Transiting planets - lightcurve analysis for eccentric orbits

Transiting planet lightcurves have historically been used predominantly for measuring the depth and hence ratio of the planet-star radii, p. Equations have been previously presented by Seager & Mallen-Ornelas (2003) for the analysis of the total and trough transit lightcurve times to derive the ratio of semi-major 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 lightcurve solutions for eccentricity, e>0 ii) the asymmetry of the lightcurve and the resulting shift in the mid-transit time, Tmid iii) the effect of eccentricity on the ingress and egress slopes. It is shown that a system with changing eccentricity and inclination may produce a long period transit time variation (LTTV). Furthermore, we use our model in a reanalysis of HD 209458 b archived data by Richardson et al. (2006), where we include the confirmed non-zero eccentricity and derive a 24 micron planetary radius of R_P = 1.275 +- 0.082 R_J (where R_J = 1 Jovian radius), which is 1% larger than is we assume a circular orbit.