The Dependence of the Extinction Coefficient on Reddening for Galactic Cepheids

TL;DR

This study reveals a significant anti-correlation between the Gaia G-band extinction coefficient and reddening in Galactic Cepheids, impacting distance and metallicity estimates and highlighting the need for accurate extinction modeling.

Contribution

It demonstrates the dependence of the extinction coefficient on reddening and discusses its implications for Cepheid distance measurements and the use of Wesenheit functions.

Findings

Anti-correlation between $R_G$ and reddening quantified as $R_G = 1.918 \, ext{minus} \, 0.106 imes E(G_{BP} - G_{RP})$.

Fixed $R_G$ leads to overestimated metallicity dependence and underestimated distances for reddened Cepheids.

Infrared distances are more reliable due to insensitivity to $R_V$ and non-linear effects.

Abstract

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 anti-correlation between the $G$-band extinction coefficient and reddening for Galactic Cepheids, quantified as $R_G = 1.918 \pm 0.060 - (0.106 \pm 0.022)\,E(G_{\mathrm{BP}} - G_{\mathrm{RP}})$. We propose that this anti-correlation arises from the combination of the non-linear effects inherent to the broad $Gaia$ bands and the $R_V$ variations caused by 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 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 non-linear 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 non-linear effects in distance measurements, particularly in the optical bands.