Difference between revisions of "User:Tohline/Apps/RotatingPolytropes"
| Line 27: | Line 27: | ||
<td align="center" width="5%"> </td><td align="left"> | <td align="center" width="5%"> </td><td align="left"> | ||
<font color="green">If one ''assumes'' that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids. This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids.</font> | <font color="green">If one ''assumes'' that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids. This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids.</font> | ||
</td></tr></table> | |||
* [https://ui.adsabs.harvard.edu/abs/1964ApJ...140..552J/abstract R. A. James (1964)], 140, 552 | |||
<table border="0" align="center" width="100%" cellpadding="1"><tr> | |||
<td align="center" width="5%"> </td><td align="left"> | |||
<font color="green">Structures have been determined for axially symmetric</font> [uniformly] <font color="green">rotating gas masses, in the polytropic and white-dwarf cases … Physical parameters for the rotating configurations were obtained for values of n < 3, and for a range of white-dwarf configurations. The existence of forms of bifurcation of the axially symmetric series of equilibrium forms was also investigated. The white-dwarf series proved to lack such points of bifurcation, but they were found on the polytropic series for n < 0.808.</font> | |||
</td></tr></table> | </td></tr></table> | ||
* [https://ui.adsabs.harvard.edu/abs/1970A%26A.....4..423T/abstract J. - L. Tassoul & J. P. Ostriker (1970)], Astron. Ap., 4, 423 | * [https://ui.adsabs.harvard.edu/abs/1970A%26A.....4..423T/abstract J. - L. Tassoul & J. P. Ostriker (1970)], Astron. Ap., 4, 423 | ||
Revision as of 21:38, 16 June 2019
Rotationally Flattened Polytropes
|
|---|
| | Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
Example Equilibrium Configurations
Reviews
- N. R. Lebovitz (1967), ARAA, 5, 465
Uniform Rotation
- E. A. Milne (1923), MNRAS, 83, 118: The Equilibrium of a Rotating Star
|
Apparently, only n = 3 polytropic configurations are considered. |
- H. von Zeipel (1924), MNRAS, 84, 665: The radiative equilibrium of a rotating system of gaseous masses
- H. von Zeipel (1924), MNRAS, 84, 684: The radiative equilibrium of a slightly oblate rotating star
- S. Chandrasekhar (1933), MNRAS, 93, 390
|
The purpose of this paper is … to extend Emden's [work] to the case of rotating gas spheres which in their non-rotating states have polytropic distributions described by the so-called Emden functions. … the gas sphere is set rotating at a constant small angular velocity <math>~\omega</math>. … we shall assume that the rotation is so slow that the configurations are only slightly oblate. |
- S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1069
|
If one assumes that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids. This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids. |
- R. A. James (1964), 140, 552
|
Structures have been determined for axially symmetric [uniformly] rotating gas masses, in the polytropic and white-dwarf cases … Physical parameters for the rotating configurations were obtained for values of n < 3, and for a range of white-dwarf configurations. The existence of forms of bifurcation of the axially symmetric series of equilibrium forms was also investigated. The white-dwarf series proved to lack such points of bifurcation, but they were found on the polytropic series for n < 0.808. |
- J. - L. Tassoul & J. P. Ostriker (1970), Astron. Ap., 4, 423
- M. J. Clement (1981), ApJ, 249, 746
Differential Rotation
- S. Chandrasekhar & N. R. Lebovitz (1962), ApJ, 136, 1082
|
The oscillations of slowly rotating polytopes are treated in this paper. The initial equilibrium configurations are constructed as in Chandrasekhar (1933). |
- J. P. Ostriker & P. Bodenheimer (1973), ApJ, 155, 987 [Part III]
- P. Bodenheimer & J. P. Ostriker (1973), ApJ, 180, 159 [Part VIII]
- J. L. Friedman & B. F. Schutz (1978), ApJ, 222, 281
- R. H. Durisen & J. N. Imamura (1981), ApJ, 243, 612
- J. E. Tohline, R. H. Durisen & M. McCollough (1985), ApJ, 298, 220
- R. H. Durisen, R. A. Gingold, J. E. Tohline & A. P. Boss (1986), ApJ, 305, 281
- H. A. Williams & J. E. Tohline (1987), ApJ, 315, 594
- H. A. Williams & J. E. Tohline (1988), ApJ, 334, 449
- P. J. Luyten (1990), MNRAS, 245, 614
- P. J. Luyten (1991), MNRAS, 248, 256
- A. G. Aksenov (1996), Astronomy Letters, 22, 634
- B. K. Pickett, R. H. Durisen & G. A. Davis (1996), ApJ, 458, 714
- B. K. Pickett, R. H. Durisen & R. Link (1997), Icarus, 126, 243
- J. Toman, J. N. Imamura, B. K. Pickett & R. H. Durisen (1998), ApJ, 497, 370
- J. N. Imamura, R. H. Durisen & B. K. Pickett (2000), ApJ, 528, 946
- J. M. Centrella, K. C. B. New, L. L. Lowe & J. D. Brown (2001), ApJL, 550, 193
- M. Shibata, S. Karino & Y. Eriguchi (2002), MNRAS, 334, 27
- M. Saijo, T. W. Baumgarte & S. L. Shapiro (2003), ApJ, 595, 352
- M. Saijo & S. Yoshida (2006), MNRAS, 368, 1429
See Also
|
|
|---|
|
© 2014 - 2021 by Joel E. Tohline |