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 based on a "backbending" behaviour of the moment of inertia. We focus on a particular equation of state that has been used before to study this behaviour, and find that for the population of normal pulsars the moment of inertia does not exhibit a backbending behaviour. In contrast, for supramassive millisecond pulsars a very strong backbending behaviour is found. Essentially, once a quark core appears in a spinning-down supramassive millisecond pulsar, the star spins up and continues to do so until it reaches the instability to collapse. This strong spin-up behaviour makes it easier to distinguish a phase transition in such pulsars: a negative first time-derivative of the rotational period, P < 0, suffices and one does not have to measure the braking index. In the spin-up era, the usually adopted spin-down power law fails to describe the evolution of the angular velocity. We adopt a general-relativistic spin-down power law and derive the equations that describe the angular velocity and braking index evolution in rapidly rotating pulsars. 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. The inclusion of a quark-hadron phase transition can yield a significantly larger initial spin period of 6 ms (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 fastest Crab-like pulsar, so that a pure quark core may have formed recently in its lifetime.