New approach for modelling of transiting exoplanets for arbitrary limb-darkening law

We present a new solution of the direct problem of planet transits based on transformation of double integrals to single ones. On the basis of our direct problem solution, we created the code TAC-MAKER for rapid and interactive calculation of synthetic planet transits by numerical computations of the integrals. The validation of our approach was made by comparison with the results of the wide-spread Mandel-Agol method for the cases of linear, quadratic and squared-root limb-darkening laws and various combinations of model parameters. For the first time our approach allows the use of arbitrary limb-darkening law of the host star. This advantage together with the practically arbitrary precision of the calculations makes the code a valuable tool that faces the challenges of the continuously increasing photometric precision of the ground-based and space observations.