ROSAT Timing of the LMC Pulsar 0540-69

We present a timing study of the young rotation-powered pulsar 0540-69 in the Large Magellanic Cloud, based on 130 kiloseconds of archival ROSAT data spanning a $\sim 3$-year period. We use ``$f- \dot f$'' techniques to measure the pulsar frequency as a function of frequency derivative at 17 independent epochs. From these measurements we derive a timing solution with a braking index $n = 2.5^{+0.6}_{-0.7}$, and we compare this solution to previous timing studies of 0540-69. Using this frequency-based solution, we create 27 pulse profiles and perform a time-of-arrival (TOA) analysis to investigate further the pulsar's timing behavior. While we can successfully fit smooth spin-down models to subsets of the TOAs spanning up to 2 years, we are unable to obtain acceptable phase-coherent fits to the entire 3-year set of TOAs. This behavior provides the first clear evidence for timing noise in 0540-69. We discuss the implications of these results for understanding previous studies of the timing behavior of 0540-69.