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Very precise measurements of exoplanet transit lightcurves both from groundand space based observatories make it now possible to fit the limb-darkeningcoefficients in the transit-fitting procedure rather than fix them totheoretical values. This strategy has been shown to give better results, asfixing the coefficients to theoretical values can give rise to importantsystematic errors which directly impact the physical properties of the systemderived from such lightcurves such as the planetary radius. However, studies ofthe effect of limb darkening assumptions on the retrieved parameters havemostly focused on the widely used quadratic limb-darkening law, leaving outother proposed laws that are either simpler or better descriptions of modelintensity profiles. In this work, we show that laws such as the logarithmic,square-root and three-parameter law do a better job than the quadratic andlinear laws when deriving parameters from transit lightcurves, both in terms ofbias and precision, for a wide range of situations. We therefore recommend tostudy which law to use on a case-by-case basis. We provide code to guide thedecision of when to use each of these laws and select the optimal one in amean-square error sense, which we note has a dependence on both stellar andtransit parameters. Finally, we demonstrate that the so-called exponential lawis non-physical as it typically produces negative intensities close to the limband should therefore not be used.

Limb-darkening and exoplanets II: Choosing the Best Law for Optimal Retrieval of Transit Parameters