The Effect of a Non-universal Extinction Curve on the Wesenheit Function and Cepheid Distances

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, Rv. Recent studies have shown that Rv 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 non-universal extinction on Wesenheit indices by combining the Rv-dependent extinction curve with a grid of stellar atmosphere models. We compute the integrated extinction in optical and near-infrared passbands, derive Rv-dependent R coefficients for multiple Wesenheit indices, and examine how changes in Rv propagate into Wesenheit magnitudes and Cepheid distances in our Galaxy. We find that the R coefficients in the Wesenheit functions vary strongly with Rv. For classical Cepheids in the Milky Way disk, variations of Rv 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 Rv changes. Our results clearly show that accounting for variable Rv 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.

💡 Research Summary

The paper investigates how the common assumption of a universal extinction curve and a fixed total‑to‑selective extinction ratio (R_V) affects the reliability of Wesenheit magnitudes and Cepheid‑based distance estimates. While the Wesenheit function (W = m_λ2 − R · (m_λ1 − m_λ2)) is designed to be reddening‑free, its construction requires a constant R_V, typically taken as ≈3.1 in the Milky Way. Recent large‑scale studies, however, have demonstrated that R_V varies widely across the Galaxy (from ~2.0 up to ~8.0) and between different environments.

To quantify the impact, the authors adopt the R_V‑dependent extinction law of Gordon et al. (2023, “G23”), which provides a parametrisation (R_0) that spans the full UV‑mid‑IR range. They generate a comprehensive grid of 17 603 stellar atmosphere models (Atlas‑9) covering effective temperatures 2500–8000 K, gravities log g = −0.5–5.5, and metallicities