Interstellar extinction of classical Cepheids from neighboring stars I. Methodology and application to 16 Galactic Cepheids

Galactic Cepheid variable stars are fundamental calibrators of the cosmic distance scale through their Period-Luminosity (PL) relation. The high-precision parallaxes expected from Gaia Data Release 4 (DR4) will enable a calibration of the Milky Way PL relation with unprecedented precision. This will place stringent requirements on interstellar extinction corrections, which remain a dominant source of uncertainty. We strive to derive highly accurate extinction values for Galactic Cepheids. We present an innovative methodology relying on the analysis of neighboring field stars and apply it to a pilot sample of 16 Cepheids. We identify physically near field stars using Gaia DR3 astrometry. For these stars, we determine atmospheric parameters from medium- to high-resolution VLT/FLAMES spectroscopy. Fixing these parameters, we derive individual extinctions by fitting spectral energy distributions constructed from Gaia XP spectra and infrared photometry. We then reconstruct the three-dimensional distribution of extinction and interpolate extinction to the Cepheid position. We report extinction Av, total-to-selective extinction ratio Rv, and color excess E(B-V) for all 16 Cepheids. Our method achieves a mean precision of approximately 5%, improving upon typical literature values, with no significant systematic offset detected. We demonstrate that using field stars bypasses uncertainties associated with Cepheid variability and can provide robust extinction estimates for Galactic Cepheids.