The Effect of a Nonuniversal Extinction Curve on the Wesenheit Function and Cepheid Distances

Abstract The Wesenheit function is widely used to reduce the effects of interstellar reddening in distance measurements. Its construction, however, relies on the assumption of a universal extinction curve and on fixed values of the total-to-selective extinction ratio, R V . Recent studies have shown that R V varies significantly across the Milky Way and between different galaxies, raising concerns about systematic biases in Wesenheit magnitudes and period–Wesenheit relations. In this work, we discuss the impact of nonuniversal extinction on Wesenheit indices by combining the R V -dependent extinction curve with a grid of stellar atmosphere models. We compute the integrated extinction in optical and near-infrared passbands, derive R V -dependent R coefficients for multiple Wesenheit indices, and examine how changes in R V propagate into Wesenheit magnitudes and Cepheid distances in our Galaxy. We find that the R coefficients in the Wesenheit functions vary strongly with R V . For classical Cepheids in the Milky Way disk, variations of R V within the typical observed range (2.6–3.6) can lead to substantial differences in the Wesenheit function, reaching ± 0.7 mag from the mean for the Gaia-based Wesenheit index W G and resulting in distance errors of almost 40%. Near-infrared Wesenheit indices are much less sensitive to R V changes. Our results clearly show that accounting for variable R V is essential when applying period–Wesenheit relations, particularly in the optical regime, or that near- or mid-infrared-based distances should be used. While we present this effect for classical Cepheids, it applies to all pulsating stars for which period–Wesenheit relations are used to infer distances.