A 0.9% Calibration of the Galactic Cepheid luminosity scale based on Gaia DR3 data of open clusters and Cepheids

We have conducted a search for open clusters in the vicinity of classical Galactic Cepheids based on high-quality astrometry from the third data release (DR3) of the ESA mission Gaia to improve the calibration of the Leavitt law (LL). Our approach requires no prior knowledge of existing clusters, allowing us to both detect new host clusters and cross-check previously reported associations. Our Gold sample consists of 34 Cepheids residing in 28 open clusters, including 27 fundamental mode and 7 overtone Cepheids. Three new bona fide cluster Cepheids are reported (V0378 Cen, ST Tau, and GH Lup) and the host cluster identifications for three others (VW Cru, IQ Nor, and SX Vel) are corrected. The fraction of Cepheids occurring in open clusters within 2 kpc of the Sun is $f_{CC,2kpc} = 0.088^{+0.029}_{-0.019}$. By combining cluster and field Cepheids, we calibrate the LL for several individual photometric passbands, together with reddening-free Wesenheit magnitudes based on Gaia and HST photometry, while solving for the residual offset applicable to Cepheid parallaxes, $\Delta \varpi_{\mathrm{Cep}}$. The most direct comparison of our results with the SH0ES distance ladder yields excellent ($0.3\sigma$) agreement for both the absolute magnitude of a 10d solar metallicity Cepheid in the near-IR HST Wesenheit magnitudes, $M_{H,1}^W=-5.914\pm 0.017$ mag, and the residual parallax offset, $\Delta \varpi_{\mathrm{Cep}}=-13 \pm 5\,\mu$as. Using the larger sample of 26 Gold cluster Cepheids and $225$ MW Cepheids with recent Gaia DR3 astrometry and photometry, we determine at solar metallicity $M_{G,1}^W = -6.004 \pm 0.019$\,mag and $\Delta \varpi_{\mathrm{Cep}}=-19 \pm 3\,\mu$as. These results mark the currently most accurate absolute calibrations of the Cepheid luminosity scale based purely on observations of MW Cepheids.