The Substellar Mass Function: A Bayesian Approach

We report our efforts to constrain the form of the low-mass star and brown dwarf mass function via Bayesian inference. Recent surveys of M, L, and T dwarfs in the local solar neighborhood are an essential component of our study. Uncertainties in the age distribution of local field stars make reliable inference complicated. We adopt a wide range of plausible assumptions about the rate of galactic star formation and show that their deviations from a uniform rate produce little effect on the resulting luminosity function for a given mass function. As an ancillary result, we calculate the age distribution for M, L, and T spectral types. We demonstrate that late-L dwarfs, in particular, are systematically younger than objects with earlier or later spectral types, with a mean age of 3 Gyr. Finally, we use a Bayesian statistical formalism to evaluate the probability of commonly used mass functions in light of recent discoveries. We consider three functional forms of the mass function, include a two-segment power law, a single power law with a low-mass cutoff, and a log-normal distribution. Our results show that, at a 60% confidence level, the power-law index, α, for the low-mass arm of a two-segment power law has a value between -0.5 and 0.5 for objects with