Dynamical barmode instability of differentially rotating stars: effects of equations of state and velocity profiles
Abstract
As an extension of our previous work, we investigate the dynamical instability against nonaxisymmetric barmode deformations of differentially rotating stars in Newtonian gravity by varying the equations of state and velocity profiles. We performed the numerical simulation and the followup linear stability analysis by adopting polytropic equations of state with polytropic indices n= 1, 3/2 and 5/2, and with two types of angular velocity profiles (the socalled jconstantlike and Keplerlike laws). It is confirmed that rotating stars with a high degree of differential rotation are dynamically unstable against barmode deformation, even when the ratio of the kinetic energy to the gravitational potential energy β is of order 0.01. The criterion for the onset of barmode dynamical instability depends weakly on the polytropic index n and the angular velocity profile, as long as the degree of differential rotation is high. Gravitational waves from the final nonaxisymmetric quasistationary states are calculated using the quadrupole formula. For protoneutron stars of mass 1.4 M_{solar}, radius ~30 km and β<~ 0.1, such gravitational waves have a frequency of ~6001400 Hz, and the effective amplitude is larger than 10^{22} at a distance of about 100 Mpc, irrespective of n and the angular velocity profile.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2003
 DOI:
 10.1046/j.13658711.2003.06699.x
 arXiv:
 arXiv:astroph/0304298
 Bibcode:
 2003MNRAS.343..619S
 Keywords:

 gravitational waves;
 stars: neutron;
 stars: oscillations;
 stars: rotation;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 9 pages, 14 figures, accepted to MNRAS