Gravitational radiation from instabilities in rotating compact stars

Janet Lynn Houser

doi:10.17918/00001468

We present 3D numerical simulations of the non-axisymmetric dynamical bar mode instability in a rotating star, as well as the resulting gravitational radiation (calculated in the quadrupole approximation). This instability may operate during the collapse of rapidly rotating stellar cores or in white dwarfs spun up by accretion. Using a smoothed particle hydrodynamics (SPH) code, we have investigated the effects of the stiffness of the polytropic equation of state, and the randomness of the initial state on the gravitational wave quantities, growth rate, and pattern speed of the bar mode instability. The star is modeled as a polytrope with indicies n = 1.5, n = 1.0, and n = 0.5 and initially possesses T_rot/|W| ~ 0.30, where T_rot is the rotational kinetic energy and |W| is the gravitational potential energy of the entire system. The conclusion of this analysis shows that all models deform into a bar shape and shed mass in the form of a two-armed spiral pattern which transports angular momentum out of the core into the envelope via gravitational torques. For the softer equations of state, the system evolves toward a nearly axisymmetric state consisting of a dense core and surrounding uniform quasi-Keplerian tenuous disk with the system T_rot/|W| [less than or equal to] 0.26. A randomly generated initial model expels only ~5% of its original mass and only ~19% of its original angular momentum. However, a cooled initial model expels ~9% and ~30% of its original mass and angular momentum, respectively. We also find that a typical neutron star will radiate from ~0.1% to ~0.31% of its mass and ~0.7% to ~2.0% of its angular momentum in the form of gravitational radiation depending on the randomness of the initial state. As the equation of state stiffens, a typical neutron star will radiate from ~0.31% to ~0.67% of its mass and ~2.0% to ~5.6% of its angular momentum in the form of gravitational waves. The characteristic frequency of these waves will range from ~1kHz to ~5kHz, depending on the radius when the instability occurs, and the dimensionless amplitude will be h ~ 4.0 x 10^-22 at the distance of the Virgo Cluster.

Gravitational radiation from instabilities in rotating compact stars

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Gravitational radiation from instabilities in rotating compact stars

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