Spin-down of Relativistic Stars with Phase Transitions and PSR J0537-6910
Abstract
Using a highly accurate numerical code, we study the spin down of rotating relativistic stars, undergoing a quark deconfinement phase transition. Such phase transitions have been suggested to yield an observable signal in the braking index of spinning-down pulsars, which is assumed to be based on a ``backbending'' behaviour of the moment of inertia. In our computations, this backbending only appears as the result of low resolution in the numerical code and in the equation-of-state (EOS) table, while at the highest accuracy that our numerical code achieves and with an improved description of the EOS, the behaviour of the moment of inertia appears normal. We demonstrate that the expected event rate of the considered signal is negligible for the population of normal pulsars. We further adopt a general-relativistic version of the usual spin-down power law and derive the correct equations that describe the angular velocity and braking index evolution in rapidly rotating pulsars. Previously derived equations in the slow-rotation approximation, to order O(\Omega^2), do not take into account changes in the gravitational mass of the star, except for changes in the kinetic energy. We apply our numerical results to the fast young pulsar J0537-6910 in SNR N157B, which has been suggested to have (if spun down by magnetic dipole radiation only) an extremely small initial spin period. We show that the inclusion of a quark-hadron phase transition yields a significantly larger initial spin period of 6ms (in our example), which is in better agreement with theoretical expectations. Finally, we suggest that the frequent rate of glitches in PSR J0537-6910 could be related to the fact that it is the fasted Crab-like pulsar, so that a pure quark core may have formed recently in its lifetime.Keywords
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