We report on detection of the double pulsar system J0737-3039 in the far-UV with the ACS/SBC detector aboard HST. We measured the energy flux F = 4.5+/-1.0e-17 erg cm-2s-1 in the 1250-1550 AA band, which corresponds to the extinction-corrected luminosity L~1.5e28 erg s-1 for the distance d=1.1 kpc and a plausible reddening E(B-V)=0.1. If the detected emission comes from the entire surface of one of the neutron stars with a 13 km radius, the surface blackbody temperature is in the range T~2-5e5 K for a reasonable range of interstellar extinction. Such a temperature requires an internal heating mechanism to operate in old neutron stars, or it might be explained by heating of the surface of the less energetic Pulsar B by the relativistic wind of Pulsar A. If the far-UV emission is non-thermal (e.g., produced in the magnetosphere of Pulsar A), its spectrum exhibits a break between the UV and X-rays.
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