Predictable Glitches in PSR J0537-6910

We report the accumulated results of more than six and a half years of monitoring of J0537-6910, the 16 ms pulsar in the Large Magellanic Cloud, using data acquired with the Rossi X-ray Timing Explorer. During this campaign the pulsar experienced some 20 sudden increases in frequency ("glitches") of at least one $\mu$Hz, amounting to a gain of six parts per million of rotation frequency superposed on its normal spindown of $\sim-1.99 \times 10(exp -10)$ Hz/s. 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 120 days per 0.3 parts per million. As a result, the time of the next glitch can usually be predicted to an accuracy of a few days. The magnitude of the pulsar spindown continues to increase, and thus its timing age ($-\nu/2\dot\nu$) continues to decrease at a rate of about one year for every two year interval. The implications of these observations are discussed.