The spectroscopically determined substellar mass function of the Orion Nebula cluster

We present a spectroscopic study of candidate brown dwarf members of the Orion Nebula cluster (ONC). We obtained new J- and/or K-band spectra of similar to100 objects within the ONC that are expected to be substellar on the basis of their K magnitudes and H-K colors. Spectral classification in the near-infrared of young low-mass objects is described, including the effects of surface gravity, veiling due to circumstellar material, and reddening. From our derived spectral types and existing near-infrared photometry, we construct an H-R diagram for the cluster. Masses are inferred for each object and used to derive the brown dwarf fraction and assess the mass function for the inner 5.'1x5.'1 of the ONC, down to similar to0.02 M-circle dot. The logarithmic mass function rises to a peak at similar to0.2 M-circle dot, similar to previous initial mass function determinations derived from purely photometric methods but falls off more sharply at the hydrogen-burning limit before leveling through the substellar regime. We compare the mass function derived here for the inner ONC with those presented in recent literature for the sparsely populated Taurus cloud members and the rich cluster IC 348. We find good agreement between the shapes and peak values of the ONC and IC 348 mass distributions but little similarity between the ONC and Taurus results.