Analytic orbit propagation for transiting circumbinary planets

TL;DR

This paper develops an analytical model to describe the motion of coplanar circumbinary planets, incorporating short-term perturbations, long-term secular evolution, and relativistic corrections, validated against numerical simulations and applied to Kepler systems.

Contribution

It introduces a comprehensive analytical framework combining perturbation theory and secular dynamics for coplanar circumbinary planets, including relativistic effects, to analyze their orbital evolution.

Findings

Model accurately matches numerical integrations.

Suggests different formation histories for Kepler-34 and Kepler-413.

Eccentricity constraints imply varied formation scenarios.

Abstract

The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are used to derive short period evolution of the system, while octupole secular theory is applied to describe its long term behaviour. A post Newtonian correction on the stellar orbit is included. The planetary orbit is initially circular and the theory developed here assumes that the planetary eccentricity remains relatively small (e_2<0.2). Our model is tested against results from numerical integrations of the full equations of motion and is then applied to investigate the dynamical history of some of the circumbinary planetary systems discovered by NASA's Kepler satellite. Our results suggest that the formation history of the systems Kepler-34 and Kepler-413 has most likely been different from the one of Kepler-16, Kepler-35, Kepler-38 and Kepler-64, since the observed planetary eccentricities for those systems are not compatible with the assumption of initially circular orbits.