The projection factor, period-radius relation, and surface-brightness colour relation in classical Cepheids

Context. The projection factor (p-factor) is of crucial importance in linking radial velocity variations to radius variations in radially variable stars such as RR Lyrae of Cepheids. In turn, this is a crucial ingredient in the Baade-Wesselink method in obtaining distances to these stars using a surface-brightness (SB) colour relation. Aims. Our aim is to establish a relation between the p-factor and pulsation period based on six cepheids with interferometrically measured angular diameter variations and known distances. As a by-product, a period-radius (PR) relation is derived which in turn is used to derive the p-factor and distance for two stars. In addition, the data allows calibration of the SB colour relation. Methods. Literature values of the V-band, K-band and radial velocity curves are collected and fitted with Fourier series. For stars with known distances and measured angular diameters as a function of the pulsation phase, values for the radius and the p-factor can be obtained. A PR relation is derived based on five stars. For two cepheids, this PR relation is used to determine the radius and then solve for the p-factor and the distance. From the Fourier series, the V and K values at the times of the angular diameter measurements are derived, and the SB colour relation can be established. Allowance is made for the recent discovery of circumstellar material around some cepheids which influences both the derived angular diameters and the colours. Results. The PR relation derived is: log R = 0.686 log P + 1.134, slightly shallower than recently discussed PR-relations in the literature but in agreement with theory. Based on a total of eight stars with periods in the range 5 -35 days there is no evidence that the p-factor depends on period, and the best-fitting constant value is p = 1.27 +/- 0.05. The SB relation derived is log theta(0) = 0.275 (V -K)(0) + 0.524, in excellent agreement with that derived by Kervella et al. ( 2004b, A& A, 428, 587).