Surface brightness-colour relations of Milky Way and Magellanic Clouds classical Cepheids based on Gaia magnitudes

TL;DR

This study emits Gaia-band SBCR calibrations for classical Cepheids in the Milky Way and the Magellanic Clouds, using Gaia DR3 photometry and distances (Gaia parallaxes for MW; eclipsing-binary distances for MCs) to perform an inverse Baade–Wesselink analysis. A new interferometry-based PR relation for seven MW Cepheids, $\log(R/R_{sun}) = 1.133 \pm 0.019 + 0.688 \pm 0.016 \log(P)$, reinforces the finding that metallicity does not affect PR relations, while SBCRs in Gaia bands do depend on metallicity. The paper derives three SBCRs across MW, LMC, and SMC with explicit formulas in $F_{G_{BP}}$ and shows that their slopes and zero-points correlate with $[Fe/H]$ via linear relations, e.g. $Slope_{SBCR} = -0.0663 \pm 0.0121 [Fe/H] - 0.3010 \pm 0.0030$ and $ZP_{SBCR} = -0.1016 \pm 0.0091 [Fe/H] + 3.9988 \pm 0.0029$. The Wesenheit relations in Gaia passbands are found to have metallicity-insensitive slopes but metallicity-dependent zero-points. These results enable Gaia-based inverse BW analyses of Cepheids and highlight the need for precise Gaia DR4 metallicities to refine SBCR calibrations for distance-scale work.

Abstract

Aims: We derive SBCRs for classical Cepheids in the Milky Way and in the Magellanic Clouds using the photometric data available in the Gaia database, and we quantify the metallicity effect. Methods: We first selected the data on the basis of a number of quality criteria and chose the best photometric data and the best parallaxes available in Gaia for Milky Way classical Cepheids. Secondly, we compiled an extensive list of period-radius (PR) relations available in the literature, and we also provide a new PR relation based on interferometric data in our previous work. Thirdly, combining the radius of classical Cepheids with distance estimates (based on Gaia parallaxes for the Milky Way and on eclipsing binaries for the Magellanic Clouds), we derived the surface brightness and colour of about 1700 classical Cepheids. Results: We first derived a new PR relation based on interferometric data and distances from the literature of seven classical Cepheids: $\mathrm{\log(R/R_{\odot}) = 1.133_{\pm 0.019} + 0.688_{\pm 0.016} log(P)}$. The metallicity does not affect the PR relations. Secondly, we calculated three different SBCRs for the Milky Way and Large and Small Magellanic Cloud classical Cepheids based on this new PR relation that clearly show the dependence of the metallicity on the SBCR based on Gaia magnitudes alone. Finally, we derived relations between the slopes, the zero points (ZP), and the metallicity ([Fe/H]) of these three SBCRs: $\mathrm{Slope_{SBCR}=-0.0663_{\pm 0.0121} [Fe/H] - 0.3010_{\pm 0.0030}}$ and $\mathrm{ZP_{SBCR}=-0.1016_{\pm 0.0091} [Fe/H] + 3.9988_{\pm 0.0029}}$. Conclusions: These new SBCRs, dedicated to classical Cepheids in the Milky Way and Magellanic Clouds, are of particular importance to apply the inverse Baade-Wesselink method to classical Cepheids observed by Gaia in a forthcoming study.

Figures (12)

• Figure 1: Data selection process.
• Figure 2: Gaia all-sky view of the Milky Way and the Large and Small Magellanic Clouds. We show the total sample in grey. The final selected sample of Cepheids is shown in colour.
• Figure 3: Period-radius relation using data of seven Cepheids based on the interferometric angular diameter curve of bailleul_2025.
• Figure 4: Slope and zero points of the different period-radius relations listed in Tab. \ref{['tab:PR_relations']}.
• Figure 5: Gaia zero-point offset as a function of the distance difference that it implies. The colour represents the parallax. Only the 228 selected Cepheids (after the whole selection process shown in Fig. \ref{['fig:data_selection']}) are shown here.