Simulating Brown Dwarf Observations for Various Mass Functions, Birthrates, and Low-mass Cutoffs

TL;DR

This paper models the brown dwarf mass function by comparing predicted and observed temperature distributions, finding a power-law form with a low-mass cutoff, and providing publicly available simulation code.

Contribution

It introduces a method to infer the brown dwarf mass function using temperature distribution modeling and explores the effects of different birthrates and cutoffs.

Findings

Power-law mass function with α ≈ 0.5 is optimal.

Low-mass cutoff for star formation is ≤0.005 solar masses.

Birthrate has less impact than mass function on temperature distribution.

Abstract

After decades of brown dwarf discovery and follow-up, we can now infer the functional form of the mass distribution within 20 parsecs, which serves as a constraint on star formation theory at the lowest masses. Unlike objects on the main sequence that have a clear luminosity-to-mass correlation, brown dwarfs lack a correlation between an observable parameter (luminosity, spectral type, or color) and mass. A measurement of the brown dwarf mass function must therefore be procured through proxy measurements and theoretical models. We utilize various assumed forms of the mass function, together with a variety of birthrate functions, low-mass cutoffs, and theoretical evolutionary models, to build predicted forms of the effective temperature distribution. We then determine the best fit of the observed effective temperature distribution to these predictions, which in turn reveals the most likely mass function. We find that a simple power law ($dN/dM \propto M^{-\alpha}$) with $\alpha \approx 0.5$ is optimal. Additionally, we conclude that the low-mass cutoff for star formation is $\lesssim0.005M_{\odot}$. We corroborate the findings of Burgasser (2004) which state that the birthrate has a far lesser impact than the mass function on the form of the temperature distribution, but we note that our alternate birthrates tend to favor slightly smaller values of $\alpha$ than the constant birthrate. Our code for simulating these distributions is publicly available. As another use case for this code, we present findings on the width and location of the subdwarf temperature gap by simulating distributions of very old (8-10 Gyr) brown dwarfs.