The LMC pulsar PSR 0540-69, a young, rapidly rotating neutron star of
dynamic age approximately 1000 yr, was observed with the Position Sens
itive Proportional Counter (PSPC) onboard ROSAT for approximately 29,0
00 s in 1990 June, 1990 July, and 1991 February. The timing data are c
onsistent with contemporaneous optical ephemerides suggesting that the
optical and X-ray pulses are in phase. The characteristic broad sinus
oidal pulse profile of PSR 0540-69 is observed at a pulsed fraction of
approximately 15% measured against the pulsar plus the unresolved neb
ula. The spectral distribution of the pulsar + nebula counts is well d
escribed by a simple power law with a photon index of alpha = (2.4-1.8
5) and a neutral hydrogen column density of N(H) = (3.6-4.6) x 10(21)
cm-2 at the 90% confidence level. The implied model luminosity in the
0.1-2.4 keV.band is 1.6 x 10(37) ergs s-1 which is approximately 11 %
of the available rotational energy loss rate and similar to the value
observed in the Crab nebula + pulsar. A positive correlation between t
he X-ray hardness and the pulse phase intensity implies an underlying
spectrum for the pulsar which is harder than the nebula. A phase-resol
ved spectral fit to the pulsed component supports a harder spectrum fo
r the pulsar and gives a power-law photon index of alpha(pulsed) = 1,3
, The derived pulsed luminosity of 1.5 x 10(36) ergs s-1 is approximat
ely 9% of the total X-ray luminosity.