The Dependence of the Extinction Coefficient on Reddening for Galactic Cepheids

Cepheids are fundamental distance indicators, playing a crucial role not only in the cosmic distance ladder but also in mapping the structure, kinematics, and extinction properties of the Milky Way. Using high-precision photometry and parallaxes from Gaia Data Release 3, we identify a significant anticorrelation between the G -band extinction coefficient and reddening for Galactic Cepheids, quantified as R G = 1.918 ± 0.060 − (0.106 ± 0.022) E ( G BP − G RP ). We propose that this anticorrelation arises from the combination of the nonlinear effects inherent to the broad Gaia bands and the R V variations caused by the diverse interstellar medium. Adopting a fixed R G would not only lead to an overestimation of the metallicity dependence of Cepheid luminosities but also systematically underestimate the distances to highly reddened Cepheids. Moreover, the strong reddening dependence of R G makes the Wesenheit function based on it unsuitable for highly reddened Cepheids, since the definition of Wesenheit magnitudes requires a fixed extinction coefficient. In contrast, infrared-based distances, being less affected by nonlinear effects and insensitive to R V , provide the most reliable Cepheid distances at present. This work emphasizes the importance of accurately determining R V for Galactic Cepheids and accounting for nonlinear effects in distance measurements, particularly in the optical bands.