# High-precision stellar limb-darkening in exoplanetary transits

## TL;DR

This paper introduces a new two-coefficient limb-darkening law for exoplanet transit modeling, demonstrating its superiority and proposing strategies to improve parameter estimation with upcoming JWST data.

## Contribution

The paper proposes a novel two-coefficient limb-darkening law ('power-2') and strategies for fitting limb-darkening coefficients using prior orbital information to enhance exoplanet characterization.

## Key findings

- The 'power-2' law outperforms existing two-coefficient laws for most star types.
- Empirical limb-darkening fits can be biased even with photon-noise limited data.
- Using priors from infrared JWST data improves limb-darkening and exoplanet parameter estimates.

## Abstract

Characterization of the atmospheres of transiting exoplanets relies on accurate measurements of the extent of the optically thick area of the planet at multiple wavelengths with a precision $\lesssim$100 parts per million (ppm). Next-generation instruments onboard the James Webb Space Telescope (JWST) are expected to achieve $\sim$10 ppm precision for several tens of targets. A similar precision can be obtained in modelling only if other astrophysical effects, including the stellar limb-darkening, are accounted for properly. In this paper, we explore the limits on precision due to the mathematical formulas currently adopted to approximate the stellar limb-darkening, and to the use of limb-darkening coefficients obtained either from stellar-atmosphere models or empirically. We propose a new limb-darkening law with two coefficients, `power-2', which outperforms other two-coefficient laws adopted in the literature in most cases, and particularly for cool stars. Empirical limb-darkening based on two-coefficient formulas can be significantly biased, even if the light-curve residuals are nearly photon-noise limited. We demonstrate an optimal strategy to fitting for the four-coefficients limb-darkening in the visible, using prior information on the exoplanet orbital parameters to break some of the degeneracies that otherwise would prevent the convergence of the fit. Infrared observations taken with the James Webb Space Telescope (JWST) will provide accurate measurements of the exoplanet orbital parameters with unprecedented precision, which can be used as priors to improve the stellar limb-darkening characterization, and therefore the inferred exoplanet parameters, from observations in the visible, such as those taken with Kepler/K2, JWST, other past and future instruments.