Diversity of disc viscosities can explain the period ratios of resonant and non-resonant systems of hot super-Earths and mini-Neptunes

¹ Department of Physics, University College Cork, Cork, Ireland
² Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
³ Department of Earth, Environmental and Planetary Sciences, MS 126, Rice University, Houston, TX 77005, USA

^★ Corresponding author; bitsch@mpia.de

Received: 7 June 2024
Accepted: 15 November 2024

Abstract

Migration is a key ingredient in the formation of close-in super-Earth and mini-Neptune systems. The migration rate sets the resonances in which planets can be trapped, where slower migration rates result in wider resonance configurations compared to higher migration rates. We investigate the influence of different migration rates – set by disc viscosity – on the structure of multi-planet systems via N-body simulations, where planets grow via pebble accretion. Planets in low-viscosity environments migrate slower due to partial gap opening compared to planets forming in high-viscosity environments. Consequently, systems formed in low-viscosity environments tend to have planets trapped in wider resonant configurations (typically 4:3, 3:2, and 2:1 configurations). Simulations of high-viscosity discs mostly produce planetary systems in 7:6, 5:4, and 4:3 resonances. After the gas disc dissipates, the damping forces of eccentricity and inclination cease to exist and the systems can undergo instities on timescales of a few tens of millions of years, rearranging their configurations and breaking the resonance chains. We show that low-viscosity discs naturally account for the configurations of resonant chains, such as Trappist-1, TOI-178, and Kepler-223, unlike high-viscosity simulations, which produce chains that are more compact. Following dispersal of the gas disc, about 95% of our low-viscosity resonant chains became unstable, experiencing a phase of giant impacts. Dynamical instabilities in our low-viscosity simulations are more violent than those of high-viscosity simulations due to the effects of leftover external perturbers (P>200 days). About 50% of our final systems end with no planets within 200 days, while all our systems harbour remaining outer planets. We speculate that this process could be qualitatively consistent with the lack of inner planets in a large fraction of the Sun-like stars. Systems produced in low-viscosity simulations alone do not match the overall period ratio distribution of observations, but give a better match to the period distributions of chains, which may suggest that systems of super-Earths and mini-Neptunes form in natal discs with a diversity of viscosities.