We present the first optical observations of the unique system J0737-3039 (composed of two pulsars, hereafter PSR-A and PSR-B). Ultra-deep optical observations, performed with the High Resolution Camera of the Advanced Camera for Surveys on board the Hubble Space Telescope could not detect any optical emission from the system down to m_F435W=27.0 and m_F606W=28.3. The estimated optical flux limits are used to constrain the three-component (two thermal and one non-thermal) model recently proposed to reproduce the XMM-Newton X-ray spectrum. They suggest the presence of a break at low energies in the non-thermal power law component of PSR-A and are compatible with the expected black-body emission from the PSR-B surface. The corresponding efficiency of the optical emission from PSR-As magnetosphere would be comparable to that of other Myr-old pulsars, thus suggesting that this parameter may not dramatically evolve over a time-scale of a few Myr.
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