The extragalactic Cepheid bias: a new test using the period-luminosity-color relation

We use the Period-Luminosity-Color relation (PLC) for Cepheids to test for the existence of a bias in extragalactic distances derived from the classical Period-Luminosity (PL) relation. We calculate the parameters of the PLC using several galaxies observed with the Hubble Space Telescope and show that this calculation must be conducted with a PLC written in a form where the parameters are independent. The coefficients thus obtained are similar to those derived from theoretical models. Calibrating with a few unbiased galaxies, we apply this PLC to all galaxies of the Hubble Space Telescope Key Program (HSTKP) and compare the distance moduli with those published by the HSTKP team. The new distance moduli are larger (more exactly, the larger the distance the larger the difference), consistent with a bias. Further, the bias trend that is observed is the same previously obtained from two independent methods based either on the local Hubble law or on a theoretical model of the bias. The results are quite stable but when we force the PLC relation closer to the classical PL relation by using unrealistic parameters, the agreement with HSTKP distance moduli is retrieved. This also suggests that the PL relation leads to biased distance moduli. The new distance moduli reduce the scatter in the calibration of the absolute magnitude of supernovae SNIa at their maximum. This may also suggest that the relation between the amplitude at maximum and the decay of the light curve $\Delta m_{15}$ may not be as strong as believed.