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From planetesimals to planets with N-body simulations in the giant-planet formation region

Sebastian Lorek, Michiel Lambrechts

Abstract

The cores of wide-orbit giant planets can form via pebble accretion if large planetesimals form in the outer regions of protoplanetary discs at sufficiently early times. Streaming instability simulations support mass distributions consistent with Solar System minor body constraints, but when and where planetesimal formation took place remains uncertain. Here, we report on our N-body simulations of core formation through pebble and planetesimal accretion starting from streaming-instability inspired planetesimal mass distributions. We explore two initial radial planetesimal distributions, a ring-like and a spatially more uniform distribution, between 10 and 50 AU. To address the numerical challenge of simulating realistic planetesimal numbers, corresponding to one to ten Earth masses of planetesimals, we made use of GPU acceleration for the N-body interactions (with GENGA) and a newly developed pebble accretion module. We find that the top of the planetesimal mass distribution provides the seeds for core formation through pebble accretion, leading to the formation of multiple giant planets. This is consistent with previous studies not including N-body interactions. Planetesimal surface densities, crudely corresponding to an initial 10% formation efficiency, imply low mean collision rates (around unity) in the gas disc phase. Our simulations show that giant planet formation depends only weakly on the initial locations where planetesimals form, because of rapid dynamical scattering, and on their total mass budget, due to filtering of the pebble flux between embryos. After disc dissipation, giant planet systems stir the remnant primordial planetesimals, making a scattered disc an inherent outcome of giant planet formation. Giant impacts between planetary cores generally appear to be rare in the first 100 Myr.

From planetesimals to planets with N-body simulations in the giant-planet formation region

Abstract

The cores of wide-orbit giant planets can form via pebble accretion if large planetesimals form in the outer regions of protoplanetary discs at sufficiently early times. Streaming instability simulations support mass distributions consistent with Solar System minor body constraints, but when and where planetesimal formation took place remains uncertain. Here, we report on our N-body simulations of core formation through pebble and planetesimal accretion starting from streaming-instability inspired planetesimal mass distributions. We explore two initial radial planetesimal distributions, a ring-like and a spatially more uniform distribution, between 10 and 50 AU. To address the numerical challenge of simulating realistic planetesimal numbers, corresponding to one to ten Earth masses of planetesimals, we made use of GPU acceleration for the N-body interactions (with GENGA) and a newly developed pebble accretion module. We find that the top of the planetesimal mass distribution provides the seeds for core formation through pebble accretion, leading to the formation of multiple giant planets. This is consistent with previous studies not including N-body interactions. Planetesimal surface densities, crudely corresponding to an initial 10% formation efficiency, imply low mean collision rates (around unity) in the gas disc phase. Our simulations show that giant planet formation depends only weakly on the initial locations where planetesimals form, because of rapid dynamical scattering, and on their total mass budget, due to filtering of the pebble flux between embryos. After disc dissipation, giant planet systems stir the remnant primordial planetesimals, making a scattered disc an inherent outcome of giant planet formation. Giant impacts between planetary cores generally appear to be rare in the first 100 Myr.
Paper Structure (34 sections, 31 equations, 12 figures, 2 tables)

This paper contains 34 sections, 31 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Disc model
  4. Pebble accretion
  5. Pebble Stokes number
  6. Pebble accretion rates
  7. Pebble isolation mass
  8. Reduction of pebble flux
  9. Pebble flux
  10. Migration
  11. Type I
  12. Type II
  13. Gas accretion
  14. Planetesimal sizes
  15. GPU-accelerated N-body simulations
  16. ...and 19 more sections

Figures (12)

  • Figure 1: Pebble flux (solid) and total pebble mass (dashed) drifting through the system over time.
  • Figure 2: Initial planetesimal mass distribution. We show the initial distributions of the rings (solid coloured lines), the total distribution of all bodies (black), and Eq. \ref{['eq:imf']} (dashed cyan lines). All distributions have been averaged over all low-mass runs. The standard deviation (shaded area) shows the spread of the initial planetesimal mass distribution from the random sampling. The high-mass runs follow the same IMF but with a higher total number of bodies (see also Fig. \ref{['fig:finalccdf']}).
  • Figure 3: Snapshots of mass and semi-major axis from $0.3\,\mathrm{Myr}$ to $4.1\,\mathrm{Myr}$ for narrow ring run n05. The initial locations of the rings are $12.2\,\mathrm{AU}$ (yellow), $18.3\,\mathrm{AU}$ (orange), $27.3\,\mathrm{AU}$ (red), and $40.9\,\mathrm{AU}$ (purple). The symbol size scales with the mass of the body as ${\propto}m^{1/3}$. Planets with mass ${\ge}0.1\,M_\oplus$ have solid circles. The Solar System planets ($+$) and Pluto and Eris ($\Diamond$) are shown for reference as well as the pebble isolation mass (dashed line).
  • Figure 4: Same as Fig. \ref{['fig:snapnarrowm']} but showing the eccentricity and semi-major axis evolution.
  • Figure 5: Same as Fig. \ref{['fig:snapnarrowm']} but for $4.1\,\mathrm{Myr}$ to $100\,\mathrm{Myr}$.
  • ...and 7 more figures