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We discuss the unique spin evolution of the young X-ray pulsar PSRJ0537-6910, a system in which the regular spin down is interrupted by glitchesevery few months. Drawing on the complete timing data from the Rossi X-rayTiming Explorer (RXTE, from 1999-2011), we argue that a trend in theinter-glitch behaviour points to an effective braking index close to $n=7$,much larger than expected. This value is interesting because it would accordwith the neutron star spinning down due to gravitational waves from an unstabler-mode. We discuss to what extent this, admittedly speculative, scenario may beconsistent and if the associated gravitational-wave signal would be withinreach of ground based detectors. Our estimates suggest that one may, indeed, beable to use future observations to test the idea. Further precision timingwould help enhance the achievable sensitivity and we advocate a joint observingcampaign between the Neutron Star Interior Composition ExploreR (NICER) and theLIGO-Virgo network.

The enigmatic spin evolution of PSR J0537-6910: r-modes, gravitational waves and the case for continued timing