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Low-mass stars and sub-stellar objects are essential in tracing the initialmass function (IMF). We study the nearby young $\sigma$ Orionis cluster(d$\sim$408 pc; age$\sim$1.8 Myr) using deep NIR photometric data in J, W andH-bands from WIRCam on the Canada-France-Hawaii Telescope. We use the waterabsorption feature to photometrically select the brown dwarfs and confirm theirnature spectroscopically with the IRTF-SpeX. Additionally we select candidatelow-mass stars for spectroscopy and analyze their membership and that ofliterature sources using astrometry from Gaia DR3. We obtain the near-IRspectra for 28 very low-mass stars and brown dwarfs and estimate their spectraltype between M3-M8.5 (mass ranging between 0.3-0.01 M$_{\odot}$). Apart fromthese, we also identify 5 new planetary mass candidates which require furtherspectroscopic confirmation of youth. We compile the comprehensive catalog of170 spectroscopically confirmed members in the central region of the cluster,for a wide mass range of $\sim$19-0.004 M$_{\odot}$. We estimate the star/BDratio to be $\sim$4, within the range reported for other nearby star formingregions. With the updated catalog of members we trace the IMF down to 4M$_\mathrm{Jup}$ and we find that a two-segment power-law fits the sub-stellarIMF better than the log-normal distribution.

astrophysical journal/the astrophysical journal

A novel survey for young substellar objects with the W-band filter VI:  Spectroscopic census of sub-stellar members and the IMF of $\sigma$ Orionis  cluster