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

We have modelled the nonlinear development of the secular bar-modeinstability that is driven by gravitational radiation-reaction (GRR) forces inrotating neutron stars. In the absence of any competing viscous effects, aninitially uniformly rotating, axisymmetric $n=1/2$ polytropic star with a ratioof rotational to gravitational potential energy $T/|W| = 0.181$ is driven byGRR forces to a bar-like structure, as predicted by linear theory. The patternfrequency of the bar slows to nearly zero, that is, the bar becomes almoststationary as viewed from an inertial frame of reference as GRR removes energyand angular momentum from the star. In this ``Dedekind-like'' state, rotationalenergy is stored as motion of the fluid in highly noncircular orbits inside thebar. However, in less than 10 dynamical times after its formation, the barloses its initially coherent structure as the ordered flow inside the bar isdisrupted by what appears to be a purely hydrodynamical, short-wavelength,``shearing'' type instability. The gravitational waveforms generated by such anevent are determined, and an estimate of the detectability of these waves ispresented.