A universal approach to the calculation of the transit light curves

Abstract

We have developed a universal approach to compute accurately the brightness of eclipsing binary systems during the transit of a planet in front of the stellar disc. This approach is uniform for all values of the system parameters and applicable to most limb-darkening laws used in astrophysics. In the cases of the linear and quadratic limb-darkening laws, we obtained analytical expressions for the light curve and its derivatives in terms of elementary functions, elliptic integrals and a piecewise-defined function of one variable. In the cases of the logarithmic and square-root laws of limb darkening, the flux and its derivatives were expressed in terms of integrals which can be efficiently computed using the Gaussian quadrature formula, taking into account singularities of the integrand.