Braking index of the frequently glitching PSR J0537-6910

Context. The pulsar J0537-6910 undergoes spin-up glitches more frequently than any other known pulsar, at a rate of roughly thrice per year. Its glitches are typically large and accompanied by abrupt changes in the spin-down rate ( nu(center dot)) that partially recover with a nearly constant positive frequency second derivative ( nu<spacing diaeresis>) for the entire post-glitch interval until the next glitch. The effective long-term value of nu<spacing diaeresis>, however, is negative because nu(center dot)has decreased over the years of observations. Aims. We wished to determine if permanent shifts (non-relaxing parts of the glitch change, Delta nu(center dot), in the spin-down rate, like those observed in the Crab pulsar) can explain the long-term enhancement of the spin-down rate, which results in an effective negative braking index. We demonstrate, as a proof of concept, that the actual braking index (n) associated with the pulsar s braking torque can be similar to 3 if the internal superfluid torque and permanent shifts are considered. Methods. We used published RXTE and NICER data to calculate the average permanent shift per glitch needed to bring an underlying braking index (n) in line with the effective long-term value n congruent to - 1.2 inferred from the data. We then used this average value as the actual permanent shift in each glitch and extracted the contributions of the internal and external torques to the observed nu<spacing diaeresis> for each inter-glitch interval, under the assumption that the next glitch occurs when all glitch-induced offsets to internal torques are fully restored. Results. We find that if the braking index of the magnetospheric torque is close to similar to 3, moderate permanent changes in the spin-down rate are required, of magnitudes similar to the persistent shifts inferred for the Crab pulsar. The natural candidate mechanism to produce such permanent changes is crust-quakes. Crustal failure associated with PSR J0537-6910 glitches can have interesting - and potentially observable - consequences, such as transient changes in the X-ray emission, the activation of radio emission, or the emission of gravitational waves.