Surface brightness–colour relations of Cepheids calibrated by optical interferometry

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 LESIA (UMR 8109), Observatoire de Paris, PSL, CNRS, UPMC, Univ. Paris-Diderot, 5 place Jules Janssen, 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 Millenium Institute of Astrophysics, Avenue Libertador Bernardo O’Higgins 340, Casa Central, Santiago, Chile
⁷ Leibniz Institute for Astrophysics, An der Sternwarte 16, 14482 Potsdam, Germany
⁸ Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
⁹ European Southern Observatory, 85748 Garching, Munich, Germany

^★ Corresponding author: manon.bailleul@oca.eu

Received: 13 January 2025
Accepted: 13 March 2025

Abstract

Context. Surface brightness–colour relations (SBCRs) are widely used to determine the angular diameters of stars. They are in particular used in the Baade-Wesselink (BW) method of distance determination of Cepheids. However, the impact of the SBCR on the BW distance of Cepheids is about 8%, depending on the choice of SBCR considered in the literature.

Aims. We aim to calibrate a precise SBCR dedicated to Cepheids using the best quality interferometric measurements available as well as different photometric bands, including the Gaia bands.

Methods. We selected interferometric and photometric data in the literature for seven Cepheids covering different pulsation periods. From the phased photometry in the different bands (VJHKGG_BP G_RP) corrected from extinction and the interferometric limb-darkened angular diameters, we calculated the SBCR associated with each combination of colours.

Results. We first find that the seven Cepheids have consistent SBCRs as long as the two magnitudes considered are not too close in wavelengths. For the SBCR (F_V, V − K): F_V = −0.1336_±0.0009(V − K)₀ + 3.9572_±0.0015, we obtain a root mean square (RMS) of 0.0040 mag, which is three times lower than the latest estimate from 2004. Also, for the first time, we present an SBCR dedicated to Cepheids based on Gaia bands only: F_GBP = −0.3001_±0.0030(G_BP − G_RP)₀ + 3.9977_±0.0029, with an excellent RMS of 0.0061 mag. However, using theoretical models, we show that this SBCR is highly sensitive to metallicity. From this empirical multi-wavelength approach, we also show that the impact of the CircumStellar Environment (CSE) of Cepheids emission is not negligible and should be taken into account in the future.

Conclusions. With this study, we improve the calibration and our understanding of the SBCR of Cepheids. The overall goal of this project is to provide a purely empirical SBCR version of the BW method that takes into account the metallicity and the CSE emission of Cepheids and that could be applied to individual Cepheids in the local group in the context of JWST and ELT.