  We have monitored the phase of the main X-ray pulse of the Crab pulsar with
the Rossi X-ray Timing Explorer (RXTE) for almost eight years, since the start
of the mission in January 1996. The absolute time of RXTE's clock is
sufficiently accurate to allow this phase to be compared directly with the
radio profile. Our monitoring observations of the pulsar took place bi-weekly
(during the periods when it was at least 30 degrees from the Sun) and we
correlated the data with radio timing ephemerides derived from observations
made at Jodrell Bank. We have determined the phase of the X-ray main pulse for
each observation with a typical error in the individual data points of 50 us.
The total ensemble is consistent with a phase that is constant over the
monitoring period, with the X-ray pulse leading the radio pulse by
0.0102+/-0.0012 period in phase, or 344+/-40 us in time. The error estimate is
dominated by a systematic error of 40 us in the radio data, arising from
uncertainties in the variable amount of pulse delay due to interstellar
scattering and instrumental calibration. The statistical error is 0.00015
period, or 5 us. The separation of the main pulse and interpulse appears to be
unchanging at time scales of a year or less, with an average value of
0.4001+/-0.0002 period. There is no apparent variation in these values with
energy over the 2-30 keV range. The lag between the radio and X-ray pulses may
be constant in phase (rotational) or constant in time (linear pathlength). We
are not (yet) able to distinguish between these two interpretations.
