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Dynamical bar instability in rotating stars: effect of general relativity

Record type: Article

We study the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in the first post-Newtonian approximation of general relativity. We vary the compaction of the star M/R (where M is the gravitational mass and $R$ the equatorial circumferential radius) between 0.01 and 0.05 to isolate the influence of relativistic gravitation on the instability. For compactions in this moderate range, the critical value of $\beta \equiv T/W$ for the onset of the dynamical instability (where T is the rotational kinetic energy and W the gravitational binding energy) slightly decreases from ~ 0.26 to ~ 0.25 with increasing compaction for our choice of the differential rotational law. Combined with our earlier findings based on simulations in full general relativity for stars with higher compaction, we conclude that relativistic gravitation {\em enhances} the dynamical bar-mode instability, i.e. the onset of instability sets in for smaller values of $\beta$ in relativistic gravity than in Newtonian gravity. We also find that once a triaxial structure forms after the bar-mode perturbation saturates in dynamically unstable stars, the triaxial shape is maintained, at least for several rotational periods. To check the reliability of our numerical integrations, we verify that the general relativistic Kelvin-Helmholtz circulation is well-conserved, in addition to rest-mass energy, total mass-energy, linear and angular momentum. Conservation of circulation indicates that our code is not seriously affected by numerical viscosity. We determine the amplitude and frequency of the quasi-periodic gravitational waves emitted during the bar formation process using the quadrupole formula.

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Citation

Saijo, Motoyuki, Shibata, Masaru, Baumgarte, Thomas W. and Shapiro, Stuart L. (2001) Dynamical bar instability in rotating stars: effect of general relativity The Astrophysical Journal, 548, pp. 919-931.

More information

Published date: 2001

Identifiers

Local EPrints ID: 29408
URI: http://eprints.soton.ac.uk/id/eprint/29408
ISSN: 0004-637X
PURE UUID: fea21b55-1bff-4461-a4be-77f0881b65ad

Catalogue record

Date deposited: 11 May 2006
Last modified: 17 Jul 2017 15:58

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Contributors

Author: Motoyuki Saijo
Author: Masaru Shibata
Author: Thomas W. Baumgarte
Author: Stuart L. Shapiro

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