The initial mass function of low-mass stars and brown dwarfs in young clusters

We have obtained images of the Trapezium Cluster (140 " x 140 "; 0.3 pc x 0.3 pc) with the Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer (NICMOS). Combining these data with new ground-based K-band spectra (R = 800) and existing spectral types and photometry, we have constructed an H-R diagram and used it and other arguments to infer masses and ages. To allow comparison with the results of our previous studies of IC 348 and rho Oph, we first use the models of D'Antona & Mazzitelli. With these models, the distributions of ages of comparable samples of stars in the Trapezium, rho Oph, and IC 348 indicate median ages of similar to 0.4 Myr for the first two regions and similar to 1-2 Myr for the latter. The low-mass initial mass functions (IMFs) in these sites of clustered star formation are similar over a wide range of stellar densities (rho Oph, n = 0.2-1 x 10(3) pc(-3); IC 348, n = 1 x 10(3) pc(-3); Trapezium, n = 1-5 x 10(4) pc(-3)) and other environmental conditions (e.g., presence or absence of OB stars). With current data, we cannot rule out modest variations in the substellar mass functions among these clusters. We then make the best estimate of the true form of the IMF in the Trapezium by using the evolutionary models of Baraffe et al, and an empirically adjusted temperature scale and compare this mass function to recent results for the Pleiades and the held. All of these data are consistent with an IMF that is flat or rises slowly from the substellar regime to about 0.6 M. and then rolls over into a power law that continues from about 1 M, to higher masses with a slope similar to or somewhat larger than the Salpeter value of 1.35. For the Trapezium, this behavior holds from our completeness limit of similar to 0.02 M. and probably, after a modest completeness correction, even from 0.01-0.02 M.. These data include similar to 50 likely brown dwarfs. We test the predictions of theories of the IMF against (1) the shape of the IMF, which is not log-normal, in clusters and the field, (2) the similarity of the IMFs among young clusters, (3) the lowest mass observed for brown dwarfs, and (4) the suggested connection between the stellar IMF and the mass function of prestellar clumps. In particular, most models do not predict the formation of the moderately large numbers of isolated objects down to 0.01 M. that we find in the Trapezium.