Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes

Details Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes

Apr 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998apj...497..370t&link_type=abstract

Astrophysical Journal v.497, p.370

Astronomy and Astrophysics

Astronomy

33

Hydrodynamics, Instabilities, Stars: Rotation

Scientific paper

We study the dynamic instabilities of rotating polytropes in the linear regime using an approximate Lagrangian technique and a more precise Eulerian scheme. We consider nonaxisymmetric modes with azimuthal dependence proportional to exp (im phi ), where m is an integer and phi is the azimuthal angle, for polytropes with a wide range of compressibilities and angular momentum distributions. We determine stability limits for the m = 2-4 modes and find the eigenvalue and eigenfunction of the most unstable m-mode for given equilibrium models. To the extent that we have explored parameter space, we find that the onset of instability is not very sensitive to the compressibility or angular momentum distribution of the polytrope when the models are parameterized by T/| W |. Here T is the rotational kinetic energy, and W is the gravitational energy of the polytrope. The m = 2, 3, and 4 modes become unstable at T/| W | ~ 0.26-0.28, 0.29-0.32, and 0.32-0.35, respectively, limits consistent with those of the Maclaurin spheroids to within +/-0.015 in T/| W |. The only exception to this occurs for the most compressible polytrope we test and then only for m = 4, where instability sets in at T/| W | ~ 0.37-0.39. The eigenfunctions for the fastest growing low m-modes are similar to those of the Maclaurin spheroid eigenfunctions in that they do not show large vertical motions, are only weakly dependent on z, and increase strongly in amplitude as the equatorial radius of the spheroid is approached. The polytrope eigenfunctions are, however, qualitatively different from the Maclaurin eigenfunctions in one respect: they develop strong spiral arms. The spiral arms are stronger for more compressible polytropes and for polytropes whose angular momentum distributions deviate significantly from those of the Maclaurin spheroids. Nevertheless, our approximate Lagrangian method, which explicitly assumes nonspiral Maclaurin-like trial functions, yields reasonable estimates for the pattern periods and e-folding times of unstable m = 2 modes even for highly compressible and strongly differentially rotating polytropes. Comparisons for m = 2 between the linear analyses in this paper and nonlinear hydrodynamic simulations give excellent quantitative agreement in eigenfunctions, pattern speeds, and e-folding times for the dynamically unstable modes.

Affiliated with

Also associated with

No associations

Rating

Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonaxisymmetric Dynamic Instabilities of Rotating Polytropes. I. The Kelvin Modes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1602582