[Paper Review] Formation of planetary systems by pebble accretion and migration: Hot super-Earth systems from breaking compact resonant chains

André Izidoro, Bertram Bitsch+5 more|arXiv (Cornell University)|Feb 23, 2019

Astro and Planetary SciencePhysics and Astronomy251 references36 citations

TL;DR

This paper proposes that hot super-Earth systems form via pebble accretion and gas-driven migration, leading to compact resonant chains that break due to post-disk instability. Simulations show that >95% of such systems become dynamically unstable, naturally reproducing the observed period ratio distribution and explaining the excess of single-planet transits via mutual inclinations from planet–planet scattering.

ABSTRACT

At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to $\sim$95\% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction ($\gtrsim95\%$) of unstable systems with a sprinkling ($\lesssim5\%$) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (${ m N\geq2}$) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet--planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths (abridged).

Motivation & Objective

• To investigate the formation of hot super-Earth systems via pebble accretion and disk-planet tidal interactions.
• To explain the observed overabundance of compact, multi-planet systems with low eccentricities and near-resonant period ratios.
• To reconcile the high incidence of single-planet transits with the intrinsic multiplicity of planetary systems.
• To determine the conditions under which rocky versus ice-rich super-Earths form in the inner disk.
• To test whether the formation of hot super-Earths is compatible with the architecture of the Solar System.

Proposed method

• Conduct N-body simulations incorporating gas-assisted pebble accretion and planet-disk tidal interactions.
• Model type-I migration using the torque formula from Paardekooper et al. (2011), including Lindblad and corotation torques with eccentricity and inclination corrections.
• Implement migration timescale via angular momentum exchange: $ t_m = -L / \Gamma_{\text{tot}} $, with $ \Gamma_{\text{tot}} = \Gamma_L \Delta_L + \Gamma_C \Delta_C $.
• Include eccentricity and inclination damping via wave-drag timescales $ t_{\text{wave}} $, following Papaloizou & Larwood (2000) and Cresswell & Nelson (2006, 2008).
• Apply artificial accelerations for migration ($ a_m $), eccentricity damping ($ a_e $), and inclination damping ($ a_i $) in the FLINTSTONE N-body code.
• Use the effective adiabatic index $ \gamma_{\text{eff}} $ and viscosity/thermal diffusion parameters to compute torque saturation via $ p_\nu $, $ p_\chi $, and functions $ F(p) $, $ G(p) $, $ K(p) $.

Experimental results

Research questions

• RQ1 Can pebble accretion and gas-driven migration reproduce the observed period ratio distribution of hot super-Earths?
• RQ2 What fraction of compact resonant chains remain stable after gas disk dispersal, and how does this compare to observed systems?
• RQ3 Why do most hot super-Earths appear rocky despite forming in the inner disk where ice is expected?
• RQ4 What conditions are required to form rocky super-Earths, and how do they conflict with Solar System formation constraints?
• RQ5 How does the mutual inclination excited by planet–planet instability explain the observed excess of single-planet transits?

Key findings

• Simulations with moderate pebble flux produce multiple super-Earth-mass planets that migrate inward and pile up at the disk inner edge, forming long resonant chains.
• After gas disk dispersal, up to ~95% of these resonant chains become dynamically unstable, leading to late-stage collisions that break the original resonant configurations.
• The model naturally matches the observed period ratio distribution of planet pairs when ~95% of systems are unstable and ~5% remain in stable resonant chains (e.g., TRAPPIST-1-like systems).
• The observed excess of single-planet transits is explained by mutual inclinations excited during planet–planet instability, not by intrinsic single-planet systems.
• In simulations with seeds in both inner and outer disks, close-in super-Earths are systematically ice-rich, contradicting bulk density and radius distribution interpretations that favor rocky compositions.
• Formation of rocky super-Earths requires extreme conditions—such as highly efficient planetesimal formation inside the snow line or much faster pebble accretion—conditions that conflict with those needed to form the Solar System.