**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)

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 *H*_{0} to the
metallicity effect of the Cepheid PL relation: the effect slightly reduces
*H*_{0} 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% (*H*_{0}
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.