Modeling the Near‐Infrared Luminosity Functions of Young Stellar Clusters

Abstract

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 varia- tions in the underlying IMF, star-forming history, and premain-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 —nd that the luminosity func- tion 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 premain-sequence (PMS) mass-to-luminosity relation. Variations in a clusters star-forming history are also found to produce sig- ni—cant changes in the KLF. In particular, we —nd that the KLFs of young clusters evolve in a system- atic manner with increasing mean age. Our experiments indicate that variations in the PMS mass-to-luminosity relation, resulting from diUerences in adopted PMS tracks, produce only small eUects on the form of the model luminosity functions and that these eUects are mostly likely not detectable observationally. To illustrate the potential eUectiveness 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 under- lying IMF whose model luminosity function matches the observations. Our derived mass function for the Trapezium spans 2 orders of magnitude in stellar mass and has a peak near the (5 ( M _ ( 0.02) 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. Subject headings: infrared: starsopen clusters and associations: generalstars: interiors ¨ stars: low-mass, brown dwarfsstars: luminosity function, mass function ¨ stars: pre-main sequence