Fig. 1: Limb darkening in the Kepler passband.
From: Magnetic origin of the discrepancy between stellar limb-darkening models and observations
The x and y axes express the difference in the limb-darkening coefficients (\({h}_{1}^{{\prime} }\) and \({h}_{2}^{{\prime} }\)) between two sources: one source is always the models without magnetic fields (REFLD) and the other can be models with either fields or observations. The points marked by a cross correspond to the data averaged over the full sample of Kepler stars (green) and over a selected sample including the stars with metallicities −0.1 < M/H < 0.1 and transits with an impact factor less than 0.5 (blue). The error bars represent s.e.m. These points show the mean offset between measurements12 and REFLD15. The star symbols are our calculations based on MURaM simulations (that is, offsets between our calculations and REFLD) for different magnetization levels (see legend; HD, SSD, 100 G, 200 G, 300 G) in the Kepler passband. The sketch in the right upper corner illustrates the definition of the limb darkening coefficients, where Ic represents the intensity at the disk center, I2/3 represents the intensity at μ = 2/3 and I1/3 represents the intensity at μ = 1/3. All intensities are normalized to the intensity at the disk center. The solar symbol (Sun) is the measured solar limb darkening in the Kepler passband15. Our stellar atmosphere models, which include magnetic fields, match both the solar and the stellar observations and provide an explanation for the offsets between Kepler limb darkening relative to models without magnetic field.
