User:Tohline/Apps/RotatingPolytropes
Rotationally Flattened Polytropes
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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
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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 equilibrium of distorted polytropes. I. The rotational problem
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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
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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. |
- I. P. H. Roberts (1963), ApJ, 137, 1129: On Highly Rotating Polytropes
- R. A. James (1964), 140, 552
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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. |
- F. F. Monaghan & I. W. Roxburgh (1965), MNRAS, 131, 13: The structure of rapidly rotating polytropes
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James attacked the problem by numerically solving the partial differential equations of the problem with the aid of an electronic computer, but even this method lead to difficulties for <math>~n \ge 3</math>. Of all the methods used so far James' is undoubtedly the most accurate, but also the most laborious. Here, results are presented for values of the polytropic index n = 1, 1.5, 2, 2.5, 3, 3.5, 4. (Apparently, uniform rotation is assumed.) … no discussion of stability is given, we assume that the polytropes become unstable at the equator before a point of bifurcation is reached. |
- 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
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The oscillations of slowly rotating polytopes are treated in this paper. The initial equilibrium configurations are constructed as in Chandrasekhar (1933). |
- TORUS! J. P. Ostriker (1964), ApJ, 140, 1067: The Equilibrium of Self-Gravitating Rings
- R. Stoeckly (1965), ApJ, 142, 208: Polytropic Models with Fast, Non-Uniform Rotation [NOTE: Article not available via SAO/NASA ADS.]
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Models with polytropic index n = 1.5.… for the case of non-uniform rotation, no meridional currents, and axial symmetry. The angular velocity assigned … is a Gaussian function of distance from the axis. The exponential constant <math>~c</math> in this function is a parameter of non-uniformity of rotation, ranging from 0 (uniform rotation) to 1 (approximate spatial dependence of angular velocity that might arise during contraction from a uniformly rotating mass of initially homogeneous density). For <math>~c = 0</math>, a sequence of models having increasing angular momentum is known to terminate when centrifugal force balances gravitational force at the equator; this sequence contains no bifurcation point with non-axisymmetric models as does the sequence of Maclaurin spheroids with the Jacobi ellipsoids. For <math>~c \approx 1</math>, the distortion of interior equidensity contours of some models with fast rotation is shown to exceed that of the Maclaurin spheroids at their bifurcation point. In the absence of a rigorous stability investigation, this result suggests that a star with sufficiently non-uniform rotation reaches a point of bifurcation … Non-uniformity of rotation would then be an element bearing on star formation and could be a factor in double-star formation. |
- 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
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