T Dwarfs and the Substellar Mass Function. I. Monte Carlo Simulations

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Abstract
Monte Carlo simulations of the field substellar mass function (MF) are presented, based on the latest brown dwarf evolutionary models from Burrows et al. and Baraffe et al. Starting from various representations of the MF below 0.1 M☉ and the stellar birthrate, luminosity functions (LFs) and Teff distributions are produced for comparison with observed samples. These distributions exhibit distinct minima in the mid-type L dwarf regime followed by a rise in number density for fainter/cooler brown dwarfs, predicting many more T-type and cooler brown dwarfs in the field even for relatively shallow mass functions. Deuterium-burning brown dwarfs (0.012 M☉ ≤ M ≤ 0.075 M☉) dominate field objects with 400 K ≤ Teff ≤ 2000 K, while nonfusing brown dwarfs make up a substantial proportion of field dwarfs with Teff ≤ 500 K. The shape of the substellar LF is fairly consistent for various assumptions of the Galactic birthrate, choice of evolutionary model, and adopted age and mass ranges, particularly for field T dwarfs, which as a population provide the best constraints for the field substellar MF. Exceptions include a depletion of objects with 1200 K ≤ Teff ≤ 2000 K in halo systems (ages >9 Gyr), and a substantial increase in the number of very cool brown dwarfs for lower minimum formation masses. Unresolved multiple systems tend to enhance features in the observed LF and may contribute significantly to the space density of very cool brown dwarfs. However, these effects are small (<10% for Teff 300 K) for binary fractions typical for brown dwarf systems (10%-20%). An analytic approximation to correct the observed space density for unresolved multiple systems in a magnitude-limited survey is derived. As an exercise, surface densities as a function of Teff are computed for shallow near-infrared (e.g., 2MASS) and deep red-optical (e.g., UDF) surveys based on the simulated LFs and empirical absolute magnitude-Teff relations. These calculations indicate that a handful of L and T dwarfs, as well as late-type M and L halo subdwarfs, should be present in the UDF field depending on the underlying MF and disk scale height. These simulations and their dependencies on various factors provide a means for extracting the field substellar MF from observed samples, an issue pursued using 2MASS T dwarf discoveries in Paper II.