The distances of cepheid variables

A method for the determination of the distances of Cepheid variables proposed in a previous paper (Barnes, Evans & Parsons 1976) is applied to all cases for which the necessary observational data, namely (V, R) (Johnson) photometry and radial velocity measures, are available. The method is contrasted with the Baade–Wesselink technique. The present method depends on the calibration of the surface brightness, V–R colour relation in the Cepheid colour range and a series of numerical experiments is carried out to determine the best relationship permitted by the observational data. The theoretical models of Karp are subjected to a similar analysis. It is concluded that Cepheids adhere to the relationship as they pulsate, the best formulation being $${F}_{V}\,=\,3.966\,\pm \,0.005\,-\,0.390\,\pm 0.019\,({V-R})_{0}$$ which is the best fit to non-variable stars in the A–G range. Distances for nine of the eleven Cepheids for which data are available are determined giving a mean scale relative to the Fernie & Hube scale of 0.956 ± 0.066. The results are almost completely independent of interstellar extinction and the possibility of undiscovered duplicity. In two cases (SU Cas and Y Oph) where the pulsation amplitudes are less than 2 per cent of the mean diameter or the photometry is far from comprehensive the method does not yet yield a result of sufficient precision. The principal source of error lies in the photometry where the greatest potential for improvement lies.