Stellar Diameters and Temperatures. II. Main-sequence K- and M-stars

We present interferometric angular diameter measurements of 21 low-mass, K- and M-dwarfs made with the CHARA Array. This sample is enhanced by adding a collection of radius measurements published in the literature to form a total data set of 33 K-M-dwarfs with diameters measured to better than 5%. We use these data in combination with the Hipparcos parallax and new measurements of the star's bolometric flux to compute absolute luminosities, linear radii, and effective temperatures for the stars. We develop empirical relations for ~K0 to M4 main-sequence stars that link the stellar temperature, radius, and luminosity to the observed (B - V), (V - R), (V - I), (V - J), (V - H), and (V - K) broadband color index and stellar metallicity [Fe/H]. These relations are valid for metallicities ranging from [Fe/H] = -0.5 to +0.1 dex and are accurate to ~2%, ~5%, and ~4% for temperature, radius, and luminosity, respectively. Our results show that it is necessary to use metallicity-dependent transformations in order to properly convert colors into stellar temperatures, radii, and luminosities. Alternatively, we find no sensitivity to metallicity on relations we construct to the global properties of a star omitting color information, e.g., temperature-radius and temperature-luminosity. Thus, we are able to empirically quantify to what order the star's observed color index is impacted by the stellar iron abundance. In addition to the empirical relations, we also provide a representative look-up table via stellar spectral classifications using this collection of data. Robust examinations of single star temperatures and radii compared to evolutionary model predictions on the luminosity-temperature and luminosity-radius planes reveal that models overestimate the temperatures of stars with surface temperatures <5000 K by ~3%, and underestimate the radii of stars with radii <0.7 R _⊙ by ~5%. These conclusions additionally suggest that the models over account for the effects that the stellar metallicity may have on the astrophysical properties of an object. By comparing the interferometrically measured radii for the single star population to those of eclipsing binaries, we find that for a given mass, single and binary star radii are indistinguishable. However, we also find that for a given radius, the literature temperatures for binary stars are systematically lower compared to our interferometrically derived temperatures of single stars by ~200 to 300 K. The nature of this offset is dependent on the validation of binary star temperatures, where bringing all measurements to a uniform and correctly calibrated temperature scale is needed to identify any influence stellar activity may have on the physical properties of a star. Lastly, we present an empirically determined H-R diagram using fundamental properties presented here in combination with those in Boyajian et al. for a total of 74 nearby, main-sequence, A- to M-type stars, and define regions of habitability for the potential existence of sub-stellar mass companions in each system.