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

Monte Carlo simulations of the field substellar mass function (MF) arepresented. 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. Thesedistributions exhibit distinct minima in the mid-type L dwarf regime followedby a rise in number density for fainter/cooler brown dwarfs, predicting manymore T-type and cooler brown dwarfs in the field even for relatively shallowmass functions. Deuterium-burning brown dwarfs dominate field objects with 400$\leq$ T$_{eff}$ $\leq$ 2000 K, while non-fusing brown dwarfs make up asubstantial proportion of field dwarfs with T$_{eff}$ $\leq$ 500 K. The shapeof the substellar LF is fairly consistent for various assumptions of theGalactic birth rate, choice of evolutionary model, and adopted age and massranges, particularly for field T dwarfs, which as a population provide the bestconstraints for the field substellar MF. Exceptions include a depletion ofobjects with 1200 $\leq$ T$_{eff}$ $\leq$ 2000 K in ``halo'' systems.Unresolved multiple systems tend to enhance features in the observed LF and maycontribute significantly to the space density of very cool brown dwarfs.However, these effects are small ($<$ 10% for T$_{eff} \lesssim 300$ K) forbinary fractions typical for brown dwarf systems (10--20%). An analyticapproximation to correct the observed space density for unresolved multiplesystems in a magnitude-limited survey is derived. [ABRIDGED]Comment: 36 pages, 22 figures, accepted for ApJS 1 September 2004 issu