Dynamical Instability in Multi-Orbiter Systems with Gas Friction

Jiaru Li, Laetitia Rodet, and Dong Lai

Publication: Monthly Notices of the Royal Astronomical Society 528, 2, 2024

Abstract: Closely-packed multi-planet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A similar situation applies to stellar-mass black holes embedded in AGN discs around supermassive black holes. In this paper, we use N-body integrations to evaluate how the frictional damping of orbital eccentricity affects the growth of dynamical instability for a wide range of planetary spacing and planet-to-star mass ratios. We find that the stability of a system depends on the damping timescale τ relative to the zero-friction instability growth timescale t_inst. In a two-planet system, the frictional damping can stabilise the dynamical evolution if t_inst≳τ. With three planets, t_inst≳10τ−100τ is needed for stabilisation. When the separations between the planetary orbits are sufficiently small, t_inst can be less than the synodic period between the planets, which makes frictional stabilisation unlikely to occur. As the orbital spacing increases, the instability timescale tends to grow exponentially on average, but it can vary by a few orders of magnitude depending on the initial orbital phases of the planets. In general, the stable region (at large orbital spacings) and unstable region (at small orbital spacings) are separated by a transition zone, in which the (in)stability of the system is not guaranteed. We also devise a linear map to analyse the dynamical instability of the “planet + test-mass” system, and we find qualitatively similar results to the N-body simulations.

Paper links: [arXiv] [NASA ADS]