Protoplanetary disks around young stellar and substellar objects in the $\sigma$ Orionis cluster

Understanding the evolution and dissipation of protoplanetary disks are crucial in star and planet formation studies. We report the protoplanetary disk population in the nearby young $\sigma$ Orionis cluster (d$\sim$408 pc; age$\sim$1.8 Myr) and analyse the disk properties such as dependence on stellar mass and disk evolution. We utilise the comprehensive census of 170 spectroscopic members of the region refined using astrometry from Gaia DR3 for a wide mass range of $\sim$19-0.004 M$_\odot$. Using the near infrared (2MASS) and mid infrared (WISE) photometry we classify the sources based on the spectral index into class I, class II, flat spectrum and class III young stellar objects. The frequency of sources hosting a disk with stellar mass $<$2 M$_\odot$ in this region is 41$\pm$7% which is consistent with the disk fraction estimated in previous studies. We see that there is no significant dependence of disk fraction on stellar mass among T Tauri stars ($<$2 M$_\odot$), but we propose rapid disk depletion around higher mass stars ($>$2 M$_\odot$). Furthermore we find the lowest mass of a disk bearing object to be $\sim$ 20 M$_\mathrm{Jup}$ and the pronounced disk fraction among the brown dwarf population hints at the formation scenario that brown dwarfs form similar to low-mass stars.