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  • The formation of gas giants and ice giants by pebble accretion

    Michiel Lambrechts Anders Johansen / Alessandro Morbidelli

    Observatoire de la côte d’azur Exoplanets in Lund 6-8 May 2015

    1

  • Planets and pebbles in protoplanetary discs

    2

    HD100546, 2Msol,~5Myr. - 400 AU wide ppd - potential imaged gas giant planet at 53 AU (Quanz et al 2014)

    50AU

    Debes et al 2013 ALMA collaboration+, 2015

    TW Hya ppd (~5Myr) [left] - 80 AU planet of 6-28 ME - ~180--300 Me in pebbles (Wilner+2005, bergin+2013)

    HL tau ppd (~1Myr) [right] - formation of planets in a ~1Myr old disc - large pebble component (Greaves et al 2008)

    (1) Planets form in protoplanetary discs (few Myr, in wide circular orbits, and in multiples) (2) Simultaneously, there is a large solid component in pebbles (mm-dm sized particles)

    HL tau

    2

  • Pebble accretion dynamics 1

    3

    Bondi pebble accretion Lambrechts & Johansen, 2012

    3

  • - Hill regime starts above a transition mass:

    - accretion occurs from the full Hill radius

    - relative velocities are set by the Keplerian shear (independent of )

    Pebble accretion dynamics 2

    Mt ⇡ 3⇥ 10�3 ⇣ r 5AU

    ⌘3/4 M�

    Hill pebble accretion Lambrechts & Johansen, 2012

    4

    4

  • - Hill regime starts above a transition mass:

    - accretion occurs from the full Hill radius

    - relative velocities are set by the Keplerian shear (independent of )

    Pebble accretion dynamics 2

    Mt ⇡ 3⇥ 10�3 ⇣ r 5AU

    ⌘3/4 M�

    Hill pebble accretion Lambrechts & Johansen, 2012

    4

    4

  • Difference with planetesimals

    5

    MMSN scaling

    Ṁpeb ⇠ rHvH⌃peb

    Ṁplan ⇠ r2accvH⇢plan ⇢plan ⇠ ⌃plan/hplan hplan ⇠ vH/⌦K ⇠ rH

    Ṁpeb ⇠ rHvH⌃peb

    See also: Ormel & Klahr 2010

    Rafikov 2004 planetesimals/fragments and Levison et al 2010

    5

  • An analytic “toy model”

    +⌃p(r, t) Ṁc,p(r, t) ⇡ 2(⌧f/0.1)

    2/3rHvH⌃p ⌧f(r, t)

    

     

    

     

    6

    Birnstiel et al, 2012

    Lambrechts and Johansen, 2014

    6

  • Pebble drift planets

    7

    - start with compact configuration of 4 embryos

    - few Myr in disc with pebble surface density reduced by a factor ~5 with respect to MMSN

    - inside out planet formation

    - pebble flux filtering

    17% for one core and about 50% for a ‘Solar System’

    - mass budget: total mass: ~120-160 Me terrestrial mass: 50 Me/2 (inside the ice line)

    f = Ṁc

    ṀF =

    5

    ⇣ ⌧f 0.1

    ⌘�1/3 ⌘�1

    ⇣rH r

    ⌘2

    ⇡ 0.034 ⇣ ⌧f 0.1

    ⌘�1/3 ✓Mc ME

    ◆2/3 ⇣ r 10AU

    ⌘�1/2

    Lambrechts and Johansen, 2014

    7

  • - overcome type I migration ice giants form ~ in situ -> cross over mass

    - steep initial dust-to-gas ratio dependency

    Characteristics of the model

    8 Bucchave et al, 2012

    For mor

    e tal k by

    Ber t!

    8

  • 9

    Mc

    Menv

    Core growth

    Envelope growth

    Runaway gas accretion

    0.07 g/cm2, r=10 AUp Pebble accretion scenario

    0 2 4 6 8 10 0

    10

    20

    30

    40

    50

    t /Myr

    M /M

    E

    Core accretion with pebbles:

    - rapid formation of the core without enhancements of the solid surface density

    - faster contraction of the gaseous envelope, because of pebble isolation mass

    - particular attention at forming ice giants

    The core accretion scenario with

    peb bles

    9

  • The critical core mass

    10

    - Protoplanetary disc lifetimes constrain accretion rates to be high to complete cores

    - critical core mass increase with accretion rate (Rafikov 2006)

    - The high accretion rates necessary to form the cores lead to core masses much too large compared to the gas giants in the Solar System

    - Therefore halting the accretion is a necessity in the core accretion scenario (or a lot of ice pollution)

    Lambrechts et al 2014

    10

  • The pebble isolation mass

    11

    - gravity of the core perturbs gas disc - creates a pressure bump (shallow gap) that traps particles outside the accretion radius, thereby halting solid accretion - pebble isolation mass ~ critical core mass

    Mc

    M iso

    Menv

    Core growth

    Envelope contraction

    Runaway gas accretion

    p 0.07 g/cm2, r=10 AU Pebble accretion scenario

    0 2 4 0

    10

    20

    30

    40

    50

    t /Myr

    M /M

    E

    M iso

    ⇡ 20 ⇣ r 5AU

    ⌘ 3/4

    M E

    / ✓ H

    r

    ◆3

    11

  • Ice giant / gas giant divide

    Lambrechts et al 2014

    - radial and compositional dichotomy between gas and ice giants

    - gas giants in the inner disc (

  • Exoplanets with envelopes

    13

    H2

    H2O

    SiO2

    10-1 100 101 102 103 104

    100

    101

    M /ME

    R /R E

    Data from open exoplanets catalogue

    13

  • Expanding the scenario

    • full disc models see following talk by Bertram Bitsch

    • terrestrial embryo/planet formation (Guillot+2014, Johansen+2015, Morbidelli+2015, Levison/Kretke group+2015, Lambrechts in prep)

    • (hybrid) N-body codes Kretke & Levison, 2014, Levison+2015 , Chambers, 2014, and above

    • doing the gas envelope contraction carefully Piso & Youdin 2014, Mordasini+a,b 2014, Ormel, 2014

    14

    1. 2. 3. 10-4 ME 0.01-10ME

    Mc

    M iso

    Menv

    Core growth

    Envelope contraction

    Runaway gas accretion

    p 0.07 g/cm2, r=10 AU Pebble accretion scenario

    0 2 4 0

    10

    20

    30

    40

    50

    t /Myr

    M /M

    E

    14

  • Questions?

    15

    Lambrechts & Johansen, 2014 Lambrechts, Johansen, Morbidelli, 2014 Lambrechts & Johansen, 2012 Morbidelli, Lambrechts +, 2015 submitted Bitsch, Lambrechts & Johansen, 2015 submitted

    • formation in a few Myr

    • halting solid accretion (~20 Me) form gas giants and ice giants

    • dust-to-planet efficiency (~50%)

    • metallicity correlation (steep)

    • overcome type I migration

    15