The Cepheid Period-Luminosity (PL) relation is a classical tool widely used to estimate the distance to Local Group galaxies and to external galaxies with Hubble Space Telescope (HST) observations, as well as, through the calibration of secondary distance indicators, to even more distant stellar systems. This explains the dominant role of these variables on the route to solve cosmological problems such as the evaluation of the Hubble constant and, in turn, of the age of the Universe.
The basic physics underlying the Cepheid variability suggests that the pulsation period P depends on the mass, luminosity and effective temperature of the pulsator. From stellar evolution theory one expects a close relation between mass and luminosity, and the natural result of these theoretical prescriptions is a Period-Luminosity-Color (PLC) relation, where the pulsator absolute magnitude in each given photometric passband j is a linear function of the period and color index [CI], as given by
However, since the pulsation occurs within a finite zone of the HR diagram, the color term in the PLC relation is often neglected and Cepheid distances are usually estimated from the most favourite PL relation
where is now the average of the Cepheid magnitudes for each given period. It should be noticed that whereas the PLC relation holds for any individual pulsator, PL is a "statistical" solution which depends both on the pulsation boundaries and on the distribution of pulsators within the instability strip. This explains why distance determinations based on PL relations require statistically significant numbers of Cepheids in order to reduce the effects of deviations from the ridge line.
The PL relation in bolometric magnitude is traditionally assumed to be metal-insensitive (see, e.g., Iben & Renzini 1984, Freedman & Madore 1990) and Cepheid distances are generally derived by adopting universal PL relations at different wavelengths, having the slope provided by the Cepheids in the LMC and the zero-point referenced to the LMC distance, as obtained with independent methods (see Freedman 1988; Kennicutt et al. 1998; Walker 1999, and reference therein), or to calibrating Galactic Cepheids (see Feast & Catchpole 1997; Lanoix et al. 1999).
In the last years, we have deeply investigated the Cepheid pulsational behavior through the computations of nonlinear, nonlocal and time-dependent convective pulsating models which take into account the coupling between pulsation and convection. With respect to linear-nonadiabatic models computed by different authors (e.g., Chiosi et al. 1993; Saio & Gautschy 1998; Alibert et al. 1999), our theoretical approach allows reliable predictions on the temperature of both the blue and red edges of the instability strip, as well as about the amplitude and morphology of the light-curve (see Bono et al. 1999a [Paper I], 2000a [Paper III], 2000b [Paper VI]). Concerning the assumptions on the input physics, computing procedures and the adopted mass-luminosity relation, the reader is referred to Paper I and Paper III, which contain also the detailed comparison of our models with the linear results in the literature. Here we only remark that from pulsating models computed with three different chemical abundances (Z=0.004, 0.008 and 0.02) we derived that the bolometric magnitude of metal-rich variables is, on average, fainter than that of metal-poor stars with the same period (Bono et al. 1999b [Paper II]). Moreover, we found that both the slope and zero-point of synthetic PL relations at different wavelengths depend on the pulsator metallicity, with the amplitude of the metallicity effect decreasing from visual to near-infrared magnitudes (see Paper II; Caputo et al. 2000 [Paper V]). Also the predicted PLC relations at the different wavelengths turned out to be, in various degrees, metallicity dependent: as an example, for a given period and color, metal-rich pulsators are brighter than metal-poor ones, whereas they are fainter if the color is adopted (see Paper V). On these grounds, it has been shown that Cepheid observations in three filters (BVI or BVK) allow to simultaneously constrain distance, reddening and metallicity of variables in the Magellanic Clouds (Caputo et al. 1999 [Paper IV]) and in the Milky Way (Caputo et al., in preparation).
In this paper we will apply our theoretical scenario to the Cepheids observed within two HST surveys: the "Extragalactic Distance Scale Key Project" (hereafter KP, see Freedman et al. 1994a) and the "Type Ia Supernova Calibration" (hereafter SNP, see Saha et al. 1994). The adopted procedure is briefly presented in Sect. 2 and the predicted reddenings and distances are given in Sect. 3. The metallicity effects on the Cepheid distance scale and on the value of the Hubble constant are discussed in Sect. 4. The concluding remarks close the paper.
© European Southern Observatory (ESO) 2000
Online publication: July 13, 2000