We report the analysis of the first deep optical observations of three isolated \gamma -ray pulsars detected by the Fermi Gamma-ray Space Telescope : the radio-loud PSR J0248+6021 and PSR J0631+1036 , and the radio-quiet PSR J0633+0632 .
The latter has also been detected in the X rays .
The pulsars are very similar in their spin-down age ( \tau \sim 40–60 kyrs ) , spin-down energy ( \dot { E } \sim 10 ^ { 35 } erg s ^ { -1 } ) , and dipolar surface magnetic field ( B \sim 3 – 5 \times 10 ^ { 12 } G ) .
These pulsars are promising targets for multi-wavelength observations , since they have been already detected in \gamma rays and in radio or X-rays .
None of them has been detected yet in the optical band .
We observed the three pulsar fields in 2014 with the Spanish 10.4m Gran Telescopio Canarias ( GTC ) .
We could not find any candidate optical counterpart to the three pulsars close to their most recent radio or Chandra positions down to 3 \sigma limits of g ^ { \prime } \sim 27.3 , g ^ { \prime } \sim 27 , g ^ { \prime } \sim 27.3 for PSR J0248+6021 , J0631+1036 , and J0633+0632 , respectively .
From the inferred optical upper limits and estimated distance and interstellar extinction , we derived limits on the pulsar optical luminosity .
We also searched for the X-ray counterpart to PSR J0248+6021 with Chandra  but we did not detect the pulsar down to a 3 \sigma flux limit of 5 \times 10 ^ { -14 } erg cm ^ { -2 } s ^ { -1 } ( 0.3–10 keV ) .
For all these pulsars , we compared the optical flux upper limits with the extrapolations in the optical domain of the \gamma -ray spectra and compared their multi-wavelength properties with those of other \gamma -ray pulsars of comparable age .