| Abstract | I investigate the dependence on metallicity of the apparent distance modulus of a galaxy as inferred from Cepheids. I compare data from Cepheids in three fields in M31 with Cepheids in the Large Magellanic Cloud (LMC), taking account of the high degree of correlations among the BVRI magnitude measurements. I find a significant dependence of apparent distance modulus on metallicity over the range -0.5 < [Fe/H] <0.2. Taking all the available data at face value, I estimate that the distance modulus of a galaxy as inferred from Cepheids should be corrected by an amount {DELTA}mu_ = (0.88 +/- 0.16){DELTA}[Fe/H], where {DELTA}[Fe/H] is the difference in metallicity between the galaxy and that of the LMC (where the Cepheids are calibrated). The sign is such that the distances to metal-rich galaxies such as M31 and M81 would be underestimated if the effect were not taken into account. However, there are important systematic uncertainties in this determination. In particular, if the R data are ignored, I find {DELTA}mu_ = (0.56+/- 0.20){DELTA}[Fe/H]. I investigate the possible origins of this discrepancy and the further observations which would be required to resolve it. I discuss the implications for the problem of the determining the Hubble parameter and for the problem of measuring large-scale motions. |
