fargo_terrestrial :: Early terrestrial planet formation

Here we present materials from the paper Early terrestrial planet formation by torque-driven convergent migration of planetary embryos by Broz, Chrenko, Nesvorny & Dauphas (Nature Astronomy, 5, 898-902, 2021).

See paper on: NA website (final vers.) | ShareIt | Arxiv (original submission) | Arxiv (accepted vers.; after 6 months) | Editorial | Youtube (Seminar) | Slides | ADS | DOI | Materials for rev. 1, rev. 2

Protoplanets orbiting in a gaseous disk. Gravitational interactions between protoplanets and the disk induce convergent migration towards 0.7-1 au. Proto-Earth is visible in the foreground; Venus and Mercury far away. Gas also contains dust and pebbles (cm-sized particles); the latter are affected by aerodynamic drag and contribute to the accretion of planets. See more Illustrations.

Major results and implications:

  1. Terrestrial planets formed early in a gas disk (within 10 My).
  2. The surface density profile Σ(r) was inverted for r < 1 au.
  3. There was a convergence zone, with protoplanets migrating towards r ~ 1 au.
  4. This explains the mass concentration, or small separation of Venus and Earth (0.3 au).
  5. This also explains small Mercury as well as Mars -- as bodies naturally remaining at the convergence zone boundaries (mass removal by an external mechanism is not needed).
  6. Mercury iron core could have been formed in a hot gas disk, next to the evaporation lines of Fe and Mg-rich silicates, by (evaporating) pebbles drifting to 0.4 au from larger r. This is very different from old nebular hypotheses, where the source was limited to a local material (ring).
  7. Delivery of (moderate) volatiles on Mercury is possible by pebbles in a cold gas disk.
  8. Water delivery on Earth is also possible by icy pebbles in a cold disk (with snowline temporarily at 1 au); if not totally blocked by Jupiter (cf. pressure bump which could have been overcome if there is a pile-up of solids).
  9. Eccentricity of Earth or Venus, e = 0.015-0.02, can be induced by the hot-trail effect in gas (a late excitation by an external mechanism is not needed)
  10. Planetary orbits can be detached not only by mergers, but also by differential migration and eccentricity damping.
  11. A 5-planet system was likely formed at the end of the gas phase.
  12. The Moon-forming impact must have been delayed to 45 My (due to geochemical constraints); an instability could have been intrinsic (or external).
  13. 0.5-Earth's impacts are equally probable as the canonical ones (0.1 ME).
  14. There was a divergence zone between 2-3 au (i.e., between terrestrial- and giant-planet convergence zones).
  15. This implies a mass depletion in the asteroid belt (by a factor of 102).
  16. Inclined asteroid-belt orbits were scattered by planetary embryos migrating away in a gas disk (aerodynamic drag on asteroids is weak).
  17. Dry asteroid belt may be due to a low efficiency of pebble accretion (for low m's, high i's).
  18. Venus remained dry if the snowline was always at r > 0.7 au (and there is no missing-oxygen problem after a runaway greenhouse effect).

Supplementary animations:

Mercury- to Mars-size protoplanets, RHD simulation, relative surface density (Σ-Σ(r))/Σ(r) (animated vers. of Fig. 1). Convergence of protoplanets towards r = 1 au and their growth by mutual collisions within 10 My, N-body simulation (animated vers. of Fig. 3). An alternative available in white colour. 0.5Earth protoplanet at 1 au, nominal disk w. Σ0 = 750 g cm-2, streamlines (vr, vφ) and surface density Σ; a circular orbit is a horizontal line in (φ, r) coordinates. 5-planet system in a dissipating disk w. Σ0 = 75 g cm-2, temperature excess T-T(r) (animated vers. of Fig. 4). A detail of the hot-trail effect, which increased the eccentricity up to the Earth's observed value e = 0.016. The co-rotating frame is used.

Supplementary files:

fargo_thorin_DEBUG.tar.gza version of Fargo-Thorin RHD code used for simulations, cf. Git
FIGURES.tar.gzall figures (see data below)
5planet_inverse_NU2.0_-0.5.tar.gzRHD simulation files, inverse Σ(r) profile; Fig. 2, SI Figs. 3, 4, 5
5planet_stable_FLUX2e-4.tar.gznominal disk, Σ0 = 750 g cm-2; Fig. 4
5planet_stable_SEMENOV.tar.gzdtto w. different opacities
5planet_1over10.tar.gzΣ0 = 75 g cm-2; Fig. 4, SI Figs. 7, 8
5planet_1over10_EARTH.tar.gzSI Fig. 1
5planet_1over10_PEBBLEGRAV.tar.gzSI Fig. 2
marssize_inverse_NU2.0_-0.5_2048.tar.gzMercury- to Mars-size embryos; Fig. 1
mainbelt.tar.gzSI Fig. 13
symba9.tar.gzSI Fig. 10
symba11_reductions3.tar.gzN-body simulation files
symba11b_reductions3.tar.gzFig. 3
symba11b_reductions5.tar.gzSI Fig. 6
symba28_pebbleflux2e-7.tar.gzSI Fig. 15
symba28c_pebbleflux2e-7_5MY_0.33SIZE.tar.gzSI Fig. 17
w182.tar.gzε182W anomaly computation (Yu & Jacobson 2011)
symba36_longterm.tar.gzSI Fig. 16
mercury_REBOUND_VENUSECC_0.44.tar.gzSI Fig. 11
mars_REBOUND_0.5EARTH_1.35.tar.gzSI Fig. 12

MMSN is dead

Miroslav Broz (miroslav.broz@email.cz), Apr 18th 2021