Calibration of the Barnes-Evans relation using interferometric observations of Cepheid variables

Abstract

Direct diameter measurements of Cepheid variables are used to calibrate the Barnes-Evans Cepheid surface brightness relation. More than 50 separate Cepheid diameter measurements from four different optical interferometers are used to calculate surface brightnesses as a function of magnitude and color. For two Cepheids, η Aquilae and ζ Geminorum, high precision diameter measurements as a function of pulsation phase are available from the Palomar Testbed Interferometer (PTI). Relations using only these diameters are found for each individual Cepheid in order to search for differences between Cepheids of different pulsation period. In all cases the best-fit relations are simple linear relations between surface brightness and color with the constraint that for a spectral type A0 star (where all colors equal zero) all relations must yield the same surface brightness (i.e., there must be a common zero-point). The derived relations found using interferometric Cepheid diameters are consistent with functions in the literature found using interferometric observations of non-variable giant and supergiant stars. In addition, while the separate relations for η Aquilae and ζ Geminorum are marginally consistent within the errors they do differ in the direction predicted for Cepheids of differing pulsation period. Using these new surface brightness relations the distance is calculated to the nearby Cepheid δ Cephei for which a new distance has been found using trigonometric parallax with the Hubble Space Telescope. These distances are well within the errors of the distance derived from trigonometric parallax.