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

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.

💡 Research Summary

The paper presents a comprehensive calibration of surface‑brightness–colour relations (SBCRs) for classical Cepheids in the Milky Way (MW), Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) using Gaia DR3 photometry (G, BP, RP) and parallaxes. The authors first apply stringent quality cuts to the Gaia catalogue: they retain only fundamental‑mode DCEP variables, discard sources flagged for poor photometry, require at least one observation per 0.1 phase bin, limit relative parallax errors to <10 %, and enforce RUWE ≤ 1.4. MW Cepheids are further restricted to distances <5 kpc and |z| < 400 pc to focus on the solar neighbourhood; LMC and SMC stars are selected within 3° and 0.6° of the respective galaxy centres to minimise depth effects. After all cuts the final sample comprises 1 383 MW, 912 LMC and 597 SMC Cepheids, roughly 1 700 objects in total.

A key ingredient of the analysis is a reliable period‑radius (PR) relation. The authors compile more than thirty PR relations from the literature (both empirical and theoretical) and derive a new empirical PR relation from seven Cepheids with interferometric angular‑diameter curves (Bailleul et al. 2025). By fitting log R versus log P they obtain

log(R/R⊙) = 1.133 ± 0.019 + 0.688 ± 0.016 log P

with an RMS of 0.015 dex. Importantly, no dependence on metallicity (