Magnetic Inflation and Stellar Mass II: On the Radii of Single, Rapidly Rotating, Fully Convective M Dwarf Stars

Abstract: Main sequence, fully-convective M dwarfs in eclipsing binaries are observed to be larger than stellar evolutionary models predict by as much as $10-15\%$. A proposed explanation for this discrepancy involves effects from strong magnetic fields, induced by rapid-rotation via the dynamo process. Although, a handful of single, slowly-rotating M dwarfs with radius measurements from interferometry also appear to be larger than models predict, suggesting that rotation or binarity specifically may not be the sole cause of the discrepancy. We test whether single, rapidly rotating, fully convective stars are also larger than expected by measuring their $R \sin i$ distribution. We combine photometric rotation periods from the literature with rotational broadening ($v \sin i$) measurements reported in this work for a sample of 88 rapidly rotating M dwarf stars. Using a Bayesian framework, we find that stellar evolutionary models underestimate the radii by $10-15\% \substack{+3 \ -2.5}$, but that at higher masses ($0.18<M<0.4 M_{Sun}$) the discrepancy is only about $6\%$ and comparable to results from interferometry and eclipsing binaries. At the lowest masses ($0.08<M<0.18 M_{Sun}$), we find the discrepancy between observations and theory is $13-18\%$, and we argue that the discrepancy is unlikely to be due to effects from age. Furthermore, we find no statistically significant radius discrepancy between our sample and the handful of M dwarfs with interferometric radii. We conclude that neither rotation nor binarity is responsible for the inflated radii of fully convective M dwarfs, and that all fully-convective M dwarfs are larger than models predict.