Where are the r-modes of isentropic stars?

Keith H. Lockitch; John L. Friedman

doi:10.1086/307580

paper

Where are the r-modes of isentropic stars?

arXiv:gr-qc/9812019 · doi:10.1086/307580

Abstract

Almost none of the r-modes ordinarily found in rotating stars exist, if the star and its perturbations obey the same one-parameter equation of state; and rotating relativistic stars with one-parameter equations of state have no pure r-modes at all, no modes whose limit, for a star with zero angular velocity, is a perturbation with axial parity. Similarly (as we show here) rotating stars of this kind have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. Where have these modes gone? In spherical stars of this kind, r-modes and g-modes form a degenerate zero-frequency subspace. We find that rotation splits the degeneracy to zeroth order in the star's angular velocity $Ω$ , and the resulting modes are generically hybrids, whose limit as $Ω \to 0$ is a stationary current with axial and polar parts. Because each mode has definite parity, its axial and polar parts have alternating values of $l$ . We show that each mode belongs to one of two classes, axial-led or polar-led, depending on whether the spherical harmonic with lowest value of $l$ that contributes to its velocity field is axial or polar. We numerically compute these modes for slowly rotating polytropes and for Maclaurin spheroids, using a straightforward method that appears to be novel and robust. Timescales for the gravitational-wave driven instability and for viscous damping are computed using assumptions appropriate to neutron stars.

54 pages including 4 ps tables and 11 PSTeX figures, AAS latex. To appear in the Astrophysical Journal

Where are the r-modes of isentropic stars?

Abstract

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