Astron. Astrophys. 324, 471-482 (1997)

1. Introduction

The Cepheid  period-luminosity (PL) relation is widely accepted as being one of the most accurate primary distance indicators to nearby galaxies. It has now been applied as far as the Virgo cluster of galaxies (Freedman et al. 1994b, Pierce et al. 1994, Sandage et al. 1994, Tanvir et al. 1995) and holds the greatest promise to settle the debate over the value of the Hubble constant by providing a % accurate determination (the goal of the HST Key Project).

The Cepheid variable stars offer a simple way of measuring distances: their pulsation periods (easy to obtain) are strongly correlated with their luminosities; then distances are determined from their apparent brightness via the PL relation. The reliability of these distances stems from the good theoretical understanding of the Cepheids and their PL relation (Iben & Tuggle 1975). Theory predicts a small, but not negligible, abundance effect on the PL zero point (see Stothers 1988 for review). However the ambiguous results of previous empirical tests for this effect have led all recent HST studies quoted above to assume that the Cepheid  PL relation is insensitive to metallicity.

Three sources contribute to an abundance dependence of the PL relation: (1) theory of stellar pulsation, through the dependence of period on mass and radius; (2) theory of stellar evolution, through the mass-luminosity relation; and (3) theory of stellar atmospheres, through line blanketing and backwarming, the relations between effective temperature, absolute magnitudes in bandpasses, and bolometric correction. As a result, a metal-poor Cepheid is always fainter than a metal-rich Cepheid (at a fixed period and temperature); metal-poor Cepheids are also hotter (bluer) on the average. Given the sensitivity of each of the above three sources to metallicity, the overall weakness of the effect on the bolometric PL relation is remarkable (Stothers 1988, Chiosi et al. 1993). Theory predicts that the slope of the PL relation is nearly independent of metallicity, only the zero point is affected. The observed PL relations are not bolometric, hence the effect would depend on the bandpass. Most of the above predictions are valid for a limited range of Cepheid pulsation periods - Cepheids with P 50 days are expected (and observed) to deviate from a linear PL relation.

Theory in itself predicts a period-luminosity-color relation (Sandage 1958). However we study the PL relation, because this is the current one of choice in the determination of . Theory predicts abundance effects on the PL relation due to helium (Y) and heavy elements (Z). However we only know the heavy elements abundances (Z) in Magellanic Clouds Cepheids , hence we speak of metallicity effects in this paper.

Previous studies have looked for metallicity effects on the Cepheid PL relation since the beginning of the 70s, but the issue remains unsettled observationally. Partly to blame is the near degeneracy between three important observed properties of Cepheids: the lines of constant period, reddening, and metallicity, in optical and near-infrared bandpasses. The lines of constant period represent the range of temperatures over which a star can sustain a stable Cepheid pulsation in a given mode and period; this introduces a natural width (in luminosity) to the PL relation. The amount of obscuration (reddening) is a more serious problem, as it is common practice to derive it from the photometry of the Cepheids themselves - thus the color difference due to metallicity will affect the reddening estimate and the inferred distance (Stothers 1988, Freedman & Madore 1990).

The first large scale comparison between SMC, LMC, and Galaxy Cepheids  is due to Payne-Gaposchkin & Gaposchkin (1973). Payne-Gaposchkin (1974) concluded that there was no evidence for composition differences. However, Gascoigne (1974) reinvestigated the apparent color differences between LMC and SMC Cepheids  as a metallicity effect and found that the SMC Cepheids would be fainter than LMC Cepheids  by 0.1 mag (in V). The color shift between LMC and SMC Cepheids  was confirmed by Martin, Warren, & Feast (1979) and clearly distinguished from differential extinction. Subsequently, Iben & Tuggle (1975) and Iben & Renzini (1984) argued for a much smaller effect, mostly from theoretical considerations. Stothers (1988) offered a critical review of all these attempts and pointed out the effect of the reddening correction. In a different approach to the problem, Caldwell & Coulson (1985, 1986) merged theoretical and empirical relations and individual reddenings from color-color diagrams to derive PL relations adjusted for abundance differences. These fit well their data-set of about 130 Cepheids in LMC and SMC. Caldwell & Coulson's results confirm the existence of a metallicity effect. Their very different approach provides no base for a detailed comparison with the current extragalactic use (Stothers 1988, Madore & Freedman 1991). In addition, Caldwell & Coulson's sample of about 130 Cepheids  appears to be too small for quantifying the tiny effect. This can be seen in a recent comparison of primary distance indicators to 15 galactic and extragalactic objects in which Caldwell & Coulson's PL relations (adjusted for metallicity) were used (Huterer, Sasselov, & Schechter 1995) - the uncertainties within and between the four primary indicators are larger than the weak metallicity dependence.

The main reason extragalactic distance measurements have assumed that Cepheid luminosity does not depend on metallicity is the work by Freedman & Madore (1990). They found that any distance differences in three M 31 fields with varying metallicity are consistent with statistical noise, and much smaller than Stothers'(1988) prediction. The conclusion is based on a sample of 38 Cepheids and 152 BVRI observations; the method used is the same used in all recent distance determinations. The situation was reviewed by Feast (1991), who urged for the need to test the metallicity corrections empirically. This was partially accomplished by Laney & Stobie (1994), who concluded that their VJHK data on 21 Galactic and 115 MC Cepheids  do not support the implications of Freedman & Madore's result that intrinsic Cepheid  color is independent of metallicity. At the same time Gould (1994) challenged Freedman & Madore's conclusion by pointing out the high degree of correlation among the BVRI measurements (treated by Freedman & Madore as independent). Gould obtained a PL zero-point shift similar to that of Stothers (1988) by reanalyzing the same BVRI observations of 36 Cepheids  in M 31. However, he showed that the data-set suffers from some systematic uncertainty, which affects the derived size of the effect. Stift (1995) confirmed independently Gould's conclusions using current theoretical evolutionary and atmosphere models. Thus the issue remained unsettled. As a result all recent HST measurements of Cepheid distances assume that no metallicity effects are present at V and I (Freedman et al. 1994b,Sandage et al. 1994,Tanvir et al. 1995).

In this paper we use a new data-set of two-color photometry ( 3 million observations) of about 500 Cepheids  in the LMC and SMC to derive the dependence of the optical PL relations on metallicity. We find that the apparent distance modulus depends on metallicity roughly as: . The dependence is weaker than some previous claims, though by no means negligible. It is derived from a differential LMC-SMC analysis which incorporates all correlations between Cepheid  measurements, independently derived metal abundances for Cepheids  and supergiants, and known limits to the extinction laws. The photometric database is a byproduct of the EROS microlensing survey (Aubourg et al. 1993a, Beaulieu et al. 1995, Beaulieu et al. 1996).

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

helpdesk.link@springer.de