Rotational effects on stellar structure and stability

Details Rotational effects on stellar structure and stability Rotational effects on stellar structure and stability

Aug 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...288..191k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 288, no. 1, p. 191-203

Mathematics

1

Angular Momentum, Stability, Stellar Interiors, Stellar Oscillations, Stellar Rotation, Stellar Structure, Analysis (Mathematics), Energy Distribution, Equilibrium Equations, Frequencies, Moments Of Inertia, Nonlinear Equations, Perturbation

Scientific paper

We present a non-linear analysis of rotational effects (i.e. effects of changes in the angular momentum distribution) in slightly distorted stars. The discussion is universal, i.e. approximately valid for any rotation law. The quantities involved (energies, moment of inertia, fundamental frequency etc.) are integral quantities. The discussion is based on universal relations between integral quantities. The law of energy conservation and the virial theorem are linear universal relations. Ledoux's formula is a non-linear universal relation. Two further non-linear universal relations are derived in this paper. The resulting set of equations is sufficient for a discussion of rotational effects. In case of constant gamma the rotational effects on integral quantities can be described by simple analytic expressions. A special case are polytropes in differential rotation. Linear rotational effects are shown to be destabilizing. This extends results of Sidorov. Non-linear effects in stable configurations are also destabilizing. In unstable systems however non-linear effects can be stabilizing. This explains the stabilizing influence of rotation which is seen from Ledoux's formula. In marginally unstable systems an increase of angular momentum is impossible, i.e. incompatible with hydrostatic equilibrium. In systems with gamma less than 4/3 there is an upper limit for the angular momentum. Loss of stability occurs when the angular momentum distribution prevents hydrostatic equilibrium.

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