arXiv2016
We report the analysis of the first deep optical observations of three isolated $γ$-ray pulsars detected by the {\em 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 ($τ\sim$40--60 kyrs), spin-down energy ($\dot{E} \sim10^{35}$ erg s$^{-1}$), and dipolar surface magnetic field ($B \sim 3$--$5\times10^{12}$ G). These pulsars are promising targets for multi-wavelength observations, since they have been already detected in $γ$ 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 {\em Chandra} positions down to $3 σ$ limits of $g'\sim27.3$, $g'\sim27$, $g'\sim27.3$ 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 \chan\ but we did not detect the pulsar down to a 3$σ$ 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 $γ$-ray spectra and compared their multi-wavelength properties with those of other $γ$-ray pulsars of comparable age.