Transiting planets - light-curve analysis for eccentric orbits

Transiting planet light curves have historically been used predominantly for measuring the depth and hence ratio of the planet-star radii, p. Equations have previously been presented by Seager & Mallen-Ornelas for the analysis of the total and trough transit light-curve time to derive the ratio of semimajor axis to stellar radius, a/R*, in the case of circular orbits. Here, a new analytic model is proposed which operates for the more general case of an eccentric orbit. We aim to investigate three major effects our model predicts: (i) the degeneracy in transit light-curve solutions for eccentricity, e > 0; (ii) the asymmetry of the light curve and the resulting shift in the mid-transit time, T-MID; (iii) the effect of eccentricity on the ingress and egress slopes. It is also shown that a system with changing eccentricity and inclination may produce a long-term transit time variation (LTTV). Furthermore, we use our model in a re-analysis of HD 209458b archived data by Richardson et al., where we include the confirmed non-zero eccentricity and derive a 24-mu m planetary radius of R-P = 1.275R(J) +/- 0.082R(J) (where R-J = 1 Jovian radius), which is similar to 1 per cent larger than if we assume a circular orbit.