Barnes-Evans relations for dwarfs with an application to the   determination of distances to cataclysmic variables
  Barnes-Evans type relations provide an empirical relationship between the surface brightness of stars and their color. They are widely used for measuring the distances to stars of known radii, as the Roche-lobe filling secondaries in cataclysmic variables (CVs). The calibration of the surface brightness of field dwarfs of near-solar metalicity with spectral types A0 to L8 covers all secondary spectral types detectable in CVs and related objects and will aid in the measurement of their distances. The calibrations are based on the radii of field dwarfs measured by the Infrared Flux Method and by interferometry. Published photometry is used and homogenized to the Cousins Rc and Ic and the CIT JHK photometric systems. The narrow band surface brightness at 7500A is based on our own and published spectrophotometry. Care is taken to select the dwarfs for near-solar metalicity, appropriate to CVs, and to avoid errors caused by unrecognized binarity. Relations are provided for the surface brightness in V, Rc, Ic, J, H, K and in a narrow band at 7500A as functions of V-K and of spectral type. The method is tested with selected CVs for which independent information on their distances is available. The observed spread in the radii of early M-dwarfs of given mass or luminosity and its influence on the distance measurements of CVs is discussed. As long as accurate trigonometric parallaxes are not routinely available for a large number of CVs, the surface brightness method remains a reliable means of determining distances to CVs in which a spectral signature of the secondary star can be discerned. 
K. Beuermann