A new method to compute limb-darkening coefficients for stellar atmosphere models with spherical symmetry: the space missions TESS, Kepler, Corot, and MOST
One of the biggest problems we can encounter while dealing with the limb-darkening coefficients for stellar atmospheric models with spherical symmetry is the difficulty of adjusting both the limb and the central parts simultaneously. In particular, the regions near the drop-offs are not well reproduced for most models, depending on Teff, log g, or wavelength. Even if the law with four terms is used, these disagreements still persist. Here we introduce a new method that considerably improves the description of both the limb and the central parts and that will allow users to test models of stellar atmospheres with spherical symmetry more accurately in environments such as exoplanetary transits, eclipsing binaries, etc. The method introduced here is simple. Instead of considering all the $\mu $ points in the adjustment, as is traditional, we consider only the points until the drop-off ($\mu_{cri}$) of each model. From this point, we impose a condition ${I(\mu)}/{I (1)} = 0$. All calculations were performed by adopting the least-squares method. The resulting coefficients using this new method reproduce the intensity distribution of the PHOENIX spherical models (COND and DRIFT) quite well for the photometric systems of the space missions {{\sc TESS}}, {{\sc KEPLER}}, {{\sc COROT}}, and {{\sc MOST}}. The calculations cover the following ranges of local gravity and effective temperatures: 2.5 $\leq$ log g $\leq$ 6.0 and 1500 K $\leq$ T$_{\rm eff}$ $\leq$ 12000 K. The new spherical coefficients can easily be adapted to the most commonly used light curve synthesis codes.