A JWST transiting survey of FGK stellar limb darkening: empirical evidence for quadratic laws and atmospheric model comparisons
We present a study of stellar limb-darkening using JWST transit observations of seven exoplanets orbiting FGK host stars, spanning 4200-6800 K. The wide wavelength coverage and high S/N of NIRISS/SOSS and NIRSpec/PRISM enable precise constraints on the wavelength-dependent limb-darkening. Using Bayesian model selection, we find that the quadratic limb-darkening law is statistically preferred over higher-order laws for most FGK stars, recovers consistent intensity profiles for $>$95% of the stellar disk area, and introduces a minimal bias in the derived transit depths of only $\sim$14 ppm (1$\sigma$) for 6/7 targets. This contrasts with previous studies relying on stellar models. We compare the empirically derived quadratic coefficients to predictions from the PHOENIX, MPS-ATLAS, MURaM, and Stagger stellar atmosphere grids. We introduce a quadratic limb-darkening parameterization in terms of limb intensity ($\ell$) and curvature at mid-$\mu$ ($\delta$), finding that empirical FGK limb darkening is generally more linear than models predict ($\delta \lesssim 0.1$). We identify wavelength-independent offsets between data and model quadratic coefficients, minimized by adopting $\mu_{\rm min} = 0.2$ in intensity calculations; we attribute this in part to models overpredicting limb-darkening near the limb where the plane-parallel approximation breaks down. For spherical PHOENIX models, we derive a $\mu$ rescaling method using a $\tau = 1$ photospheric radius. With these corrections, residual offsets are minimized and all stellar models achieve statistically acceptable fits. We provide recommended limb-darkening offset priors for use in JWST transit analyses, enabling more accurate constraints on exoplanet transmission spectra while accounting for residual stellar model uncertainties.