Coplanar circumbinary planets can be unstable to large tilt oscillations in the presence of an inner polar planet

TL;DR

This paper investigates the dynamics of two circumbinary planets with large mutual inclinations, revealing that a polar inner planet can induce large tilt oscillations in the outer planet, affecting their stability and detectability.

Contribution

It provides new insights into how an inner polar planet influences the tilt oscillations and stability of an outer coplanar circumbinary planet through simulations and analytic estimates.

Findings

A coplanar inner planet causes prograde precession and stabilizes the outer planet's inclination.

A polar inner planet causes retrograde precession and can induce large tilt oscillations in the outer planet.

Highly inclined circumbinary planets are difficult to detect via transits due to tilt oscillations.

Abstract

Mutually misaligned circumbinary planets may form in a warped or broken gas disc or from later planet-planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semi-major axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect -- it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.