The EBLM project -- XIV. TESS light curves for eclipsing binaries with very low mass companions

Accurate limb-darkening models are needed for accurate characterisation of eclipsing binary stars and transiting exoplanets from the analysis of their light curves. The limb-darkening observed in solar-type stars from the analysis of light curves for transiting hot-Jupiter exoplanets are systematically less steep than predicted by stellar model atmospheres that do not account for the stellar magnetic field. Hot-Jupiter host stars tend to be metal rich ([Fe/H] ~0.25) leading to a lack of low- and solar-metallicity targets in previous studies, so we have analysed the TESS light curves for a sample of 19 stars with transiting M-dwarf companions to extend the range of limb-darkening measurements to [Fe/H] values more typical for solar-type stars. We find that the systematic offset between the observed and predicted limb-darkening profiles observed in metal-rich hot-Jupiter systems is also observed for these solar-type stars at lower metallicity. These observations provide additional measurements to explore the impact of magnetic fields on the atmospheres of solar-type stars. We have also used the TESS light curves to make precise estimates of the radius and effective temperature of the M-dwarf companions in these 19 binary systems. We confirm the results from previous studies that find very low mass stars tend to be about 3 per cent larger than predicted by stellar models that use a mixing length prescription calibrated on the Sun.