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Stellar limb-darkening impacts a wide range of astronomical measurements. Theaccuracy to which it is modelled limits the accuracy in any covariantparameters of interest, such as the radius of a transiting planet. With theever growing availability of precise observations and the importance of robustestimates of astrophysical parameters, an emerging trend has been to freely fitthe limb-darkening coefficients (LDCs) describing a limb-darkening law ofchoice, in order to propagate our ignorance of the true intensity profile. Inpractice, this approach has been limited to two-parameter limb-darkening laws,such as the quadratic law, due to the relative ease of sampling the physicallyallowed range of LDCs. Here, we provide a highly efficient method for samplingLDCs describing a more accurate three-parameter non-linear law. We first deriveanalytic criteria which can quickly test if a set of LDCs are physical,although naive sampling with these criteria leads to an acceptance rate lessthan 1%. We then show that the loci of allowed LDCs can be transformed into acone-like volume, from which we are able to draw uniform samples. We show thatsamples drawn uniformly from the conal region are physically valid in 97.3% ofrealizations and encompass 94.4% of the volume of allowed parameter space. Weprovide Python and Fortran code (LDC3) to sample from this region (and performthe reverse calculation) at https://github.com/davidkipping/LDC3, which alsoincludes a subroutine to efficiently test whether a sample is physically validor not.

Efficient, uninformative sampling of limb-darkening coefficients for a three-parameter law