A unitary model for the formation of terrestrial planets

and (rocky) close-in super-EarthsA. Morbidelli (OCA, Nice), M.Lambrechts, S.Jacobson,

A.Johansen, A.Izidoro, S.Raymond, B.Bitsch

Mercury

Mars

Earth

Venus

SuperEarths

JupiterSaturn

Uranus

Neptune

Planet populations

K11b

K11f

Owen and Wu, 2017Data from Fulton et al., 2017

Dressing et al., 2015

Because of their unveiled rocky nature, SuperEarths are often considered as scaled-up versions of the Solar System’s terrestrial planets. Is this correct?

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WHAT IS THE EARTH?

Tform= 2-4 My

Tform=40-120 My

WHAT ABOUT PLANETS MORE MASSIVE THAN EARTH?

• Not just a 1 ME planet @ 1 AU• Long accretion timescale

• Late Moon-forming event• Protracted core formation

• Assemblage from Mars-mass embryos

• The small mass of the embryos explain why they did not migrate close to the Sun

More massive final planets -> more mass available

Planetary embryos are expected to grow by pebble accretion. So, more mass available -> higher pebble flux

We have done simulations of pebble accretion featuring:• Pebble accretion, migration, mutual interactions (scattering, merging)• An initial system of Moon-mass planetesimals• Gas disk decaying as exp(-t/1My) from MMSN-like density• Pebble-flux decaying as exp(-t/1My) from different initial fluxes• Pebble Stokes number: 3x10-3

Inner disk’s edge

Integrated pebble flux = 38 ME

Total final mass ~ 1ME

Inner disk’s edge

Integrated pebble flux = 114 ME

Total final mass ~ 9ME

Inner disk’s edge

Integrated pebble flux = 190 ME

Total final mass ~ 20-30 ME

Discontinuities mark merging events

accretion -> some migrationaccretion -> strong migration

No Earth-mass planets formed within disk’s lifetime No Earth-mass planets formed within disk’s lifetime

SuperEarths formed within disk’s lifetime

Final distribution of planetary systems, at the end of gas-disk lifetime

pb. flux = 38 ME

pb. flux = 114 ME

pb. flux = 190 ME

pb. flux = 340 ME

Solar System embryos

Low pebble flux: Small migrationOrdered accretionDifferent sims. -> same results

High pebble flux: Large migrationFeedback of migration on accretionDifferent sims. -> different results

Beyond the gas-disk lifetime: Instabilities!

Beyond the gas-disk lifetime: Instabilities!

Instability causes multiple merging events of embryos.This leads to planets up to 4 ME on a timescale much longer than the disk’s lifetime.

Analog to Earth formation in the Solar System

Beyond the gas-disk lifetime: Instabilities!

Beyond the gas-disk lifetime: Instabilities!

Instabilities break resonant chains (Izidoro et al., 2017). Systems spread. Merging events possible.Reproduces Kepler observations well in terms of period-ratio distribution

Summary of final systems

Earth-like formation mode

Migration-dominated formation mode

• Overlapping mass-range• Overlapping distances from host star

For individual planets, it may not be easy to say which way they formed

Best diagnostic: the presence of a H-rich atmosphere• planets formed in the migration dominated mode acquire a

large mass within the lifetime of the disk, so they can accrete primitive atmospheres

• They can suffer a few post-gas giant impacts but these are ineffective in removing atmospheres (Schlichting & Mukhopadhyay, 2018)

• Exception: evaporation for strongly irradiated planets

But the planetary systems formed in the different regimes are clearly distinct!

CONCLUSIONS

We have produced a unitary model for the formation of terrestrial planets and rocky super-Earths• The pebble mass-flux is the key parameter -> see next slide• Two different formation regimes • Two distinct final populations

Mercury

Mars

EarthVenus

These results, and the observed distribution of extrasolar planets suggest that we have not discovered truly terrestrial planets yet

What sets the pebble mass-flux?

Unclear!Certainly:• Disk mass• Metallicity• Size

But it can be much more complicated than that:• Fraction of pebble sequestered planetesimal formation• Possibility to generate “late pebbles” as debris• Apparition of pressure bumps (e.g. giant planet formation) blocking the pebble flux

Not just the mass-flux matters but also the pebble accretion efficiency, which depends on:• Pebbles’ stokes number (dependent on pebble size and gas density)• Size of the embryos’ seeds• Scale height of pebbles layer (depends on disk’s turbulence and pebbles Stokes number)

In the case of the Solar System, it is likely that the early formation of Jupiter (<1My; Kruijer et al., 2017) was the key factor limiting the pebble mass flux