Title:PSR J0537-6910: Exponential recoveries detected for 12 glitches

Abstract:Pulsar glitches are unresolved increments of the rotation rate that sometimes trigger an enhancement of the spin-down rate. On occasions, the augmented spin-down decays gradually in an exponential manner, particularly after the largest glitch events. The young pulsar PSR J0537-6910 exhibits the highest known glitching rate, with 60 events detected in nearly 18 years of monitoring. Despite most PSR J0537-6910 glitches being large, only one exponential recovery has been reported, following its first discovered glitch. This is puzzling, as pulsars of similar characteristics typically present significant exponential recoveries. We aim to determine whether this reflects an intrinsic difference in PSR J0537-6910 or a detectability issue, for example due to its high glitch frequency. The full dataset, including recent NICER observations, was systematically searched for exponential relaxations. Each glitch was tested for evidence of a recovery over a broad range of trial timescales. Promising candidates were investigated further by comparing recovery models with and without an exponential term using Bayesian evidence. We discovered six new glitches, bringing the total to 66. Our criteria strongly indicates the presence of 11 previously undetected exponential recoveries. We presente updated glitch and timing solutions. Exponential recoveries are detected only for the largest glitches, though not all of them. The inferred timescales range from 4 to 37 d, with the decaying frequency increment generally below $1\%$ of the total. We find that $\ddot\nu$ can remain stable across several glitches, with persistent changes associated with only some events. In particular, it tends to be lowest after glitches with exponential recoveries, yielding inter-glitch braking indices between 6 and 9. Following glitches without recoveries, $\ddot\nu$ is higher, leading to braking indices between 10 and 35.