T Dwarfs and the Substellar Mass Function. I. Monte Carlo Simulations
Monte Carlo simulations of the field substellar mass function (MF) are presented. Starting from various representations of the MF below 0.1 M$_{\sun}$ and the stellar birth rate, luminosity functions (LFs) and T$_{eff}$ 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 dominate field objects with 400 $\leq$ T$_{eff}$ $\leq$ 2000 K, while non-fusing brown dwarfs make up a substantial proportion of field dwarfs with T$_{eff}$ $\leq$ 500 K. The shape of the substellar LF is fairly consistent for various assumptions of the Galactic birth rate, 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 $\leq$ T$_{eff}$ $\leq$ 2000 K in ``halo'' systems. 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 T$_{eff} \lesssim 300$ 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. [ABRIDGED]