Dynamical non-axisymmetric instabilities in rotating relativistic stars

We present new results on dynamical instabilities in rapidly rotating neutron-stars. In particular, using numerical simulations in full General Relativity, we analyse the effects that the stellar compactness has on the threshold for the onset of the dynamical bar-mode instability, as well as on the appearance of other dynamical instabilities. By using an extrapolation technique developed and tested in our previous study [1], we explicitly determine the threshold for a wide range of compactnesses using four sequences of models of constant baryonic mass comprising a total of 59 stellar models. Our calculation of the threshold is in good agreement with the Newtonian prediction and improves the previous post-Newtonian estimates. In addition, we find that for stars with sufficiently large mass and compactness, the m=3 deformation is the fastest growing one. For all of the models considered, the non-axisymmetric instability is suppressed on a dynamical timescale with an m=1 deformation dominating the final stages of the instability. These results, together with those presented in [1], suggest that an m=1 deformation represents a general and late-time feature of non-axisymmetric dynamical instabilities both in full General Relativity and in Newtonian gravity.