A New Class of Unstable Modes of Rotating Relativistic Stars
Abstract
The first numerical study of axial (toroidal) pulsation modes of a slowly rotating relativistic star is presented. The calculation includes terms of first order in ɛ ≡ Ω(R^{3}/M)^{1/2} << 1 (R is the radius, M is the mass, and Ω is the rotation frequency of the star) and accounts for effects due to the Coriolis force. Effects due to the centrifugal flattening of the star enter at order ɛ^{2} and are not included in the analysis. It is shown that increased rotation tends to decrease the damping times for prograde modes, while retrograde modes become longer lived. Specifically, we show that rotation affects the axial gravitational wave wmodes in this way. We also present the first relativistic calculation of the socalled rmodes (analogous to Rossby waves in the Earth's oceans). These have frequencies of the same order of magnitude as the rotation frequency of the star. The presented results indicate that the rmodes are unstable due to the emission of gravitational radiation for all rotating perfect fluid stars. This is interesting, since the previously considered gravitational wave instability associated with (for example) the fmode of the star sets in at a critical rotation rate. Because they are also unstable for the slowest rotating stars, the rmodes may well be of considerable astrophysical importance.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1998
 DOI:
 10.1086/305919
 arXiv:
 arXiv:grqc/9706075
 Bibcode:
 1998ApJ...502..708A
 Keywords:

 RELATIVITY;
 STARS: OSCILLATIONS;
 STARS: ROTATION;
 Relativity;
 Stars: Oscillations;
 Stars: Rotation;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 14 pages, latex