Empirical relations for the accurate estimation of stellar masses and radii

In this work, we have taken advantage of the most recent accurate stellar characterizations carried out using asteroseismology, eclipsing binaries and interferometry to evaluate a comprehensive set of empirical relations for the estimation of stellar masses and radii. We have gathered a total of 934 stars -- of which around two-thirds are on the Main Sequence -- that are characterized with different levels of precision, most of them having estimates of M, R, Teff, L, g, density, and [Fe/H]. We have deliberately used a heterogeneous sample (in terms of characterizing techniques and spectroscopic types) to reduce the influence of possible biases coming from the observation, reduction, and analysis methods used to obtain the stellar parameters. We have studied a total of 576 linear combinations of Teff, L, g, density, and [Fe/H] (and their logarithms) to be used as independent variables to estimate M or R. We have used an error-in-variables linear regression algorithm to extract the relations and to ensure the fair treatment of the uncertainties. We present a total of 38 new or revised relations that have an adj-R2 regression statistic higher than 0.85, and a relative accuracy and precision better than 10% for almost all the cases. The relations cover almost all the possible combinations of observables, ensuring that, whatever list of observables is available, there is at least one relation for estimating the stellar mass and radius.