Some (mostly young) pulsars are experiencing sudden changes in their frequency evolution; changes in the spin frequency are called ‘‘glitches’’. PSR J0537 is special in this respect, because its glitches are amazingly regular. We have recently studied this behaviour using the NICER timing in this paper:
From the point of view of gravitational-wave emission, we hypothesize that the (unknown) glitch mechanism is somehow related to the global mass-energy motion within the neutron star, hence it may be causing a detectable gravitational waves. We have tested this hypothesis in two LIGO-Virgo-KAGRA articles:
Diving below the Spin-down Limit: Constraints on Gravitational Waves from the Energetic Young Pulsar PSR J0537-6910, where the gravitational-wave emission at both once and twice the rotation frequency of the pulsar were searched in the LIGO O3 data,
Constraints from LIGO O3 Data on Gravitational-wave Emission Due to R-modes in the Glitching Pulsar PSR J0537-6910, where we searched for r-mode emission in the epochs between glitches by using a contemporaneous timing ephemeris obtained from NICER data.
No evidence for GW emission was found, but we are already probing physical range of parameters of the neutron star equation of state, so definitely the next observing run (O4, starting December 2022) will reveal more details of this very interesting object.