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Context. Surface brightness–colour relations (SBCRs) are used to derive the stellar angular diameters from photometric observations. They have various astrophysical applications, such as the distance determination of eclipsing binaries or the determination of exoplanet parameters. However, strong discrepancies between the SBCRs still exist in the literature, in particular for early and late-type stars. Aims. We aim to calibrate new SBCRs as a function of the spectral type and the luminosity class of the stars. Our goal is also to apply homogeneous criteria to the selection of the reference stars and in view of compiling an exhaustive and up-to-date list of interferometric late-type targets. Methods. We implemented criteria to select measurements in the JMMC Measured Diameters Catalog. We then applied additional criteria on the photometric measurements used to build the SBCRs, together with stellar characteristics diagnostics. Results. We built SBCRs for F5/K7–II/III, F5/K7–IV/V, M–II/III and M–V stars, with respective rms of σ F V  = 0.0022 mag, σ F V  = 0.0044 mag, σ F V  = 0.0046 mag, and σ F V  = 0.0038 mag. This results in a precision on the angular diameter of 1.0%, 2.0%, 2.1%, and 1.7%, respectively. These relations cover a large V  −  K colour range of magnitude, from 1 to 7.5. Our work demonstrates that SBCRs are significantly dependent on the spectral type and the luminosity class of the star. Through a new set of interferometric measurements, we demonstrate the critical importance of the selection criteria proposed for the calibration of SBCR. Finally, using the Gaia photometry for our samples, we obtained ( G  −  K ) SBCRs with a precision on the angular diameter between 1.1% and 2.4%. Conclusions. By adopting a refined and homogeneous methodology, we show that the spectral type and the class of the star should be considered when applying an SBCR. This is particularly important in the context of PLATO. 

Context . The Gl 486 system consists of a very nearby, relatively bright, weakly active M3.5 V star at just 8 pc with a warm transiting rocky planet of about 1.3 R ⊕ and 3.0 M ⊕ . It is ideal for both transmission and emission spectroscopy and for testing interior models of telluric planets. Aims . To prepare for future studies, we aim to thoroughly characterise the planetary system with new accurate and precise data collected with state-of-the-art photometers from space and spectrometers and interferometers from the ground. Methods . We collected light curves of seven new transits observed with the CHEOPS space mission and new radial velocities obtained with MAROON-X at the 8.1 m Gemini North telescope and CARMENES at the 3.5 m Calar Alto telescope, together with previously published spectroscopic and photometric data from the two spectrographs and TESS. We also performed near-infrared interferometric observations with the CHARA Array and new photometric monitoring with a suite of smaller telescopes (AstroLAB, LCOGT, OSN, TJO). This extraordinary and rich data set was the input for our comprehensive analysis. Results . From interferometry, we measure a limb-darkened disc angular size of the star Gl 486 at θ LDD = 0.390 ± 0.018 mas. Together with a corrected Gaia EDR3 parallax, we obtain a stellar radius R * = 0.339 ± 0.015 R ⊕ . We also measure a stellar rotation period at P rot = 49.9 ± 5.5 days, an upper limit to its XUV (5-920 A) flux informed by new Hubble /STIS data, and, for the first time, a variety of element abundances (Fe, Mg, Si, V, Sr, Zr, Rb) and C/O ratio. Moreover, we imposed restrictive constraints on the presence of additional components, either stellar or sub-stellar, in the system. With the input stellar parameters and the radial-velocity and transit data, we determine the radius and mass of the planet Gl 486 b at R p = 1.343 −0.062 +0.063 R ⊕ and M p = 3.00 −0.12 +0.13 M ⊕ , with relative uncertainties of the planet radius and mass of 4.7% and 4.2%, respectively. From the planet parameters and the stellar element abundances, we infer the most probable models of planet internal structure and composition, which are consistent with a relatively small metallic core with respect to the Earth, a deep silicate mantle, and a thin volatile upper layer. With all these ingredients, we outline prospects for Gl 486 b atmospheric studies, especially with forthcoming James Webb Space Telescope ( Webb ) observations.