2010ApJ...715..277B

We present a detailed investigation of the Cepheid distance scale by using both theory and observations. Through the use of pulsation models for fundamental mode Cepheids, we found that the slope of the period-luminosity (P-L) relation covering the entire period range (0.40 ≤ log P ≤ 2.0) becomes steeper when moving from optical to near-infrared (NIR) bands, and that the metallicity dependence of the slope decreases from the B- to the K band. The sign of the metallicity dependence for the slopes of the P-L_V and P-L_I relation is at odds with some recent empirical estimates. We determined new homogeneous estimates of V- and I-band slopes for 87 independent Cepheid data sets belonging to 48 external galaxies with nebular oxygen abundance 7.5 ≤ 12 + log (O/H) ≤ 8.9. By using Cepheid samples including more than 20 Cepheids, the χ² test indicates that the hypothesis of a steepening of the P-L_V,I relations with increased metal content can be discarded at the 99% level. On the contrary, the observed slopes agree with the metallicity trend predicted by pulsation models, i.e., the slope is roughly constant for galaxies with 12+log (O/H) < 8.17 and becomes shallower in the metal-rich regime, with confidence levels of 62% and 92%, respectively. The χ² test concerning the hypothesis that the slope does not depend on metallicity gives confidence levels either similar (PL_V, 62%) or smaller (PL_I, 67%). We investigated the dependence of the period-Wesenheit (P-W) relations on the metal content and we found that the slopes of optical and NIR P-W relations in external galaxies are similar to the slopes of Large Magellanic Cloud (LMC) Cepheids. They also agree with the theoretical predictions suggesting that the slopes of the P-W relations are independent of the metal content. On this ground, the P-W relations provide a robust method to determine distance moduli relative to the LMC, but theory and observations indicate that the metallicity dependence of the zero point in the different passbands has to be taken into account. To constrain this effect, we compared the independent set of galaxy distances provided by Rizzi et al. using the tip of the red giant branch with our homogeneous set of extragalactic Cepheid distances based on the P-W relations. We found that the metallicity correction on distances based on the P-WBV relation is γ_B,V= -0.52 mag/dex, whereas it is vanishing for the distances based on the P-WVI and on the P-WJK relations. These findings fully support Cepheid theoretical predictions.