Spontaneous Symmetry Breaking of Rapidly Rotating Stars in General Relativity
Abstract
We investigate the effects of general relativity upon the nonaxisymmetric "bar" mode secular instability of rapidly rotating stars, i.e., the relativistic and compressible analog of the transition from Maclaurin spheroids to Jacobi ellipsoids. Our method consists of perturbing a stationary axisymmetric configuration, constructed by a twodimensional general relativistic numerical code, and taking into account only the dominant terms in the nonaxisymmetric part of the threedimensional relativistic equations. For a polytropic equation of state, we have determined, as a function of the degree of relativity, the critical adiabatic index γ_{crit} above which rapidly rotating stars can break their axial symmetry. A byproduct of the present study is the confirmation of the Newtonian value γ_{crit} = 2.238 obtained by James. We have also considered neutron star models constructed upon 12 nuclear matter equations of state taken from the literature. We found that five equations of state from this sample allow the symmetry breaking for sufficiently high rotation velocities. For the others, the Keplerian velocity (mass shedding from the equator) is reached before the axisymmetry is broken. Rotating neutron stars that break their axial symmetry can be an important source of gravitational waves for the LIGO/VIRGO interferometric detectors.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1996
 DOI:
 10.1086/176977
 arXiv:
 arXiv:grqc/9509023
 Bibcode:
 1996ApJ...460..379B
 Keywords:

 GRAVITATION;
 RELATIVITY;
 STARS: INTERIORS;
 STARS: ROTATION;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 29 pages, uuencoded compressed PostScript file. Accepted for publication in ApJ