The substellar mass function in σ Orionis. II. Optical, near-infrared and IRAC/Spitzer photometry of young cluster brown dwarfs and planetary-mass objects

Aims. We investigate the mass function in the substellar domain down to a few Jupiter masses in the young \sigma Orionis open cluster (3\pm2 Ma, d = 360\rm +70}_{\rm-60} pc). Methods. We have performed a deep IJ-band search, covering an area of 790 arcmin super(2) close to the cluster centre. This survey was complemented with an infrared follow-up in the HK_{\rm s}- and Spitzer 3.6-8.0 \mum-bands. Using colour-magnitude diagrams, we have selected 49 candidate cluster members in the magnitude interval 16.1 mag < I < 23.0 mag. Results. Accounting for flux excesses at 8.0 \mum and previously known spectral features of youth, we identify 30 objects as bona fide cluster members. Four are first identified from our optical-near infrared data. Eleven have most probable masses below the deuterium burning limit which we therefore classify as candidate planetary-mass objects. The slope of the substellar mass spectrum (\Delta N / \Delta {M} \approx a - \alpha}) in the mass interval 0.11 M_\odot < M < 0.006 M_\odot is \alpha = +0.6 \pm 0.2. Any mass limit to formation via opacity-limited fragmentation must lie below 0.006 M_\odot. The frequency of \sigma Orionis brown dwarfs with circumsubstellar discs is 47\pm9 %. Conclusions. The continuity in the mass function and in the frequency of discs suggests that very low-mass stars and substellar objects, even below the deuterium-burning mass limit, share the same formation mechanism.