Stellar variability on timescales of days and longer is attributed to magnetic surface features, such as dark spots and bright faculae. The spectral variability of these features introduces noise and systematics to planetary transit spectroscopy by affecting the shape and depth of observed transit curves. To ensure that the correct planetary parameters are obtained from these observations, accurate facular contrasts and limb darkening must be accounted for in their extraction. Facular contrasts have been observed only in a few wavelength bands on the Sun and cannot be resolved on other stars. Therefore, for full spectral coverage, spectra must be derived from atmospheric models. Until now, only 1D atmospheric models have been widely available. These 1D models do not fully reproduce the observed centre-to-limb variations of faculae, as they neglect the 3D geometry of the faculae.
In this thesis, I derive the first spectral contrasts from the UV (149.5~nm) to the infrared (160\,000~nm) for small-scale magnetic features as a function of limb distance and magnetic activity using 3D magneto-convection simulations for multiple cool main-sequence spectral types (F3V-M2V). I find that facular contrasts have a complex relationship with magnetic field strength, limb distance, wavelength and spectral type.
The spectral facular contrasts are used to provide centre-to-limb variation coefficients for multiple exoplanetary mission filters. In addition to the magnetic centre-to-limb variations, field-free limb darkening coefficients across the spectral types are derived. Crucially, our calculations provide a direct link between facular contrast and magnetic field that has allowed reconstruction of total solar irradiance without the need for a free parameter.