SONYC -- Substellar Objects in Nearby Young Clusters -- is a program to investigate the frequency and properties of young substellar objects with masses down to a few times that of Jupiter. Here we present a census of very low mass objects in the ~1 Myr old cluster NGC1333. We analyze near-infrared spectra taken with FMOS/Subaru for 100 candidates from our deep, wide-field survey and find 10 new likely brown dwarfs with spectral types of M6 or later. Among them, there are three with >~M9 and one with early L spectral type, corresponding to masses of 0.006 to <~0.02 Msol, so far the lowest mass objects identified in this cluster. The combination of survey depth, spatial coverage, and extensive spectroscopic follow-up makes NGC1333 one of the most comprehensively surveyed clusters for substellar objects. In total, there are now 51 objects with spectral type M5 or later and/or effective temperature of 3200 K or cooler identified in NGC1333; 30-40 of them are likely to be substellar. NGC1333 harbours about half as many brown dwarfs as stars, which is significantly more than in other well-studied star forming regions, thus raising the possibility of environmental differences in the formation of substellar objects. The brown dwarfs in NGC1333 are spatially strongly clustered within a radius of ~1 pc, mirroring the distribution of the stars. The disk fraction in the substellar regime is <66%, lower than for the total population (83%) but comparable to the brown dwarf disk fraction in other 2-3 Myr old regions.
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