PSR J0537–6910: Exponential recoveries detected for 12 glitches

Context. Pulsar rotational glitches are unresolved increments of the rotation rate that sometimes trigger an enhancement of the spin-down rate. On occasion, the augmented spin-down decays gradually over days or months in an exponential manner. This is observed particularly after the largest glitch events. Glitches and their exponential recoveries are attributed to the presence of a neutron superfluid inside pulsars. The young pulsar PSR J0537−6910 exhibits the highest known glitching rate, with 60 events detected over nearly 18 years of monitoring. Aims. 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 age, rotational properties, and glitching behaviour typically present significant exponential recoveries. We wish to understand if this is an intrinsic difference of PSR J0537−6910 or a detectability issue due, for example, to its high glitch frequency. Methods. The full dataset, including recent NICER observations, was systematically searched for evidence of exponential relaxations. Each glitch was first tested for evidence of recovery across a broad range of trial timescales. Good candidates were further investigated by identifying the best recovery models with and without an exponential term, then comparing them using Bayesian evidence. Results. We discovered six new glitches, bringing the total number of glitches in this pulsar to 66. Our search and selection criteria strongly indicate the presence of 11 additional, previously undetected, exponential recoveries. We provide updated glitch and timing solutions. Exponential recoveries were detected only for the largest glitches (Δν > 20 μHz), though not for all of them. The inferred exponential timescales vary between 4 and 37 d, with the decaying frequency increment being close to or below 1% of the total in general. We find that the second derivative of the spin frequency ($ \ddot\nu $) can remain fairly stable across several glitches, and only some glitches are associated with persistent $ \ddot{\nu} $ changes. In particular, $ \ddot\nu $ tends to take its lowest values after glitches with exponential recoveries, corresponding to inter-glitch braking indices nig ∼ 6–9. On the other hand, following glitches without exponential recoveries – even large ones – $ \ddot{\nu} $ tends to be higher, with varied values that typically lead to braking indices above 9 (inferred nig mostly clustered between 10 and 35).