A Novel Survey for Young Substellar Objects with the W-band Filter. VI. Spectroscopic Census of Substellar Members and the IMF of the σ Orionis Cluster

Low-mass stars and substellar objects are essential in tracing the initial mass function (IMF). We study the nearby young σ Orionis cluster (d ~ 408 pc, age ~ 1.8 Myr) using deep near-infrared (NIR) photometric data in the J, W, and H bands from WIRCam on the Canada-France-Hawaii Telescope. We use the water absorption feature to select brown dwarfs photometrically and confirm their nature spectroscopically with IRTF-SpeX. Additionally we select candidate low-mass stars for spectroscopy and analyze their membership and those of literature sources using astrometry from Gaia DR3. We obtain NIR spectra for 28 very-low-mass stars and brown dwarfs and estimate their spectral type between M3 and M8.5 (masses ranging between 0.3 and 0.01 M _⊙). Apart from these, we also identify five new planetary-mass candidates which require further spectroscopic confirmation of youth. We compile a comprehensive catalog of 170 spectroscopically confirmed members in the central region of the cluster, for a wide mass range of ~19-0.004 M _☉. We estimate the star-to-brown-dwarf ratio to be ~4, within the range reported for other nearby star-forming regions. With the updated catalog of members we trace the IMF down to 4 M _Jup and we find that a two-segment power law fits the substellar IMF better than a log-normal distribution.