ROSAT HRI Observations of the Crab Pulsar: An Improved Temperature upper limit for PSR 0531+21

ROSAT HRI observations have been used to determine an upper limit of the Crab pulsar surface temperature from the off-pulse count rate. For a neutron star mass of 1.4 \Mo and a radius of 10 km as well as the standard distance and interstellar column density, the redshifted temperature upper limit is/ $T_s^{\mathrm{\infty }}\le 1.55\times {10}^6$ K $(3\sigma )$. This is the lowest temperature upper limit obtained for the Crab pulsar so far. Slightly different values for $T_s^{\mathrm{\infty }}$ are computed for the various neutron star models available in the literature, reflecting the difference in the equation of state.