As part of a search for thermal surface radiation from nearby neutron
stars, we have carried out a 45,000 s observation of the nearby radio
pulsar PSR 1929 + 10 with the ROSA T PSPC. After background subtractio
n, a net of 420 +/- 25 photons in the 0.1-2.0 keV band were detected a
t the position of the pulsar, corresponding to a luminosity of 1.2 x 1
0(30) ergs s-1 for a source distance of 250 pc, or approximately 3 x 1
0(-4) of the pulsar's spin-down luminosity. We find coherent pulsation
s from PSR 1929+10 at the radio period of 0.2265 s. The folded light c
urve is well fitted by a sinusoidal oscillation with a pulsed fraction
of about 30%. The total spectrum is fitted by a blackbody with a temp
erature T(infinity) almost-equal-to 3.2 x 10(6) K; the implied emittin
g area has a radius of less than 50 m. The maximum of the X-ray light
curve coincides with the radio pulse, suggesting that we are detecting
the hot magnetic polar cap of the star. The temperature limit for the
remainder of the stellar surface is T(infinity) < 3 x 10(5) K. The sp
atial distribution of the photons is consistent with the instrument po
int-spread function. We discuss the implications of these results for
the temperature distribution over the surface of the star and use this
detection to constrain various heating mechanisms for rotation-powere
d neutron stars. We also use a simple model of general relativistic li
ght bending near the stellar surface in conjunction with the radio emi
ssion geometry and the X-ray pulsed fraction to derive a radius for th
e neutron star of R = 9 +/- 3 km.