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

TL;DR

This paper evaluates various limb-darkening laws for exoplanet transit modeling, recommending the most accurate ones for different scenarios and providing tools to select the optimal law to improve parameter retrieval accuracy.

Contribution

It compares multiple limb-darkening laws beyond the quadratic, offering a method to choose the best law case-by-case and providing code for optimal selection.

Findings

Logarithmic, square-root, and three-parameter laws outperform quadratic and linear laws.

Exponential law is non-physical and should be avoided.

Guidelines and code are provided for selecting the best limb-darkening law.

Abstract

Very precise measurements of exoplanet transit lightcurves both from ground and space based observatories make it now possible to fit the limb-darkening coefficients in the transit-fitting procedure rather than fix them to theoretical values. This strategy has been shown to give better results, as fixing the coefficients to theoretical values can give rise to important systematic errors which directly impact the physical properties of the system derived from such lightcurves such as the planetary radius. However, studies of the effect of limb darkening assumptions on the retrieved parameters have mostly focused on the widely used quadratic limb-darkening law, leaving out other proposed laws that are either simpler or better descriptions of model intensity 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 and linear laws when deriving parameters from transit lightcurves, both in terms of bias and precision, for a wide range of situations. We therefore recommend to study which law to use on a case-by-case basis. We provide code to guide the decision of when to use each of these laws and select the optimal one in a mean-square error sense, which we note has a dependence on both stellar and transit parameters. Finally, we demonstrate that the so-called exponential law is non-physical as it typically produces negative intensities close to the limb and should therefore not be used.