Magnetic origin of the discrepancy between stellar limb-darkening models and observations

Stars appear darker at their limbs than at their disk centres because at the limb we are viewing the higher and cooler layers of stellar photospheres. Yet, limb darkening derived from state-of-the-art stellar atmosphere models systematically fails to reproduce recent transiting exoplanet light curves from the Kepler, TESS and JWST telescopes-stellar brightness obtained from measurements drops less steeply towards the limb than predicted by models. Previous models assumed stellar atmospheres devoid of magnetic fields. Here we use stellar atmosphere models computed with the three-dimensional radiative magnetohydrodynamic code MURaM to show that a small-scale concentration of magnetic fields on the stellar surface affects limb darkening at a level that allows us to explain the observations. Our findings provide a way forward to improve the determination of exoplanet radii and especially the transmission spectroscopy analysis for transiting planets, which relies on a very accurate description of stellar limb darkening from the visible to the infrared. Furthermore, our findings imply that limb darkening allows estimates of the small-scale magnetic field strength on stars with transiting planets. An outstanding discrepancy between observations and models of stellar limb darkening is resolved here by the inclusion of stellar surface magnetism in models. This will enable an improved characterization of transiting exoplanets.