The Instability Mechanism of Compact Multiplanet Systems

Abstract

Abstract To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of N -body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that account for small sets of resonant interactions between the planets can accurately recover N -body instability times. This points toward a simple physical picture in which a handful of three-body resonances, generated by interactions between nearby two-body mean motion resonances, overlap and drive chaotic diffusion, leading to instability. Motivated by this, we show that instability times are well described by a power law relating instability time to planet separations, measured in units of fractional semimajor axis difference divided by the planet-to-star mass ratio to the 1/4 power, rather than the frequently adopted 1/3 power implied by measuring separations in units of mutual Hill radii. For idealized systems, the parameters of this power-law relationship depend only on the ratio of the planets’ orbital eccentricities to the orbit-crossing value, and we report an empirical fit to enable quick instability time predictions. This relationship predicts that observed systems comprised of three or more sub-Neptune-mass planets must be spaced with period ratios <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">P</mml:mi> <mml:mspace width="0.15em"/> <mml:mo>≳</mml:mo> <mml:mspace width="0.15em"/> <mml:mn>1.35</mml:mn> </mml:math> and that tightly spaced systems ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">P</mml:mi> <mml:mspace width="0.15em"/> <mml:mo>≲</mml:mo> <mml:mspace width="0.15em"/> <mml:mn>1.5</mml:mn> </mml:math> ) must possess very low eccentricities ( e ≲ 0.05) to be stable for more than 10 9 orbits.

Topics & Concepts