The surface brightness-colour relations based on eclipsing binary stars and calibrated with EDR3

Aims. The surface brightness-colour relation (SBCR) is a basic tool for establishing precise and accurate distances within the Local Group. Detached eclipsing binary stars with accurately determined radii and trigonometric parallaxes allow calibration of the SBCRs with unprecedented accuracy.Methods. We analysed four nearby eclipsing binary stars containing late F-type main sequence components: AL Ari, AL Dor, FM Leo, and BN Scl. We determined very precise spectroscopic orbits and combined them with high-precision ground- and space-based photometry. We derived the astrophysical parameters of their components with mean errors of 0.1% for mass and 0.4% for radius. We combined those four systems with another 24 nearby eclipsing binaries with accurately known radii from the literature for which Gaia EDR3 parallaxes are available in order to derive the SBCRs.Results. The resulting SBCRs cover stellar spectral types from B9 V to G7 V. For calibrations, we used Johnson optical B and V, GaiaG(BP) and G, and 2MASS JHK bands. The most precise relations are calibrated using the infrared K band and allow angular diameters of A-, F-, and G-type dwarf and subgiant stars to be predicted with a precision of 1%