How to Constrain Your M Dwarf: measuring effective temperature, bolometric luminosity, mass, and radius

Precise and accurate parameters for late-type (late K and M) dwarf stars are important for characterization of any orbiting planets, but such determinations have been hampered by these stars' complex spectra and dissimilarity to the Sun. We exploit an empirically calibrated method to estimate spectroscopic effective temperature ($T_{\rm{eff}}$) and the Stefan-Boltzmann law to determine radii of 183 nearby K7-M7 single stars with a precision of 2-5%. Our improved stellar parameters enable us to develop model-independent relations between $T_{\rm{eff}}$ or absolute magnitude and radius, as well as between color and $T_{\rm{eff}}$. The derived $T_{\rm{eff}}$-radius relation depends strongly on [Fe/H], as predicted by theory. The relation between absolute $K_S$ magnitude and radius can predict radii accurate to $\simeq$3%. We derive bolometric corrections to the $VR_CI_CgrizJHK_S$ and Gaia passbands as a function of color, accurate to 1-3%. We confront the reliability of predictions from Dartmouth stellar evolution models using a Markov Chain Monte Carlo to find the values of unobservable model parameters (mass, age) that best reproduce the observed effective temperature and bolometric flux while satisfying constraints on distance and metallicity as Bayesian priors. With the inferred masses we derive a semi-empirical mass-absolute magnitude relation with a scatter of 2% in mass. The best-agreement models over-predict stellar $T_{\rm{eff}}$s by an average of 2.2% and under-predict stellar radii by 4.6%, similar to differences with values from low-mass eclipsing binaries. These differences are not correlated with metallicity, mass, or indicators of activity, suggesting issues with the underlying model assumptions e.g., opacities or convective mixing length.