Equations for the analysis of the light curves of extra-solar planetary transits

Research and Scientific Support Department, European Space Agency, ESTEC, Keplerlaan 1, 2200 AG Noordwijk ZH, The Netherlands e-mail: agimenez@rssd.esa.int

Received: 31 October 2005
Accepted: 29 December 2005

Abstract

Easy to use analytical formulae are presented for the computation the of light curves of extra-solar planetary transits. The equations are a function of the fractional radii of the planet and the parent star, the inclination of the orbit, and the limb-darkening coefficients of the star. Light curves can be solved for these parameters depending on the precision of the available observations. When the radial velocity curve is also available, as is normally the case to ensure the nature of the system, the masses, radii, and average density of both the star and the planet can be determined. The equations are valid for any degree of limb darkening, as well as for any type of transit. The cases of eccentric orbits, third light, or a non-zero relative luminosity of the planet can be easily taken into account. The basic assumption is that the projections of both the star and the planet on the plane of the sky are well represented by circular discs. The effects in case this assumption is not valid are also discussed. Practical applications are shown, beginning with the light curve of the photometrically discovered planet OGLE-TR-113, obtained with a ground-based telescope. As a second example, results are shown from the study of the light curve obtained for the transit of the giant planet in HD 209458 with the Hubble Space Telescope. Procedures to get the best fit parameters are briefly discussed.