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

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France
² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warszawa, Poland
³ LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS, 5 place Jules Janssen, 92195 Meudon, France
⁴ French-Chilean Laboratory for Astronomy, IRL 3386, CNRS, Casilla 36-D, Santiago, Chile
⁵ Universidad de Concepción, Departamento Astronomía, Casilla 160-C, Concepción, Chile
⁶ Leibniz Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany
⁷ Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 6 November 2025
Accepted: 10 January 2026

Abstract

Context. Surface brightness–colour relations (SBCRs) are widely used to estimate the angular diameters of stars. In particular, they are employed in the Baade–Wesselink distance determination method, which relies on the comparison between the linear and angular amplitudes of Cepheids. The SBCR can be calibrated by combining different photometric systems. An SBCR was recently calibrated based on Gaia DR3 magnitudes alone for fundamental-mode classical Cepheids with solar metallicity. This relation appears to be strongly affected by metallicity, however.

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: log(R/R_⊙) = 1.133_±0.019 + 0.688_±0.016log(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: Slope_SBCR = −0.0663_±0.0121[Fe/H] − 0.3010_±0.0030 and ZP_SBCR = −0.1016_±0.0091 [Fe/H] + 3.9988_±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.