgements (p. 27):"We acknowledge valuable interactions that we have had with J. Frank, G. Clayton, P. M. Motl, and W. Even over the course of this project. We also acknowledge the referee for his thorough analysis of our work and his insightful comments. This work has been supported, in part, by grants PHY-0803629, AST-0708551, EPS-1006891, OIA-0963375, and DGE-0504507 from the U. S. National Science Foundation and, in part, by NASA/ATP grants NNX10AC72G and NNX07AG84G. This research also has been made possible by grants of high-performance computing time on the TeraGrid (TG-AST090104), at LSU, and across LONI (Louisiana Optical Network Initiative), especially awards loni_astro08 and loni_astro09." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

#### BTZ2012

W. H. Ball, C. A. Tout, & A. N. Żytkow (2012)
Quasi-stars, Giants and the Schönberg-Chandrasekhar Limit
Monthly Notices of the Royal Astronomical Society, Vol. 421, issue 3, pp. 2713 - 2721
 Acknowledgements (p. 2720):"WHB and ANŻ are grateful to Ramesh Narayan for the discussion that led to the authors pursuing this line of work. We also thank Peter Eggleton for discussing the formation of giants. CAT thanks Churchill College for a fellowship." Click to list chapter(s) on this wiki site that either … cite or display an image/figure/table from this article.

# 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] 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

## 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