Dynamical bar instability in rotating stars: effect of general relativity
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, 919931.
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Description/Abstract
We study the dynamical stability against barmode deformation of rapidly and differentially rotating stars in the first postNewtonian 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 barmode 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 barmode 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 KelvinHelmholtz circulation is wellconserved, in addition to restmass energy, total massenergy, 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 quasiperiodic gravitational waves emitted during the bar formation process using the quadrupole formula.
Item Type:  Article  

Related URLs:  
Subjects:  Q Science > QB Astronomy Q Science > QA Mathematics 

Divisions :  University Structure  Pre August 2011 > School of Mathematics > Applied Mathematics 

ePrint ID:  29408  
Accepted Date and Publication Date: 


Date Deposited:  11 May 2006  
Last Modified:  31 Mar 2016 11:55  
URI:  http://eprints.soton.ac.uk/id/eprint/29408 
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