Predicting the starquakes in PSR J0537-6910

We report on more than 7 yr of monitoring of PSR J0537-6910, the 16 ms pulsar in the LMC, using data acquired with RXTE. During this campaign the pulsar experienced 23 sudden increases in frequency (glitches) amounting to a total gain of over 6 ppm of rotation frequency superposed on its gradual spin-down of v = -2 x 10(-10) Hz s(-1). The time interval from one glitch to the next obeys a strong linear correlation to the amplitude of the first glitch, with a mean slope of about 400 days ppm(-1) (6.5 days mu Hz(-1)), such that these intervals can be predicted to within a few days, an accuracy that has never before been seen in any other pulsar. There appears to be an upper limit of similar to 40 mu Hz for the size of glitches in all pulsars, with the 1999 April glitch of PSR J0537-6910 the largest so far. The change of its spin-down across the glitches, Delta v, appears to have the same hard lower limit, -1.5 x 10(-13) Hz s(-1), as that observed in all other pulsars. The spin-down continues to increase in the long term, v = -10(-21) Hz s(-2), and thus the timing age of PSR J0537-6910 (-0.5vv(-1)) continues to decrease at a rate of nearly 1 yr every year, consistent with movement of its magnetic moment away from its rotational axis by 1 rad every 10,000 yr, or about 1 m yr(-1). PSR J0537-6910 was likely to have been born as a nearly aligned rotator spinning at 75-80 Hz, with a vertical bar v vertical bar considerably smaller than its current value of 2 x 10(-10) Hz s(-1). Its pulse profile consists of a single pulse that is found to be flat at its peak for at least 0.02 cycles.