  We observed the gamma-ray pulsar Geminga with the HST STIS/MAMA detectors to
measure the Geminga's UV spectrum and pulsations. The slope of the far-UV (FUV)
spectrum is close to that of a Rayleigh-Jeans spectrum, suggesting that the FUV
radiation is dominated by thermal emission from the neutron star (NS) surface.
The measured FUV flux, F_FUV=(3.7+/-0.2)x10^-15 ergs cm^-2 s^-1 in 1155-1702 A
band, corresponds to a brightness temperature T_RJ=(0.3-0.4)(d_200/R_13)^2 MK.
The soft thermal component of the Geminga's X-ray spectrum measured with the
XMM-Newton observatory corresponds to a temperature T_s=0.49+/-0.01 MK and
radius R_s = (12.9+/-1.0)d_200 km. Unlike other NSs detected in the UV-optical,
the FUV spectrum of Geminga lies below the extrapolation of the soft thermal
component, which might be associated with the Geminga's very low temperature.
Surprisingly, the thermal FUV radiation is strongly pulsed, showing a narrow
dip at a phase close to that of a broader minimum of the soft X-ray light
curve. The strong pulsations might be attributed to partial occultations of the
thermal UV radiation by regions of the magnetosphere filled with
electron/positron plasma. In contrast with the FUV spectrum, the near-IR (NIR)
through near-UV (NUV) spectrum of Geminga is clearly nonthermal. It can be
described by a power-law model, F_nu \propto nu^{-alpha} with a slope alpha =
0.43+/-0.15, close to alpha = 0.56+/-0.24 of the hard X-ray (E>2.5 keV)
magnetospheric component. The observed NIR-optical-NUV spectrum is marginally
consistent with the extrapolation of the X-ray magnetospheric spectrum. The NUV
pulsations, however, do not show a clear correlation with the hard X-ray
pulsations.
