Predicting the Existence of Circumbinary Planet Kepler-47d

Predicting a third planet in the Kepler-47 circumbinary system

Authors:

Hinse et al

Abstract:

We have explored the possibility of a third circumbinary planet having a dynamically stable orbit in the Kepler-47 system and producing the single, unexplained transit event (not associated with either the binary star or the two known circumbinary planets) reported in the discovery paper (Orosz et al. 2012). We applied the dynamical mapping MEGNO technique to identify regions in the phase space of the system where this third planet can maintain stable, quasi-periodic orbits. The long-term, Lagrangian stability of the entire 5-body configuration (eclipsing binary + three planets) is confirmed by direct numerical integrations for 10 Myr. We identified several long-term stable regions between the two confirmed planets, and also an extended region beyond the orbit of the outer planet Kepler-47c. To further constrain the orbit of the hypothetical third planet, we compared the synthetic single transit duration it produces from the ensemble of stable orbits to the measured duration of the unexplained transit event (~4.15 hours). Due to the rich dynamics of the system, different stable orbits of such a hypothetical, third circumbinary planet can produce similar single-transit durations. To remove this degeneracy, we fixed the planet's orbit as circular and use the observed duration of the unexplained transit to analytically place an upper limit of 424 days for the planetary period. Our analysis strongly suggests that, if the yet unexplained single transit event is indeed due to a planetary object, then the most probable orbit for this undetected planet will be between Kepler-47b and Kepler-47c -- a region characterized by low-order mean motion resonances. We present our methodology in details, and discuss the implication of our results.