Cepheid Luminosity Versus Galaxy Rotation Speed: L ~ v^{0.7}

The distance modulus of a galaxy determined from Cepheids differs from its distance modulus determined from Tully-Fisher by an amount that is proportional to the galaxy's line width, W: Delta mu ~ (-1.73\pm 0.46)log(W). While a miscalibration of the slope of Tully-Fisher could in principle produce this effect, we argue that such a miscalibration is very unlikely. The other possible explanation is that the inferred Cepheid luminosity is correlated with the rotation speed v (and hence W) of its parent galaxy: L ~ v^{0.7}. This proportionality is superposed on the well-established relation between period and luminosity.) Such a dependence would be expected if Cepheid luminosity is correlated with metallicity, since galaxies with deeper potential wells tend to retain more of their metals. It would induce a discrepancy of 0.83 mag between H_0 determinations that are calibrated using M31 (log W=2.71) and the H_0 determination from SNIa, which is calibrated in galaxies with mean line width <log W>=2.23. A discrepancy of 0.83 mag corresponds to the difference between 80 km/s/Mpc and 55 km/s/Mpc, very similar to the actual discrepancy reported in the current literature.