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A middle-aged radio-quiet pulsar J0357+3205 was discovered in gamma-rays with$Fermi$ and later in X-rays with $Chandra$ and $XMM$-$Newton$ observatories. Itproduces an unusual thermally-emitting pulsar wind nebula observed in X-rays.Deep optical observations were obtained to search for the pulsar opticalcounterpart and its nebula using the Gran Telescopio Canarias (GTC). The directimaging mode in the Sloan $g'$ band was used. Archival X-ray data werereanalysed and compared with the optical data. No pulsar optical counterpartwas detected down to $g'\geq~28_{\cdotp}^{\text{m}}1$. No pulsar nebula waseither identified in the optical. We confirm early results that the X-rayspectrum of the pulsar consists of a nonthermal power-law component of thepulsar magnetospheric origin dominating at high energies and a soft thermalcomponent from the neutron star surface. Using magnetised partially ionisedhydrogen atmosphere models in X-ray spectral fits we found that the thermalcomponent can come from entire surface of the cooling neutron star with atemperature of 36$^{+9}_{-6}$ eV, making it one of the coldest among coolingneutron stars known. The surface temperature agrees with the standard neutronstar cooling scenario. The optical upper limit does not put any additionalconstraints on the thermal component, however it implies a strong spectralbreak for the nonthermal component between the optical and X-rays as isobserved in other middle-aged pulsars. The thermal emission from the entiresurface of the neutron star likely dominates over the nonthermal emission inthe UV range. Observations of the PSR J0357+3205 in this range are promising toput more stringent constraints on its thermal properties.

Deep optical observations of the gamma-ray pulsar J0357+3205