Return of the Big Glitcher: NICER timing and glitches of PSR J0537-6910

PSR J0537-6910, also known as the Big Glitcher, is the most prolific glitching pulsar known, and its spin-induced pulsations are only detectable in X-ray. We present results from analysis of 2.7 yr of NICER timing observations, from 2017 August to 2020 April. We obtain a rotation phase-connected timing model for the entire time span, which overlaps with the third observing run of LIGO/Virgo, thus enabling the most sensitive gravitational wave searches of this potentially strong gravitational wave-emitting pulsar. We find that the short-term braking index between glitches decreases towards a value of 7 or lower at longer times since the preceding glitch. By combining NICER and RXTE data, we measure a long-term braking index n = -1.25 ± 0.01. Our analysis reveals eight new glitches, the first detected since 2011, near the end of RXTE, with a total NICER and RXTE glitch activity of $8.88\times 10^{-7}\, \mathrm{yr^{-1}}$. The new glitches follow the seemingly unique time-to-next-glitch-glitch-size correlation established previously using RXTE data, with a slope of $5\, \rm {d} \, \mu \mathrm{Hz}^{-1}$. For one glitch around which NICER observes 2 d on either side, we search for but do not see clear evidence of spectral nor pulse profile changes that may be associated with the glitch.