Modeling the near-infrared luminosity functions of young stellar clusters

We present the results of numerical experiments designed to evaluate the usefulness of near-infrared (NIR) luminosity functions for constraining the initial mass function (IMF) of young stellar populations. We test the sensitivity of the NIR K-band luminosity function (KLF) of a young stellar cluster to variations in the underlying IMF, star-forming history, and pre-main-sequence mass-to-luminosity relations. Using Monte Carlo techniques, we create a suite of model luminosity functions systematically varying each of these basic underlying relations. From this numerical modeling, we find that the luminosity function of a young stellar population is considerably more sensitive to variations in the underlying initial mass function than to either variations in the star-forming history or assumed pre-main-sequence (PMS) mass-to-luminosity relation. Variations in a cluster's star-forming history are also found to produce significant changes in the KLF. In particular, we find that the KLFs of young clusters evolve in a systematic manner with increasing mean age. Our experiments indicate that variations in the PMS mass-to-luminosity relation, resulting from differences in adopted PMS tracks, produce only small effects on the form of the model luminosity functions and that these effects are mostly likely not detectable observationally. To illustrate the potential effectiveness of using the KLF of a young cluster to constrain its IMF, we model the observed KLF of the nearby Trapezium cluster. With knowledge of the star-forming history of this cluster obtained from optical spectroscopic studies, we derive the simplest underlying IMF whose model luminosity function matches the observations. Our derived mass function for the Trapezium spans 2 orders of magnitude in stellar mass (5 > M. > 0.02) and has a peak near the hydrogen-burning limit. Below the hydrogen-burning limit, the mass function steadily decreases with decreasing mass throughout the brown dwarf regime. Comparison of our IMF with that derived by optical and spectroscopic methods for the entire Orion Nebula Cluster suggests that modeling the KLF is indeed a useful tool for constraining the mass function in young stellar clusters particularly at and below the hydrogen-burning limit.