Stability Limits of Circumbinary Planets: Is There a Pile-up in the Kepler CBPs?

TL;DR

This study develops numerical tools to determine the stability limits of circumbinary planets, compares these limits with Kepler data, and finds no strong evidence for a planet pile-up near the stability boundary.

Contribution

The paper introduces a fast, accurate method for stability analysis of circumbinary planets and applies it to assess the presence of a planet pile-up in Kepler systems.

Findings

55% of Kepler CBP systems could host an additional interior planet.

No strong evidence for a pile-up of planets near the stability limit.

Numerical tools and simulation data are publicly available.

Abstract

The stability limit for circumbinary planets (CBPs) is not well defined and can depend on initial parameters defining either the planetary orbit or the inner binary orbit. We expand on the work of Holman & Wiegert (1999, AJ 117, 621) to develop numerical tools for quick, easy, and accurate determination of the stability limit. The results of our simulations, as well as our numerical tools, are available to the community through $\texttt{Zenodo}$ and $\texttt{GitHub}$, respectively. We employ a grid interpolation method based on $\sim$150 million full N-body simulations of initially circular, coplanar systems and compare to the 9 known Kepler CBP systems. Using a formalism from planet packing studies, we find that 55% of the Kepler CBP systems allow for an additional equal-mass planet to potentially exist on an interior orbit relative to the observed planet. Therefore, we do $\textit{not}$ find strong evidence for a pile-up in the Kepler CBP systems and more detections are needed to adequately characterize the formation mechanisms for the CBP population. Observations from the Transiting Exoplanet Survey Satellite are expected to substantially increase the number of detections using the unique geometry of CBP systems, where multiple transits can occur during a single conjunction.