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

Abstract

We examine the multi-wavelength period-luminosity-color 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 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 HST and Gaia parallaxes, the residuals from multi-wavelength PL fits are also found to be achromatic, identical in sign and amplitude across all passbands, in this case indicating that parallax errors are the dominant source of 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 two. In addition, they show no statistically significant correlation with metallicity over the range -0.2 < Fe/H < 0.05 dex. The final extinction- and reddening-corrected PLC relation yields an rms scatter of 0.04 mag, corresponding to 2 percent precision in distance per star. 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.

Figures (37)

• Figure 1: Multi-wavelength period-luminosity relations (upper, red points) and period-color relations (lower, purple and black points) for LMC Cepheids.
• Figure 2: VIJHK residuals from their respective PL relations plotted against the corresponding reddening-free PC Q-color residuals. The expected correlations for each bandpass are shown by solid blue lines, with $\pm$ two-sigma bounds given by parallel broken blue lines. A single downward-pointing arrow indicates one example of an achromatic offset noted for one of the many such correlated residuals easily tracked across the five panels.
• Figure 3: Same as Figure 1, expect the PL data are corrected for tilt-induced magnitude deflections. Colors are unaffected by distance errors and/or corrections.
• Figure 4: The same as Figure 2 except the data plotted here have been corrected for the individual, achromatic (delta distance modulus) offsets by the application of one number to each Cepheid at each of the wavelengths. The data are now extremely well fit to the expected (blue) trends of magnitude with intrinsic color.
• Figure 5: Sky plot of our sample of Cepheids in the LMC, color-coded by their line-of-sight distances relative to the adopted distance to the galaxy as a whole. Blue points grow in size as their distances behind the LMC increase; red points are nearer. The dashed line is the approximate line of nodes for the LMC (e.g., Persson et al. 2004).