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. 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, $\alpha$, for the low-mass arm of a two-segment power law has a value between -0.5 and 0.5 for objects with masses between $0.04 M_{\odot}$ and $0.10 M_{\odot}$. The best-fit index is $\alpha = 0.3\pm0.6$ at the 60% confidence level for a single-segment mass function. Current data require this function extend to at least $0.05 M_{\odot}$ with no restrictions placed on a lower mass cutoff. Inferences of the parameter values for a log-normal mass function are virtually unaffected by recent estimates of the local space density of L and T dwarfs. We find 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.