Instability of rapidly rotating polytropes

Details Instability of rapidly rotating polytropes Instability of rapidly rotating polytropes

Apr 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995sjam...55..298b&link_type=abstract

SIAM Journal on Applied Mathematics (ISSN 0036-1399), vol. 55, no. 2, p. 298-331

Astronomy and Astrophysics

Astrophysics

2

Astrophysics, Eigenvalues, Gravitation, Motion Stability, Polytropic Processes, Rotating Matter, Approximation, Asymptotic Series, Compressibility Effects, Differential Equations, Fluid Dynamics, Integral Equations

Scientific paper

The linear stability theory of rapidly rotating, self-gravitating polytropes is developed by an asymptotic, shallow-layer method. This reduces the general three-dimensional stability problem to an integro-differential eigenvalue problem (a Fredholm integral equation of the second kind) for normal modes. At leading order, the asymptotic analysis produces familiar, zero-thickness disk equations. In subsequent orders, stabilizing effects due to compressibility enter. We solve the stability equations numerically and construct approximate solutions using short-wavelength arguments. The eigenspectrum of a disk can have various forms; instabilities of a pressure-less configuration form a continuous piece of the spectrum, but polytropic disks can have discrete, unstable eigenvalues. A further example is provided by the rigidly rotating disk, which, at leading order, can be solved exactly.

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