Astron. Astrophys. 359, 1059-1067 (2000)

4. Metallicity effects on Cepheid distances and

Fig. 3 shows the difference between the empirical KP data ³ and the predicted true distance modulus when the oxygen abundance of the Cepheid fields is taken into account. As expected, the almost flat distribution in Fig. 1 now shows a clear correlation to the HII region metallicity, with the discrepancy between LMC-calibrated and theoretical distances increasing when moving from metal-poor to metal-rich galaxies. However, one notices that for very few galaxies the discrepancy overcomes the threshold of 10% (dashed line). Of particular interest is the behaviour of the eight galaxies (the six SNP galaxies plus NGC 3368 and NGC 4414; filled circles) which give Cepheid-calibrated SNIa luminosities (see later).

Fig. 3. The difference between KP empirical distances and predicted metallicity-corrected values, plotted against the HII metallicity of the host galaxy. The filled circles depict the eight galaxies which give Cepheid-calibrated SNIa luminosities.

As a first straightforward test to the actual occurrence of a metallicity effect, we consider the KP distance to galaxies members of groups or clusters. The lower panel of Fig. 4 shows the residuals and [O/H] of each galaxy from the distance modulus and O/H metallicity as averaged over the galaxies of the same group or cluster. A correlation between the metallicity and distance deviations from the mean values can be detected, best-fitted by the relation (dotted line)

in the sense that galaxies whose O/H metallicity is larger than the average appear to have a larger distance. We believe that depth-effects within a given group or cluster cannot be invoked since there is no reason for which the metal-richest galaxies are also the most distant ones.

Fig. 4a and b. a Residuals of each galaxy from the average true distance modulus and O/H metallicity of the host cluster or group. Symbols as follows: Fornax cluster: filled circles, NGC 3184 group: triangles, Leo I group: squares, M87 sub-cluster: open circles, NGC 4472 sub-cluster: asterisks. The dotted line is the best fit to the points [Eq. (4)]. b  As below, but with the Kennicutt et al. (1998) metallicity correction to the absolute distance moduli [Eq. (5)].

This unexpected result, which appears surprisingly in agreement with our predicted correction [Eq. (3)], disagrees with earlier observational clues. It is known that studies of different fields in M31 (Freedman & Madore 1990) and M101 (Kennicutt et al. 1998) suggested an opposite metallicity correction on distance (see also Kochanek 1997; Sasselov et al. 1997). Following Kennicutt et al. (1998), the correction (in magnitude) to the true distance modulus is given by

We show in the upper panel of the same Fig. 4 that adopting such an empirical correction would imply an even stronger correlation between distance and metallicity, with a slope of +0.53 (dotted line) hard to accept.

Applying the predicted metallicity correction to the absolute distance moduli [Eq. (3)], obviously results in a correction to the -values based on LMC-calibrated distances. Assuming , one has [O/H] +0.124 dex^-1, i.e. an increase of 6% in the LMC-based value of any SNIa calibrator whose metallicity is 0.5 dex larger than that of the LMC. This is a not dramatic variation, nevertheless it seems interesting to settle whether it works to decrease or increase the present dispersion of values. Within this context, it is worth noticing that the well known disagreement between the "high" and "low" values claimed by KP and SNP studies, respectively, are not due entirely to the already mentioned different distances to SNIa calibrating galaxies. As discussed by Gibson et al. (2000), the methodology adopted by the SNP group with KP distances leads to 63 km s^-1 Mpc^-1 dex^-1, which is 9% higher than the SNP average value ( 58 km s^-1 Mpc^-1 dex^-1). Moreover, the calibration of SNIa luminosities presents a variety of different approaches and the same KP distances, coupled with the Suntzeff et al. (1999) procedure, would give 67 km s^-1 Mpc^-1 dex^-1. However, the absolute value of the Hubble constant is out the purpose of this paper. We aim only at determining the metallicity-correction to LMC-based values, with the hope of providing new elements for reducing the present uncertainty of 10% to a 5% level.

Taking at the face value the estimates given by Gibson et al. (2000, see their Table 6) we show in the lower panel of Fig. 5 that they agree to each other to within 10% (dashed lines), but with a mild tendency to increase as the oxygen abundance of the host galaxy decreases. The linear regression to the points (dotted line) is

suggesting a metallicity correction as [O/H] +0.069 dex^-1 which is roughly half the amount predicted on the basis of Eq. (3), but it runs towards the same direction. On the contrary, applying the Kennicutt et al. (1998) correction to the true distance moduli [Eq. (5)], results in a correction as /[O/H]0.111 dex^-1 to the LMC-based values. The upper panel of Fig. 5 shows that this would produce a more evident correlation between and [O/H], with two estimates overcoming the discrepancy of 10% from the average value (dashed lines). On the other hand, the lower panel of Fig. 6 shows that our predicted metallicity correction /[O/H]0.124 dex^-1 would yield values which agree to within 10%, but slightly increasing as the [O/H] abundance increases. Eventually, in order to remove any dependence of on the galaxy metallicity (see upper panel in Fig. 6), we suggest that at least the empirical evidence in Fig. 5a should be taken into consideration, i.e., /[O/H]0.069 dex^-1, leading to a slight upward revision of the KP unweighted mean of =67.04.3 km s^-1 Mpc^-1 to =68.63.9 km s^-1 Mpc^-1.

Fig. 5. a  The KP values from LMC-based Cepheid distance to the eight SNIa calibrating galaxies. The average value is labelled. The dashed lines depict the uncertainty of 10%. The dotted line depicts Eq. (6) in the text; b  As below, but with the Kennicutt et al. (1998) metallicity correction to the absolute distance moduli. The resulting correction to is /[O/H]0.111 dex-1 (see text).

Fig. 6. a As in Fig. 5b, but with the predicted metallicity correction /[O/H]+0.124 dex-1; b  As below, but with the metallicity correction /[O/H]+0.069 dex-1, as suggested by the dotted line in Fig. 5a.

As said before, the determination of deals with several factors apart from the distance to the SNIa calibrating galaxies. Thus, we are not giving the predicted value of the Hubble constant, but only the result of the predicted metallicity-correction to the KP estimates, still holding their adopted approach in the treatment of SNIa data and distance to LMC.

© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000
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