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Rotational modes of relativistic stars: analytical results

Rotational modes of relativistic stars: analytical results
Rotational modes of relativistic stars: analytical results
We study the r modes and rotational "hybrid" modes (inertial modes) of relativistic stars. As in Newtonian gravity, the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey the same one-parameter equation of state (as with barotropic stars), there exist no pure r modes at all—no modes whose limit, for a star with zero angular velocity, is an axial-parity perturbation. Rotating stars of this kind similarly have no pure g modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. In spherical stars of this kind, the 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 Omega, and the resulting modes are generically hybrids, whose limit as Omega-->0 is a stationary current with both 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 the lowest value of l that contributes to its velocity field is axial or polar. Newtonian barotropic stars retain a vestigial set of purely axial modes (those with l = m); however, for relativistic barotropic stars, we show that these modes must also be replaced by axial-led hybrids. We compute the post-Newtonian corrections to the l = m modes for uniform density stars. On the other hand, if the star is nonbarotropic (that is, if the perturbed star obeys an equation of state that differs from that of the unperturbed star), the r modes alone span the degenerate zero-frequency subspace of the spherical star. In Newtonian stars, this degeneracy is split only by the order-Omega2 rotational corrections. However, when relativistic effects are included, the degeneracy is again broken at zeroth order. We compute the r modes of a nonbarotropic, uniform density model to first post-Newtonian order.
1550-7998
024019-[26pp]
Lockitch, Keith H.
e5c44256-3ae5-42e8-989b-f5d07683c3ba
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Friedman, John L.
b27c1258-264f-4ec7-89e1-d02939b7dd66
Lockitch, Keith H.
e5c44256-3ae5-42e8-989b-f5d07683c3ba
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Friedman, John L.
b27c1258-264f-4ec7-89e1-d02939b7dd66

Lockitch, Keith H., Andersson, Nils and Friedman, John L. (2000) Rotational modes of relativistic stars: analytical results. Physical Review D, 63 (2), 024019-[26pp]. (doi:10.1103/PhysRevD.63.024019).

Record type: Article

Abstract

We study the r modes and rotational "hybrid" modes (inertial modes) of relativistic stars. As in Newtonian gravity, the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey the same one-parameter equation of state (as with barotropic stars), there exist no pure r modes at all—no modes whose limit, for a star with zero angular velocity, is an axial-parity perturbation. Rotating stars of this kind similarly have no pure g modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. In spherical stars of this kind, the 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 Omega, and the resulting modes are generically hybrids, whose limit as Omega-->0 is a stationary current with both 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 the lowest value of l that contributes to its velocity field is axial or polar. Newtonian barotropic stars retain a vestigial set of purely axial modes (those with l = m); however, for relativistic barotropic stars, we show that these modes must also be replaced by axial-led hybrids. We compute the post-Newtonian corrections to the l = m modes for uniform density stars. On the other hand, if the star is nonbarotropic (that is, if the perturbed star obeys an equation of state that differs from that of the unperturbed star), the r modes alone span the degenerate zero-frequency subspace of the spherical star. In Newtonian stars, this degeneracy is split only by the order-Omega2 rotational corrections. However, when relativistic effects are included, the degeneracy is again broken at zeroth order. We compute the r modes of a nonbarotropic, uniform density model to first post-Newtonian order.

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Published date: 2000

Identifiers

Local EPrints ID: 29435
URI: http://eprints.soton.ac.uk/id/eprint/29435
ISSN: 1550-7998
PURE UUID: 8ac3b26e-4a5d-456d-8663-9d3a1f77863b
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 12 May 2006
Last modified: 28 Jun 2022 01:36

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Contributors

Author: Keith H. Lockitch
Author: Nils Andersson ORCID iD
Author: John L. Friedman

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