A multi-wavelength investigation of candidate milli-second pulsars in unassociated γ-ray sources

About one third of the 3033 $\gamma$-ray sources in the Third Fermi-LAT Gamma-ray Source Catalogue (3FGL) are unidentified and do not have even a tentative association with a known object, hence they are defined as unassociated. Among Galactic $\gamma$-ray sources, pulsars represent the largest class, with over 200 identifications to date. About one third of them are milli-second pulsars (MSPs) in binary systems. Therefore, it is plausible that a sizeable fraction of the unassociated Galactic $\gamma$-ray sources belong to this class. We collected X-ray and optical observations of the fields of twelve unassociated Fermi sources that have been classified as likely MSPs according to statistical classification techniques. To find observational support for the proposed classification, we looked for periodic modulations of the X-ray and optical flux of these sources, which could be associated with the orbital period of a MSP in a tight binary system. Four of the observed sources were identified as binary MSPs, or proposed as high-confidence candidates, while this work was in progress. For these sources, we present the results of our follow-up investigations, whereas for the others we present possible evidence of new MSP identifications. In particular, we discuss the case of 3FGL J0744.1-2523 that we proposed as a possible binary MSP based upon the preliminary detection of a 0.115 d periodicity in the flux of its candidate optical counterpart. We also found very marginal evidence of periodicity in the candidate optical counterpart to 3FGL J0802.3-5610, at a period of 0.4159 d, which needs to be confirmed by further observations.