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

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Abstract
We use the results of a new multiepoch, multiwavelength, near-infrared census of the Trapezium cluster in Orion to construct and 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 substellar 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☉ where the IMF flattens and forms a broad peak extending to the hydrogen-burning limit, below which the IMF declines into the substellar regime. Independent of the details, we find that substellar objects account for no more than ~22% of the total number of likely cluster members. Further, the substellar 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 substellar objects in the cluster. Below this substellar IMF peak, our K-band luminosity function (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.
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