The Bar‐Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity

Abstract

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with diUerential rotation. We perform fully relativistic three-dimensional simulations of compact stars with M/R 0.1, where M is the total gravitational mass and R the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index ! 2. As in Newtonian theory, we —nd that stars above a critical value of b 4 T /W (where T is the rotational kinetic energy and W the gravita- tional binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation pro—le, the critical value of is D0.24¨0.25, only slightly smaller than b b dGR the well-known Newtonian value D0.27 for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of diUerential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large b subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large do not develop spiral arms or eject mass but adjust to form dynamically stable b Z b dGR ellipsoidal-like con—gurations. If the bar-mode instability is triggered in supernova collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies. Subject headings: dense matterrelativitystars: neutronstars: rotation