We report on our analysis of the VISTA Orion ZY JHKs photometric data (completeness magnitudes of Z?= 22.6 and J?= 21.0?mag) focusing on a circular area of 2798.4 arcmin2 around the young σ Orionis star cluster (~3?Myr, ~352?pc, and solar metallicity). The combination of the VISTA photometry with optical, WISE and Spitzer data allows us to identify a total of 210 σ Orionis member candidates with masses in the interval 0.25-0.004 M ☉, 23 of which are new planetary-mass object findings. These discoveries double the number of cluster planetary-mass candidates known so far. One object has colors compatible with a T spectral type. The σ Orionis cluster harbors about as many brown dwarfs (69, 0.072-0.012 M ☉) and planetary-mass objects (37, 0.012-0.004 M ☉) as very low mass stars (104, 0.25-0.072 M ☉). Based on Spitzer data, we derive a disk frequency of ~40% for very low mass stars, brown dwarfs, and planetary-mass objects in σ Orionis. The radial density distributions of these three mass intervals are alike: all are spatially concentrated within an effective radius of 12' (1.2?pc) around the multiple star σ Ori, and no obvious segregation between disk-bearing and diskless objects is observed. Using the VISTA data and the Mayrit catalog, we derive the cluster mass spectrum (ΔN/ΔM ~ M –α) from ~19 to 0.006 M ☉ (VISTA ZJ completeness), which is reasonably described by two power-law expressions with indices of α = 1.7 ± 0.2 for M 0.35 M ☉, and α = 0.6 ± 0.2 for M 0.35 M ☉. The σ Orionis mass spectrum smoothly extends into the planetary-mass regime down to 0.004 M ☉. Our findings of T-type sources (0.004 M ☉) in the VISTA σ Orionis exploration appear to be smaller than what is predicted by the extrapolation of the cluster mass spectrum down to the survey J-band completeness.
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