2.4. Metallicity Problems with Cepheids

In most applications of the Cepheid PL relation, metallicity effects are neglected, motivated by theoretical arguments that they will be very small. This results from double cancellations of the metallicity dependences between core luminosity and atmosphere, as well as between the effects of the helium abundance and of heavier elements. The expected effect is (Stothers 1988, Iben & Tuggle 1975; Chiosi et al. 1993)

(8)

for the = V, I pass bands. A new calculation of Sandage et al. (1999) gives || < 0.1 for = B, V, I.

When one is concerned with a 10% systematic error in the cosmic distance scale, the metallicity effect must be scrutinised. If it were as large as -0.5, say, the true Cepheid distance to normal spiral galaxies would be longer by 10% relative to LMC ([O/H] = -0.4). The calibrator SNe used in earlier papers (SN1937C, SN1972E, 1981B and 1990N) all reside in low Z galaxies, but recent additions include SNe in high Z galaxies (1989B, and notably 1998bu), thus the sample spans a wider metallicity range (see Figure 1 above). There is now no relative difference in metallicity effects any more between the SBF and SNIa calibrator samples (the offset is [O/H] < 0.1). Therefore, we cannot ascribe the difference in H₀ to the metallicity effect of the Cepheid PL relation: the effect slightly reduces H₀ from both methods if the sign of is negative.

However, it is important to know the magnitude of . Observationally, Freedman & Madore (1990: FM) showed with the M31 data that the metallicity dependence is small (_BVRI = -0.32 ± 0.21). Gould (1994), however, reanalysed the same data and concluded it to be as large as = -0.88 ± 0.16. The EROS collaboration derived _VI = -0.44 from a comparison between LMC and SMC (Beaulieu et al. 1997). Kochanek (1997) suggested _VI = -0.14 ± 0.14 from a global fit of galaxies with Cepheid observations. The metallicity dependence for Galactic Cepheids discussed in section 2.3.2 corresponds to _VJHK -2. Kennicutt et al. (1998) pointed out that the metallicity gradient of M31 used by Freedman & Madore is a factor of three too large and argued that the above values should be _BVRI = -0.94 ± 0.78 (FM) and -2.1 ± 1.1 (Gould).

Kennicutt et al. (1998) derived from HST observations of two fields in M101 that _VI = -0.24 ± 0.16, which is the value currently adopted in metallicity dependence analyses of the HST-KP group. If this is the true value, the effect on the distance scale is of the order of 5 ± 3% (H₀ gets smaller). I would emphasize, however, that independent confirmations are necessary for this value, since the M101 analysis is based only on V and I bands, and the effect of extinction might not be completely disentangled.