Limb-Darkening Coefficients for the 4-Term and Power-2 Laws for the JWST Space Mission, Adopting PHOENIX Spherical Models at High Resolution

Abstract

Modeling observations of transiting exoplanets or close binary systems by comparing the observations with theoretical light curves requires precise knowledge of the distribution of specific intensities across the stellar disk. We aim to facilitate this type of research by providing extensive tabulations of limb-darkening coefficients for 11 frequently used near- and mid-infrared passbands on the NIRCam, NIRISS, and NIRSpec instruments installed on board the James Webb Space Telescope. The calculation of the limb-darkening coefficients was based on spherically symmetric atmosphere models from the PHOENIX series, with high spectral resolution (approximately $10^{6}$ wavelengths), and covering the wavelength range $0.1-6.0~μ$m. The models were computed for solar composition, and a microturbulent velocity of 1.0 km s$^{-1}$. We adopted two of the more accurate parametrizations for the coefficients: the 4-term law, and the power-2 law. We applied the Levenberg-Marquardt least-squares minimization method, with a strategy to determine the critical value $μ_{\rm crit}$ of the cosine of the viewing angle near the limb that is designed to improve numerical accuracy. The limb-darkening coefficients were derived based on a total of 306 atmosphere models covering an effective temperature range of $2400-7800$ K, and a $\log g$ interval between 3.0 and 5.5. We discuss the quality of the fits to the specific intensities provided by the power-2 and 4-term laws, as well as by the often used quadratic law. Based on a comparison, we recommend the use of the 4-term or power-2 laws, in that order of preference.