Exoplanetary Transit Constraints Based Upon Secondary Eclipse Observations

Transiting extrasolar planets provide an opportunity to study the mass-radius relation of planets as well as their internal structure. The existence of a secondary eclipse enables further study of the thermal properties of the the planet by observing at infrared wavelengths. The probability of an observable secondary eclipse depends upon the orbital parameters of the planet, particularly eccentricity and argument of periastron. Here we provide analytical expressions for these probabilities, investigate their properties, and calculate their values for the known extrasolar planets. We furthermore quantitatively discuss constraints on existence and observability of primary transits if a secondary eclipse is observed. Finally, we calculate the a-posteriori transit probabilities of the known extrasolar planets, and we present several case studies in which orbital constraints resulting from the presence of a secondary eclipse may be applied in observing campaigns.

💡 Research Summary

The paper addresses the problem of estimating the likelihood that a known exoplanet will exhibit a secondary eclipse (the disappearance of the planet’s thermal emission as it passes behind its host star) and how that information can be used to refine the probability of observing a primary transit. The authors begin by noting that while transits have long been used to measure planetary radii, masses, and bulk densities, secondary eclipses provide a direct probe of planetary thermal emission and atmospheric composition at infrared wavelengths. However, the geometric probability of a secondary eclipse is not the same as that of a transit; it depends sensitively on the orbital eccentricity (e) and the argument of periastron (ω).

To quantify these dependencies, the authors derive analytical expressions for the transit probability (P_{\rm tra}) and the secondary‑eclipse probability (P_{\rm sec}) for a Keplerian orbit with arbitrary e and ω. The expressions are:

\