The Structure and Stability of Rotating Gas Masses.

James, R. A.

doi:10.1086/147949

Cited by 212 publications

(183 citation statements)

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“…This is consistent with previous studies that have indicated that the Jacobi sequence cannot exist for n > 0:808 (James 1964;Hachisu & Eriguchi 1982;Lai et al 1993). Furthermore, as was pointed out by Hachisu & Eriguchi (1982) in their analysis of uniformly rotating polytropes, the mass-shedding limit never extends much beyond the bifurcation point (where the Jacobi/ Dedekind sequence branches off the Maclaurin spheroid sequence) even for very small n: for 0:1 n 0:5, this mass-shedding limit corresponds to 0:14 T /jW j 0:16.…”

Section: Resultssupporting

confidence: 94%

An Approximate Solver for Riemann and Riemann‐like Ellipsoidal Configurations

2006

ApJ

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We introduce a new technique for constructing three-dimensional models of incompressible Riemann S-type ellipsoids and compressible triaxial configurations that share the same velocity field as that of Riemann S-type ellipsoids. Our incompressible models are exact steady-state configurations; our compressible models represent approximate steady-state equilibrium configurations. Models built from this method can be used to study a variety of relevant astrophysical and geophysical problems.

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Section: Resultssupporting

confidence: 94%

An Approximate Solver for Riemann and Riemann‐like Ellipsoidal Configurations

2006

ApJ

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“…Finding the ratio of Rp/Re corresponding to the critical configuration is a subtle numerical issue. James (1964 , Table 4) and Hurley & Roberts (1964 , Table 1) give the values 0.558 and 0.493, respectively. Cook et al (1992 , Table 7), who consider general-relativistic configurations report a Newtonian-limit polytropic solution with n = 1 and Rp/Re = 0.552.…”

Section: Numerical Solutionsmentioning

confidence: 99%

The shape of a rapidly rotating polytrope with index unity

Knopik¹,

Mach²,

Odrzywołek³

2017

Mon. Not. R. Astron. Soc.

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We show that the solutions obtained in the paper 'An exact solution for arbitrarily rotating gaseous polytropes with index unity' by Kong, Zhang, and Schubert represent only approximate solutions of the free-boundary Euler-Poisson system of equations describing uniformly rotating, self-gravitating polytropes with index unity. We discuss the quality of such solutions as approximations to the rigidly rotating equilibrium polytropic configurations.

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“…On the other hand, for uniformly rotating polytropes, the m ¼ 2 secular instability cannot occur for polytropes with the polytropic index N > 0:808, because equilibrium sequences terminate due to mass shedding from the equatorial surface before the instability sets in (James 1964).…”

Section: Introductionmentioning

confidence: 99%

Gravitational Radiation Reaction Driven Secular Instability off‐Mode Oscillations in Differentially Rotating Newtonian Stars

Karino

Eriguchi

2002

ApJ

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We have carried out the linear stability analysis of equilibrium sequences of differentially rotating Newtonian polytropic stars. In particular, we have found critical points along the equilibrium sequences for the gravitational radiation reaction driven secular instability of f-mode oscillations with azimuthal wavenumbers m ¼ 2, 3, and 4. We show that the critical values of T=jW j where the instability sets in strongly depend on the degree of differential rotation of the models. Here, T and W are the rotational kinetic energy and the gravitational energy of the star, respectively. We also find that as the degree of differential rotation is increased, the dependence of the critical value of T=jW j on the equations of state becomes weaker.

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The Structure and Stability of Rotating Gas Masses.

Cited by 212 publications

References 0 publications

An Approximate Solver for Riemann and Riemann‐like Ellipsoidal Configurations

An Approximate Solver for Riemann and Riemann‐like Ellipsoidal Configurations

The shape of a rapidly rotating polytrope with index unity

Gravitational Radiation Reaction Driven Secular Instability off‐Mode Oscillations in Differentially Rotating Newtonian Stars

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