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 the light of recent discoveries. We consider three functional forms of the mass function, including a two-segment power law, a single power law with a low-mass cutoff, and a lognormal 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 -0.6 and 0.6 for objects with masses between 0.04 and 0.10 M-⊙. The best-fit index is α = 0.3 ± 0.6 at the 60% confidence level for a single-segment mass function. Current data require this function to extend to at least 0.05 M-⊙ with no restrictions placed on a lower mass cutoff. Inferences of the parameter values for a lognormal mass function are virtually unaffected by recent estimates of the local space density of L and T dwarfs. We find that we have no preference among these three forms using this method. We discuss current and future capabilities that may eventually discriminate between mass function models and refine estimates of their associated parameter values.