Calibration of the Barnes-Evans relation using interferometric observations of Cepheids

Direct diameter observations of Cepheid variables are used to calibrate the Barnes-Evans Cepheid surface brightness relation. Fifty-nine separate Cepheid diameter measurements from four different optical interferometers are used to calculate surface brightnesses as a function of magnitude and color. The linear fit to Cepheid surface brightness versus color is in excellent agreement with functions in the literature found using interferometric observations of non-variable giant and supergiant stars (Fouqué & Gieren 1997). Using these relations the distance is calculated to δ Cephei, for which an independent distance is known from trigonometric parallax. The distance from the relation in this paper differs from that derived by the previously published relation by 4% but is still marginally within the combined errors. Both distances are well within the errors of the distance derived from trigonometric parallax. Subject headings: Cepheids — stars: fundamental parameters — stars: individual (δ Cephei, η Aquilae, ζ Geminorum)