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-infrared census of the Trapezium Cluster in Orion to construct and to analyze the structure of its infrared (K band) luminosity function. Specifically, we employ an improved set of model luminosity functions to derive this cluster's underlying Initial Mass Function (IMF) across the entire range of mass from OB stars to sub-stellar objects down to near the deuterium burning limit. We derive an IMF for the Trapezium Cluster that rises with decreasing mass, having a Salpeter-like IMF slope until near ~0.6 M_sun where the IMF flattens and forms a broad peak extending to the hydrogen burning limit, below which the IMF declines into the sub-stellar regime. Independent of the details, we find that sub-stellar objects account for no more than ~22% of the total number of likely cluster members. Further, the sub-stellar Trapezium IMF breaks from a steady power-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 IMF peak, our KLF modeling requires a subsequent sharp decline toward the planetary mass regime. Lastly, we investigate the robustness of pre-main sequence luminosity evolution as predicted by current evolutionary models, and we discuss possible origins for the IMF of brown dwarfs.