A Self-consistent Model for Brown Dwarf Populations

We present a self-consistent model of the Milky Way to reproduce the observed distributions (spectral type, absolute J-band magnitude, effective temperature) and total velocity dispersion of brown dwarfs. For our model, we adopt parametric forms for the star formation history and initial-mass function, published evolutionary models, and theoretical age-velocity relations. Using standard Markov Chain Monte Carlo methods, we derive a power-law index of the initial-mass function of alpha = -0.71 +/- 0.11, which is an improvement over previous studies. We consider a gamma-function form for the star formation history, though we find that this complex model is only slightly favored over a declining exponential. We find that a velocity variance that linearly increases with age and has an initial value of sigma(0) = 9.0(-9.0)(+11) km s(-1) best reproduces the total velocity dispersions. Given the similarities to main-sequence stars, this suggests brown dwarfs likely form via similar processes, but we recognize that the sizable uncertainties on sigma(0) preclude firm conclusions. To further refine these conclusions, we suggest that wide-field infrared imaging or low-resolution spectroscopic surveys, such as with the Nancy Grace Roman Space Telescope or Euclid, could provide large samples of brown dwarfs with robust spectral types that could probe the thickness of the thin disk. In this way, the number counts and population demographics could probe the same physical processes as with the kinematic measurements, however may provide larger samples and be subject to different selection biases.