Substellar Mass Function of Young Open Clusters as Determined through a Statistical Approach Using Two Micron All Sky Survey and Guide Star Catalog Data

In this paper we present the mass functions in the substellar regime of three young open clusters, IC 348, σ Orionis, and Pleiades, as derived using the data from the Two Micron All Sky Survey catalog, which has a limiting magnitude of K_s ~ 15, and the latest version of the Guide Star Catalog, which has a limiting magnitude of F ~ 21. Based on recent evolutionary models for low-mass stars, we have formulated the selection criteria for stars with masses below 0.5 M_☉. Using a statistical approach to correct for the background contamination, we derive the mass function of objects with masses ranging from 0.5 M_☉ down to the substellar domain, well below the hydrogen-burning mass limit. The lowest mass bins in our analysis are 0.025, 0.045, and 0.055 M_☉ for IC 348, σ Orionis, and Pleiades, respectively. The resultant slopes of the mass functions are 0.8 ± 0.2 for IC 348, 1.2 ± 0.2 for σ Orionis, and 0.5 ± 0.2 for Pleiades, which are consistent with the previous results. The contribution of objects below 0.5 M_☉ to the total mass of the cluster is ~40%, and the contribution of objects below 0.08 M_☉ to the total mass is ~4%.