The Luminosity and Mass Function of the Trapezium Cluster: From B Stars to the Deuterium‐burning Limit

We use the results of a new, multi-epoch, multi-wavelength, near-infraredcensus of the Trapezium Cluster in Orion to construct and to analyze thestructure of its infrared (K band) luminosity function. Specifically, we employan improved set of model luminosity functions to derive this cluster'sunderlying Initial Mass Function (IMF) across the entire range of mass from OBstars to sub-stellar objects down to near the deuterium burning limit. Wederive an IMF for the Trapezium Cluster that rises with decreasing mass, havinga Salpeter-like IMF slope until near ~0.6 M_sun where the IMF flattens andforms a broad peak extending to the hydrogen burning limit, below which the IMFdeclines into the sub-stellar regime. Independent of the details, we find thatsub-stellar objects account for no more than ~22% of the total number of likelycluster members. Further, the sub-stellar Trapezium IMF breaks from a steadypower-law decline and forms a significant secondary peak at the lowest masses(10-20 times the mass of Jupiter). This secondary peak may contain as many as\~30% of the sub-stellar objects in the cluster. Below this sub-stellar IMFpeak, our KLF modeling requires a subsequent sharp decline toward the planetarymass regime. Lastly, we investigate the robustness of pre-main sequenceluminosity evolution as predicted by current evolutionary models, and wediscuss possible origins for the IMF of brown dwarfs.