Axial instability of rotating relativistic stars

Details Axial instability of rotating relativistic stars Axial instability of rotating relativistic stars

1997-06-23

arxiv.org/abs/gr-qc/9706073v3

Astrophys.J. 502 (1998) 714-720

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of timescales is corrected and updated

Scientific paper

10.1086/305920

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\phi}$ for all values of $m\geq 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $\Omega$, to be proportional to a high power of $\Omega$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.

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