The Dependence of Brown Dwarf Radii on Atmospheric Metallicity and Clouds: Theory and Comparison with Observations

Employing realistic and consistent atmosphere boundary conditions, we have generated evolutionary models for brown dwarfs and very-low-mass stars (VLMs) for different metallicities ([Fe/H]), with and without clouds. We find that the spread in radius at a given mass and age can be as large as $\sim$10% to $\sim$25%, with higher-metallicity, higher-cloud-thickness atmospheres resulting quite naturally in larger radii. For each 0.1 dex increase in [Fe/H], radii increase by $\sim$1% to $\sim$2.5%, depending upon age and mass. We also find that, while for smaller masses and older ages brown dwarf radii decrease with increasing helium fraction ($Y$) (as expected), for more massive brown dwarfs and a wide range of ages they increase with helium fraction. The increase in radius in going from $Y=0.25$ to $Y=0.28$ can be as large as $\sim$0.025 \rj\ ($\sim$2.5%). Furthermore, we find that for VLMs an increase in atmospheric metallicity from 0.0 to 0.5 dex, increases radii by $\sim$4%, and from -0.5 to 0.5 dex by $\sim$10%. Therefore, we suggest that opacity due to higher metallicity might naturally account for the apparent radius anomalies in some eclipsing VLM systems. Ten to twenty-five percent variations in radius exceed errors stemming from uncertainities in the equation of state alone. This serves to emphasize that transit and eclipse measurements of brown dwarf radii constrain numerous effects collectively, importantly including the atmosphere and condensate cloud models, and not just the equation of state. At all times, one is testing a multi-parameter theory, and not a universal radius$-$mass relation.