Pulsars traveling at supersonic speeds are often accompanied by cometary bow shocks seen in Halpha. We report on the first detection of a pulsar bow shock in the far-ultraviolet (FUV). We detected it in FUV images of the nearest millisecond pulsar J0437-4715 obtained with the Hubble Space Telescope. The images reveal a bow-like structure positionally coincident with part of the previously detected Halpha bow shock, with an apex at 10 ahead of the moving pulsar. Its FUV luminosity, L(1250-2000 A) ~ 5x10^28 erg/s, exceeds the Halpha luminosity from the same area by a factor of 10. The FUV emission could be produced by the shocked ISM matter or, less likely, by relativistic pulsar wind electrons confined by strong magnetic field fluctuations in the bow shock. In addition, in the FUV images we found a puzzling extended (~3 in size) structure overlapping with the limb of the bow shock. If related to the bow shock, it could be produced by an inhomogeneity in the ambient medium or an instability in the bow shock. We also report on a previously undetected X-ray emission extending for about 5 ahead of the pulsar, possibly a pulsar wind nebula created by shocked pulsar wind, with a luminosity L(0.5-8 keV) ~ 3x10^28 erg/s.
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