Context. Chamaeleon II molecular cloud is an active star forming region that offers an excellent opportunity for studying the formation of brown dwarfs in the southern hemisphere. Aims. Our aims are to identify a population of pre- and proto- brown dwarfs (5 sigma mass limit threshold of ~0.015 Msun) and provide information on the formation mechanisms of substellar objects. Methods. We performed high sensitivity observations at 870 microns using the LABOCA bolometer at the APEX telescope towards an active star forming region in Chamaeleon II. The data are complemented with an extensive multiwavelength catalogue of sources from the optical to the far-infrared to study the nature of the LABOCA detections. Results. We detect fifteen cores at 870 microns, and eleven of them show masses in the substellar regime. The most intense objects in the surveyed field correspond to the submillimeter counterparts of the well known young stellar objects DK Cha and IRAS 12500-7658. We identify a possible proto-brown dwarf candidate (ChaII-APEX-L) with IRAC emission at 3.6 and 4.5 microns. Conclusions. Our analysis indicates that most of the spatially resolved cores are transient, and that the point-like starless cores in the sub-stellar regime (with masses between 0.016 Msun and 0.066 Msun) could be pre-brown dwarfs cores gravitationally unstable if they have radii smaller than 220 AU to 907 AU (1.2 to 5 at 178 pc) respectively for different masses. ALMA observations will be the key to reveal the energetic state of these pre-brown dwarfs candidates.
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