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Astron. Astrophys. 354, 77-85 (2000)

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1. Introduction

The Baade-Wesselink (BW, Baade 1926; Wesselink 1946) method on the basis of luminosity, color, and radial velocity variations along the pulsation cycle provides the key opportunity to estimate both radii and distances of variable stars. Both the physical assumptions on which this method relies and the intrinsic drawbacks have been thoroughly discussed in the literature (Oke et al. 1962; Gautschy 1987; Bono et al. 1994; Butler et al. 1996).

Different approaches have been suggested for improving both accuracy and consistency of the BW method:

a) the radius variations are estimated by adopting a maximum likelihood method (Balona 1977; Laney & Stobie 1995) which accounts for observational errors.

b) The use of light and velocity variations together with two color indices to account for both temperature and gravity changes along the pulsation cycle (Caccin et al. 1981; Sollazzo et al. 1981; Onnenbo et al. 1985, the CORS group). However, the CORS method needs photometric calibration and a good sampling of both light and velocity curves for evaluating temperatures and gravities.

c) The use of a surface brightness relation (Barnes & Evans 1976; Gieren et al. 1989; Fouqué & Gieren 1997; Gieren et al. 1997, hereinafter GFG). However, this method needs accurate calibration of the surface brightness parameter in order to provide simultaneous estimates of radii and distances.

d) A detailed comparison between theory and observations brought out that Cepheid radii and distance determinations should be based on atmosphere models constructed by adopting a microturbulence velocity of the order of 4 km s-1 (Bersier et al. 1997). Thus confirming the result originally pointed out by Lub & Pel (1977) and Pel (1978).

e) In a recent paper Ripepi et al. (1997, hereinafter RBMR) revised the CORS method by including the surface brightness calibration suggested by Barnes & Evans (1976). This method has been applied to a large sample of Galactic Cepheids and the radius estimates they obtained are in fair agreement with previous evaluations.

f) Krockenberger et al. (1997) adopted a Fourier analysis of both light and velocity curves to account for individual measurement errors.

On the basis of these developments and of accurate photometric and spectroscopic data it has been suggested that the most recent estimates of Cepheid radii are affected by very small internal errors (Di Benedetto 1997; GFG). Moreover, in a recent investigation based on new Cepheid models Bono et al. (1998, hereinafter BCM) settled a long-standing discrepancy between theoretical and empirical Period-Radius (PR) relations (Laney & Stobie 19951. In fact, they found very good agreement between theory and observations in the period range [FORMULA]. However, they also found that outside this range, at both shorter and longer periods theoretical predictions attain intermediate values between empirical radii estimated by adopting different BW methods and/or photometric bandpasses.

Even though, it has been recently suggested that period and radii of Cepheids obey to a universal PR relation, theoretical predictions support the evidence that both the slope and the zero point of this relation depend on metallicity (BCM). Moreover, it has also been estimated that the accuracy of Cepheid radii based on infrared colors is of the order of 3% (GFG) and therefore the metallicity dependence, if any, should have already been detected. However, preliminary results (Laney 1999, 2000) based on a large sample of Galactic and MC Cepheids for which multiband photometric data are available seem to support theoretical predictions, and indeed he found that the radii of MC Cepheids are, at one [FORMULA] level, systematically larger than the radii of the Galactic ones.

A similar discrepancy has been found between theoretical and empirical estimates of the Cepheid intrinsic luminosity. In fact, recent theoretical investigations support the evidence that the Cepheid PL relation depends on the metallicity, since at fixed period metal-rich Cepheids are fainter than metal-poor ones (Bono et al. 1999a, hereinafter BMS; Bono et al. 1999b, hereinafter BCCM). However, these predictions are at odds with current empirical estimates based on the BW method or on other approaches, since the latter show that the PL relation is either unaffected by the metallicity (GFG), or it presents a mild dependence but with an opposite sign, i.e. metal-rich Cepheids seem to be brighter than metal-poor ones (Sasselov et al. 1997; Kennicutt et al. 1998).

The main aim of this investigation is to test both physical and numerical assumptions adopted for developing the revised CORS method by performing a set of numerical experiments based on theoretical light, color and radial velocity curves. The pulsation models and the static atmosphere models adopted for transforming theoretical observables into the observative plane are discussed in Sect. 2. In Sect. 3 we briefly summarize the leading equations on which the revised CORS method is based and then we describe the approach adopted for testing the method. The results of the numerical experiments we performed are presented in Sects. 4.1 and 4.2, together with a detailed analysis of the dependence of radius estimates on the photometric bands currently adopted.

A new calibration of the surface brightness based on atmosphere models, which accounts for both temperature and gravity changes of classical Cepheids, is discussed in Sect. 4.3. In this section the improvements in CORS radii obtained by adopting the theoretical instead of the empirical calibration are also presented together with the limits of the quasi-static approximation close to the bump phases. A brief discussion on future developments closes the paper.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000