Computes the two quadratic limb-darkening coefficients (u1, u2) for exoplanet transit light-curve fits, throughput-integrated over your filter. * Methodology
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I(μ) / I(1) = 1 − u1·(1−μ) − u2·(1−μ)²
Stellar intensities I(μ, λ) are interpolated from the chosen model atmosphere grid (Kurucz ATLAS9 by default) at the input Teff, log(g), and [Fe/H]. The intensities are weighted by the filter throughput from the SVO Filter Profile Service and integrated over wavelength to produce a one-dimensional intensity profile I(μ). The quadratic limb-darkening law is then fit to that profile using non-linear least squares, returning a single pair of coefficients (u1, u2) integrated across the entire bandpass.
For TESS and Spitzer IRAC, the calculation uses ExoTiC-LD's native instrument modes directly. For ground-based photometric filters (Sloan/SDSS, Johnson-Cousins, Pan-STARRS, Astrodon Clear), the throughput integration is performed against SVO transmission curves.
The Astrodon CBB filter uses pre-computed coefficients from Claret, Mullen & Gary (2022) RNAAS, which were derived specifically for this filter using ATLAS9 atmosphere models. The lookup snaps stellar parameters to the nearest grid point and supports a wider Teff range (3500–50000 K) than the ExoTiC-LD pipeline. Microturbulence velocity is fixed at the standard value of 2.0 km/s.