Revising the Milky Way Cepheid Calibration: Quantifying and Correcting for Previously Undetected Distance Modulus Errors in the Gaia-based Multiwavelength Period–Luminosity Relations

Abstract We examine the multiwavelength period–luminosity–color (PLC) relations for Cepheid variables in the Large and Small Magellanic Clouds and the Milky Way. From first-principles stellar physics, the luminosity of a Cepheid is determined by its radius and surface temperature, yielding a fundamental PLC relation whose observational proxies are the pulsation period and intrinsic color. Using Cepheids in the Magellanic Clouds, we show that the PLC relation recovers the known geometries and line-of-sight tilts of their disks, confirming its ability to detect true distance modulus variations that are achromatic and consistent across all filters. Surprisingly, for Milky Way Cepheids with individually determined reddenings and Hubble Space Telescope and Gaia parallaxes, the residuals from multiwavelength PL fits are also found to be achromatic and identical in sign and amplitude across all passbands, in this case indicating that parallax errors are the dominant source of the scatter. Applying bandpass-averaged corrections to individual Cepheids recovers the theoretically expected wavelength-dependent narrowing of the instability strip and results in revised parallaxes with a median improvement in precision of roughly a factor of 2. In addition, they show no statistically significant correlation with metallicity over the range –0.2 < [Fe/H] 0 < +0.5 dex. The final extinction-and-reddening-corrected PLC relation yields an rms scatter of ±0.04 mag, corresponding to ∼2% precision in distance per star. The use of a physically grounded PLC will provide a more robust foundation for the Cepheid-based extragalactic distance scale and the determination of the Hubble constant.