## 3. Test of the revised CORS methodIn the following we briefly summarize the main features of the CORS method. The reader interested in a comprehensive discussion on the adopted physical and numerical assumptions is referred to RBMR and references therein. The CORS method relies on the definition of surface brightness : The solution is found by differentiating Eq. (2) with respect to the phase, then by multiplying the result for a color index, e.g. , and eventually by integrating along the full cycle. Since the radial velocity is tightly connected with the pulsation velocity according to: we obtain the following equation: where is the phase, The numerical solution of Eq. (4) supplies the unknown quantity
. In order to evaluate the radius as
a function of the phase we adopt Eq. (3) and finally the mean radius
is estimated by averaging along the radius curve. By neglecting the
term in Eq. (4), we obtain the
pure Baade-Wesselink method which requires a radial velocity, a
magnitude and a color curve for each individual variable. A more
precise radius determination can be obtained by including the
term. In fact, Sollazzo et al.
(1981) and RBMR demonstrated that the inclusion of this term improves
the accuracy of radius estimates, provided that
is evaluated at each pulsation
phase. The term was included in
the original CORS method (Sollazzo et al. 1981) by adopting the
empirical photometric calibration of the Walraven system provided by
Pel (1978), and in the revised CORS method (see Sect. 2.3 in RBMR) by
adopting the empirical calibration of the In order to test the accuracy of the term evaluation we apply the two previous approaches to synthetic light, color, and radial velocity curves. In particular, we adopted theoretical periods and the synthetic curves, covered with 125 points, were fitted with Fourier series which include up to 31 terms (15 sine, 15 cosine plus a constant term) and eventually the quantities B and were evaluated as well. We adopted a large number of both points and Fourier terms, since we are interested in testing the accuracy of the revised CORS method by adopting theoretical templates which should not be affected, within the intrinsic uncertainties, by systematic and/or deceptive errors. Since the modified CORS method requires an empirical estimation of the surface brightness as a function of a color, in this investigation we applied the calibrations provided by Fouqué & Gieren (1997) on the basis of stellar angular diameter measurements collected by Di Benedetto (1993) and Dyck et al. (1996), i.e.: where A similar calibration - versus - was originally suggested by Di Benedetto (1995). However, for applying the revised CORS method to different colors, we adopted the multiband calibrations provided by Fouqué & Gieren (1997). We emphasize once again that the modified CORS method adopts one magnitude and two color curves (cases 2, 3, 5 below), whereas the pure BW method adopts one magnitude and one color curve (cases 1, 4, 6 below). On the basis of the selected bands we investigated the following combinations of magnitudes and colors: -
*V*, -
*V*, , -
*V*, , -
*V*, -
*K*, ), -
*K*,
These bands were selected because they are quite common in the current literature, and also because they give a proper coverage of both optical and NIR wavelenghts. © European Southern Observatory (ESO) 2000 Online publication: January 31, 2000 |