Reliable Transmission Spectrum Extraction with a Three-Parameter Limb Darkening Law

TL;DR

This paper evaluates different limb darkening laws for exoplanet transmission spectroscopy, finding that the three-parameter law provides more accurate and robust results than the commonly used quadratic law, especially for high-impact parameter transits.

Contribution

It demonstrates that the three-parameter limb darkening law yields more reliable transmission spectra and impact parameter estimates than the quadratic law, which can introduce significant biases.

Findings

Quadratic law causes wavelength-dependent offsets in spectra.

Three-parameter law provides robust retrievals for high-impact transits.

Offsets can reach 1% of transit depth, affecting atmospheric signal detection.

Abstract

Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modelled stellar spectra or determining the coefficients empirically during light curve fitting of the data. Here, we test how accurately three common laws -- quadratic, power, and a three-parameter law -- can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters ($b$ larger than about 0.5) the amplitude of these offsets can reach 1\% of the transit depth which is some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping--Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters.