The chemical composition of a star plays a role in setting the rate of energy generation, it affects the evolution off of the main sequence, and it determines the wavelength distribution of the emergent flux. The role of metallicity in the evolution of individual Cepheids in specific, and for the forms of PL, PC and PLC, in general, has been a matter of conjecture and debate for several decades now. Stothers (1988) reviewed the theoretical aspects of this problem in great detail, concluding that at blue wavelengths the effect could be of concern to the distance scale. While the effects are generally conceded to be smaller at longer wavelengths, only recently has strict attention been paid to quantifying the effects of metallicity for near-infrared bandpasses.
Two independent physical mechanisms contribute to the effect of metallicity on the mean color of Cepheids. First of all, it is expected that the observed colors of Cepheids should vary (in a wavelength-dependent way) as a function of differing amounts of atmospheric metal-line blanketing. In addition, changes in the mean metallicity of the star as a whole are predicted to affect the interior opacities, resulting in equilibrium radius changes and different mean surface brightnesses (effective temperatures) for the same nuclear-generated luminosity. Detailed studies suggest however, that the effect of metallicity on the observed colors is largest for atmospheric line blanketing, compared to changes forced upon the interior structure of the star.
The most recent self-consistent modeling effort is that of
Chiosi et al. (1993).
These authors produced linear nonadiabatic
pulsation calculations for a grid of Cepheid models with a range of
masses, various effective temperatures, and chemical compositions
ranging from 1/4 to solar metallicity, for a variety of
mass-luminosity relations. The theoretical fluxes were then convolved
with the UBVRcIc passbands for comparison with
observations.
These authors conclude that the agreement between theory and
observation is best at longer wavelengths, noting a discrepancy
between the observed and predicted (B-V, Log P) relations between the
SMC, the
LMC, and the Galaxy. Their predicted uncertainty of
the true
distance modulus, after correcting for reddening, is 
(m-M) = -1.7 Z (at log P = 1.0). Hence, for
the entire range of chemical compositions represented by the
low-metallicity SMC (Z = 0.004) and the solar-metallicity Galactic
Cepheids (Z = 0.016), a very small abundance effect (amounting to only
0.02mag, full range) is predicted.
The predictions of Chiosi et al. (1993) are consistent with the results of a test of the metallicity sensitivity of the Cepheid PL relation by Freedman & Madore (1990). These authors undertook the first empirical test of the metallicity sensitivity of the PL relation by observing samples of Cepheids in three fields at differing distances from the nucleus of M31. The observational test is differential, and thus independent of any absolute metallicity calibration. From multiwavelength (BVRI) observations, true distance moduli and reddenings were determined for each of the three fields. The range in metallicity over the three fields is approximately a factor of 5. Large (0.80 mag) differences were found between the apparent blue moduli, whereas the maximum differences in the apparent I-band moduli amounted to only 0.3 mag. After correcting for reddening, a small (0.3 mag peak-to-peak) range in the true distance moduli was found, having low overall statistical significance, but still in the same sense as predicted by theory.
Figure 6. Multiwavelength fits of normal
reddening lines to BVRI apparent distance moduli for M31 Cepheids
(Freedman & Madore 1990).
The three fields in
M31 have distinctly
different average reddenings associated with them, however the true
modulus, as given by the intercept at 1/
= 0 is quite stable,
indicating little residual sensitivity of the Cepheid PL relation to
metallicity.
Despite the good agreement with the predictions of Chiosi et al. (1993), the results of Freedman & Madore (1990), are smaller (by about a factor of 3) than earlier predictions by Stothers (1988) for B and V-band photometry. Subsequently, the Freedman & Madore (1990) data have been reanalyzed by Gould (1994), who concludes that the M31 data are consistent with a larger metallicity dependence. However, see Chiosi et al. (1993) for their cautionary remarks about the predictions from (B-V) photometry. Furthermore, a large metallicity dependence for the Cepheid PL relation does not appear to be consistent with the very good agreement of the (lower metallicity) Population II distance indicators (e.g. RR Lyraes and first ascent red giant branch (TRGB) stars) to be discussed later.
While the importance of metallicity effects is still not totally
resolved, all theoretical models to date predict that at progressively
longer wavelengths, the effects of metallicity differences should be
very small. We are currently completing a five-year program in which
we hve obtained JHK near-infrared array photometry of the Freedman &
Madore sample of M31 Cepheids
(Freedman, Madore & Sakai 1998,
in preparation.) The longer wavelength baseline added to the optical
data will offer much tighter constraints on this empirical metallicity
calibration. As a further check of the metallicity sensitivity of the
PL relation, the M31 test has been carried over to 2 fields in
M101
(Kennicutt et al. 1998)
as part of the Key Project on the
Extragalactic Distance Scale. Once again the test indicates that as
far as the methodology of using V and I-band data to determine
extinction-corrected moduli, the metallicity effect is small, on the
order of (m-M)0 / [O / H] = -0.24 ± 0.16 mag/dex. Even at
this level of dependence it is to be emphasized that the resulting
effect on the distance scale will only amount to a few percent. This
is so because the LMC metallicity (-0.4 dex) is very close to the
mean metallicity of the galaxies being observed in the Key Project
(-0.3 dex). Obviously individual distances of galaxies with
metallicities significantly larger or smaller than the metallicity of
the LMC will systematically deviate (if not corrected
for metallicity)
but no large bias is expected in the mean. Obviously, NICMOS data would
be extremely valuable in dealing with this issue empirically.
Figure 7. A differential comparison of distance
moduli determined from the Population I Cepheid PL relation and the
Population II TRGB magnitude as a function of Hubble type of the
parent galaxy (upper left) absolute magnitude of the parent galaxy
(lower left), the TRGB modulus (lower right) and finally the
metallicity of the parent galaxy (upper right). Within the scatter no
trends are apparent, especially with metallicity. (adapted from
Lee, Freedman & Madore 1993)