Context. The knowledge of the present-day mass function of young clusters and the mass of their coolest substellar members is essential to clarify the brown dwarf formation mechanism, which still remains a matter of debate. Aims. We searched for isolated planetary-mass T-dwarfs in the ?~3?Myr old Serpens Core cluster. Methods. We performed a deep imaging survey of the central part of this cluster using the WIRCam camera at the CFHT. Observations were performed through the narrow-band CH4off and CH4on filters, to identify young T-dwarfs from their 1.6?μm methane absorption bands, and the broad-band JHKS filters, to better characterize the selected candidates. We complemented our WIRCam photometry with optical imaging data from MegaCam at CFHT and Suprime-Cam at the Subaru telescope and mid-infrared flux measurements from the Spitzer “core to disk” (c2d) Legacy Survey. Results. We report four faint T-dwarf candidates in the direction of the Serpens Core with CH4on?CH4off above 0.2?mag, estimated visual extinction in the range 1?9?mag and spectral type in the range T1?T5 based on their dereddened CH4on?CH4off colors. Comparisons with T-dwarf spectral models and optical to mid-infrared color–color and color–magnitude diagrams, indicate that two of our candidates (ID?1 and 2) are background contaminants (most likely heavily reddened low-redshift quasars). The properties of the other two candidates (ID?3 and 4) are consistent with them being young members of the Serpens Core cluster, although our analysis can not be considered conclusive. In particular, ID?3 may also be a foreground T-dwarf. It is detected by the Spitzer c2d survey but only flux upper limits are available above 5.8?μm and, hence, we can not assess the presence of a possible disk around this object. However, it presents some similarities with other young T-dwarf candidates (S?Ori?70 in the σ?Orionis cluster and CFHT_J0344+3206 in the direction of IC?348). If ID?3 and 4 belong to Serpens, they would have a mass of a few Jupiter masses and would be amongst the youngest, lowest mass objects detected in a star-forming region so far.
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