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 & Mallén-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, TMID; (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-μm planetary radius of RP= 1.275RJ± 0.082RJ (where RJ= 1 Jovian radius), which is ∼1 per cent larger than if we assume a circular orbit.