Dynamical instability in multi-orbiter systems with gas friction

Li, Jiaru; Rodet, Laetitia; Lai, Dong

doi:10.1093/mnras/stae045

Dynamical instability in multi-orbiter systems with gas friction

Journal Article · Sun Jan 07 23:00:00 EST 2024 · Monthly Notices of the Royal Astronomical Society

DOI:https://doi.org/10.1093/mnras/stae045· OSTI ID:2282680

; ; Lai, Dong

ABSTRACT

Closely packed multiplanet 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 active galactic nuclei discs around supermassive black holes. 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 K (the difference in the planetary semimajor axes in units of the mutual Hill radius) and (unequal) planet masses. We find that, in general, the stable region (large K) and unstable region (small K) are separated by a “grey zone”, where the (in)stability is not guaranteed. We report the numerical values of the critical spacing for stability Kcrit and the “grey zone” range in different systems, and provide fitting formulae for arbitrary frictional forcing strength. We show that the stability of a system depends on the damping time-scale τ relative to the zero-friction instability growth time-scale tinst: two-planet systems are stable if tinst ≳ τ; three-planet systems require tinst ≳ 10τ−100τ. When K is sufficiently small, tinst can be less than the synodic period between the planets, which makes frictional stabilization unlikely to occur. As K increases, tinst tends to grow exponentially, but can also fluctuate by a few orders of magnitude. We also devise a linear map to analyse the dynamical instability of the “planet + test mass” system, and find qualitative agreement with N-body simulations.

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Sponsoring Organization:: USDOE

OSTI ID:: 2282680

Journal Information:: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 2 Vol. 528; ISSN 0035-8711

Publisher:: Oxford University PressCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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