Substellar Mass Function of Young Open Clusters as Determined through a Statistical Approach Using 2MASS and GSC Data

In this paper we present the mass functions in the substellar regime of three young open clusters, IC 348, $\sigma$ Orionis and Pleiades, as derived using the data from the 2 Micron All Sky Survey (2MASS) catalogue which has a limiting magnitude of K_s ~ 15, and the latest version of the Guide Star Catalogue (GSC) which has a limiting magnitude of F ~ 21 where F refers to the POSS II IIIa-F passband. Based on recent evolutionary models for low mass stars, we have formulated the selection criteria for stars with masses below 0.5 solar mass. Using a statistical approach to correct for the background contamination, we derive the mass function of objects with masses ranging from 0.5 solar mass 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 solar masses for IC 348, sigma Orionis and Pleiades, respectively. The resultant slopes of the mass functions are 0.8 +/- 0.2 for IC 348, 1.2 +/- 0.2 for sigma Orionis and 0.5 +/- 0.2 for Pleiades, which are consistent with the previous results. The contribution of objects below 0.5 solar mass to the total mass of the cluster is ~40%, and the contribution of objects below 0.08 solar mass to the total mass is ~4%.