Nonlinear Development of the Secular Bar‐Mode Instability in Rotating Neutron Stars

Abstract

We have modeled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating axisymmetricn ¼ 1=2polytropic star with a ratio of rotational to gravitational potential energy T = W jj ¼0:181 is driven by GRR forces to a barlike structure, as predicted by linear theory. The pattern frequencyofthebarslowstonearlyzero,thatis,thebarbecomesalmoststationaryasviewedfromaninertialframe ofreferenceasGRRremovesenergyandangularmomentumfromthestar.Inthis‘‘Dedekind-like’’state,rotational energyisstoredasmotionofthefluidinhighlynoncircularorbitsinsidethebar.However,inlessthan10dynamical timesafteritsformationthe bar losesitsinitially coherent structure astheorderedflow insidethe baris disruptedby what appears to be a purely hydrodynamic short-wavelength ‘‘shearing’’-type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented. Subject headingg gravitational waves — hydrodynamics — instabilities — stars: neutron