The R-Mode Oscillations in Relativistic Rotating Stars

Details The R-Mode Oscillations in Relativistic Rotating Stars The R-Mode Oscillations in Relativistic Rotating Stars

1999-03-03

arxiv.org/abs/astro-ph/9903055v1

Astronomy and Astrophysics

Astrophysics

19 pages, 4 figures, AAS LaTeX, Accepted for publication in The Astrophysical Journal

Scientific paper

The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations governing the r-mode oscillations up to the second order with respect to the rotation. In the lowest order, the allowed range of the frequencies is determined, but corresponding spatial function is arbitrary. The spatial function can be decomposed in non-barotropic region by a set of functions associated with the differential equation of the second-order corrections. The equation however becomes singular in barotropic region, and a single function can be selected to describe the spatial perturbation of the lowest order. The frame dragging effect among the relativistic effects may be significant, as it results in rather broad spectrum of the r-mode frequency unlike in the Newtonian first-order calculation.

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