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We present here an efficient method for computing the visible flux for eachbody during a multi-body eclipsing event for all commonly used limb darkeninglaws. Our approach follows the idea put forth by Pal (2012) to apply Green'sTheorem on the limb darkening integral, thus transforming the two-dimensionalflux integral over the visible disk into a one-dimensional integral over thevisible boundary. We implement this idea through an iterative process whichcombines a fast method for describing the visible boundary of each body with afast numerical integration scheme to compute the integrals. For the two-bodycase, our method compares well in speed with both that of Mandel & Agol (2002)and that of Gimenez (2006a). The strength of the method is that it works forany number of spherical bodies, with a computational accuracy that isadjustable through the use of a tolerance parameter. Most significantly, themethod offers two main advantages over previously used techniques: (i) it canemploy a multitude of limb darkening laws, including all of the commonly usedones; (ii) it can compute the Rossiter-McLaughlin effect for rigid bodyrotation with an arbitrary orientation of the rotation axis, using any of theselimb darkening laws. In addition, we can compute the Rossiter-McLaughlin effectfor stars exhibiting differential rotation, using the quadratic limb darkeninglaw. We provide the mathematical background for the method and explain indetail how to implement the technique with the help of several examples andcodes which we make available.

Accurate Computation of Light Curves and the Rossiter-McLaughlin Effect in Multi-Body Eclipsing Systems