## 1. IntroductionThe importance of a proper knowledge of the radii of Cepheid variables is well known, in particular, but not only, in connection with the problem of the cosmic distance scale. Notwithstanding extensive studies by several authors (Caccin et al. 1981; Fernie 1984; Gieren 1986; Moffett & Barnes 1987; Gieren et al. 1989, Laney & Stobie 1995), there are still doubts on the correct period-radius relation. Almost all methods used for determining the radius of a cepheid from the photometric and spectroscopic (radial velocities) observations, are based on the classical Baade-Wesselink method (Wesselink, 1946). Gautschy (1987) published a review of the different methods; this comparative study outlines that the CORS method (Caccin et al., 1981, Sollazzo et al., 1981) had the most solid physical basis, together with the surface brightness technique by Barnes & Evans (1976). However, the CORS method suffered from two major drawbacks that have so far prevented its application to most observational data; that is the mathematically difficult formulation, and the need of a good and complete calibration of the colors, able to derive detailed temperatures and gravity curves. In particular, the second problem is solved so far only for the VBLUW observations by Pel (1976, 1978). The first problem is instead not a true problem, because, as we will show, the whole CORS method reduces itself to the fitting of the data and to the solution of an implicit equation which, once written in computer form, requires a fraction of a second to be solved in terms of the cepheid radius. The purpose of the present paper is to introduce a modification of the CORS method, by taking into account the surface brightness method, in order to allow the determination of cepheid radii for a wider set of data than it was originally conceived. In particular, we will face the case in which it is not possible to derive detailed gravity and temperature curves from the observations, thus making conceptually a step backward with respect to the original CORS method, but extending its practical usefulness. In the following we will first recall the original surface brightness and CORS methods, and then we introduce its modified version, discussing its characteristics. Last sections are devoted to the application of the method and to the discussion of the results. © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |