The visual surface brightness relation and the absolute magnitudes of RR Lyrae stars. I - Theory

A theoretical relation analogous to the Barnes-Evans relation between stellar surface brightness and V-R color is derived which is applicable to the temperatures and gravities appropriate to RR Lyrae stars. Values of the visual surface brightness and V-R colors are calculated for model stellar atmospheres with effective temperatures between 6000 and 8000 K, log surface gravities from 2.2 to 3.5, and A/H anbundance ratios from -0.5 to -3.0. The resulting relation is found to be in reasonable agreement with the empirical relation of Barnes, Evans and Moffet (1978), with, however, small sensitivities to gravity and metal abundance. The relation may be used to derive stellar angular diameters from (V,R) photometry and to derive radii, distances, and absolute magnitudes for variable stars when combined with a radial velocity curve. The accuracies of the radii and distances (within 10%) and absolute magnitudes (within 0.25 magnitudes) compare favorably with those of the Baade-Wesselink method currently in use.