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. We derive SBCRs for classical Cepheids in the Milky Way and in the Magellanic Clouds using the photometric data available in the database, and we quantify the metallicity effect. Gaia 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 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. Gaia We first derived a new PR relation based on interferometric data and distances from the literature of seven classical Cepheids: mathrm łog (R/R_⊙) = 1. 133_ ± 0. 019 + 0. 688_ ± 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 magnitudes alone. Finally, we derived relations between the slopes, the zero points (ZP), and the metallicity (Gaia Fe/H) of these three SBCRs: mathrm Slope_ SBCR =-0. 0663_ ± 0. 0121 Fe/H - 0. 3010_ ± 0. 0030 and mathrm ZP_ SBCR =-0. 1016_ ± 0. 0091 Fe/H + 3. 9988_ ± 0. 0029. 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.
Bailleul et al. (Wed,) studied this question.