Title: Fast Computation of Eclipse and Transit Profiles for Spherical Bodies

Abstract: The eminent astronomy Henry Norris Russell asserted “…there are ways of approach to unknown territory which lead surprisingly far, and repay their followers richly. There is probably no better example of this than eclipses of heavenly bodies.” Indeed, the study of eclipsing binary stars touches many branches of astronomy. Computing the light curves of an eclipsing binary is difficult to do in detail, and the early methods used before the advent of electronic computers (such as the Russell-Merrill method) necessarily used many approximations. Starting in the 1950, Zdenek Kopal developed the widely-used “Roche model” whereby the shapes of the stars are determined by equipotential surfaces. The Wilson & Devinney code (1971) was one of the first codes that could compute detailed eclipse profiles using Roche geometry. The two stars are divided up into tiles, and eventually the observed flux can be computed using numerical quadrature. In principle, the model light curves can be computed to any desired degree of accuracy by using more tiles on the two stars, but this obviously greatly increases the CPU time needed. In recent years, it is not uncommon to have observed eclipse profiles with signal-to-noise ratios of several hundred thousand or more (e.g. from NASA’s Kepler and TESS missions), and computing high signal-to-noise models that are needed can be a challenge.

In this talk I will focus different techniques that can be used to compute eclipse profiles when the two bodies are spherical, which is the case for most exoplanet transits and long-period, well-detached binaries. I will give a brief historical overview of techniques used to compute eclipses where both bodies are spheres, and I will then discuss a new method that we have developed which allows for the fast computation of eclipses/transits for any number of spherical bodies and for (almost) any limb darkening law.