. (Lund University) with Michiel Lambrechts, Katrin Ros, Andrew Youdin, Yoram Lithwick From Atoms to Pebbles Herschel s View of Star and Planet Formation Grenoble, March 2012 1 / 11
Overview of topics Size and time Dust µ m Pebbles cm Planetesimals 10 1,000 km Planets 10,000 km 1 From dust to pebbles by ice condensation Ros & Johansen (in preparation); poster by Katrin Ros 2 From pebbles to planetesimals by streaming instabilities Johansen, Youdin, & Lithwick (2012) 3 From planetesimals to gas-giant cores by pebble accretion Lambrechts & Johansen (submitted); poster by Michiel Lambrechts 2 / 11
Classical core accretion scenario 1 Dust grains and ice particles collide to form km-scale planetesimals 2 Large protoplanet grows by run-away accretion of planetesimals 3 Protoplanet attracts hydrostatic gas envelope 4 Run-away gas accretion as M env M core 5 Form gas giant with M core 10M and M atm M Jup 3 / 11
Planetesimal accretion Planetesimals passing within the Hill sphere get significantly scattered by the protoplanet The size of the protoplanet relative to the Hill sphere is ( α Rp r ) 1 1 R H 5 AU Rate of planetesimal accretion Ṁ = πr 2 pf H Without gravitational focusing Ṁ = α 2 R 2 HF H With gravitational focusing Ṁ = αr 2 HF H Planet Gravitational cross section Hill sphere 4 / 11
Core formation time-scales The size of the protoplanet relative to the Hill sphere: R ( p r ) 1 α 1 R H 5 AU Maximal growth rate Ṁ = αr 2 HF H Only 0.1% (0.01%) of planetesimals entering the Hill sphere are accreted at 5 AU (50 AU) Time to grow to 10 M is 10 Myr at 5 AU 50 Myr at 10 AU 5,000 Myr at 50 AU 5 / 11
Directly imaged exoplanets (Marois et al. 2008; 2010) (Kalas et al. 2008) HR 8799 (4 planets at 14.5, 24, 38, 68 AU) Fomalhaut (1 planet at 113 AU) No way to form the cores of these planets within the life-time of the protoplanetary gas disc by standard core accretion 6 / 11
Pebble accretion Most planetesimals are simply scattered by the protoplanet Planetesimal is scattered by protoplanet Pebbles spiral in towards the protoplanet due to gas friction Pebble spirals towards protoplanet due to gas friction Pebbles are accreted from the entire Hill sphere Growth rate by planetesimal accretion is Ṁ = αr 2 HF H Growth rate by pebble accretion is Ṁ = R 2 HF H 7 / 11
0 Time-scale of pebble accretion 5.0 Σ p/<σp> 0.0 z/h t=0.0 Ω 1 t=120 Ω 1 t=131 Ω 1 t=134 Ω 1 M c /M 10 1 10 0 10 1 10 2 10 3 10 4 10 5 Pluto Ceres =, Z=0.01 Hill Drift PA 0.5AU 5.0AU 5.0AU 0.5AU 50AU 50AU 5.0AU 5.0AU 50AU 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 t/yr Pebble accretion speeds up core formation by a factor 1,000 at 5 AU and a factor 10,000 at 50 AU (Lambrechts & Johansen, submitted to A&A; see also Ormel & Klahr 2010) Cores form well within the life-time of the protoplanetary gas disc, even at large orbital distances But requires large planetesimals to begin with... 8 / 11
Formation of large planetesimals Streaming instabilities lead to concentration of cm-sized pebbles (Johansen & Youdin 2007; Bai & Stone 2010) Planetesimals with d 1000 km form by gravitational collapse Asteroids born big? (Morbidelli et al. 2009) 128 3 20.0 Σ p/<σ p> 0.0 t=120.4 N=13 M bound= 1.34 M 1= 0.44 M 2= 0.19 M 13= 61 N=7 M bound= 1.35 M 1= 0.59 M 2= 0.49 M 7= 0.020 t=130.4 N=7 M bound= 1.35 M 1= 0.95 M 2= 0.16 M 7= 0.029 N=3 M bound= 1.47 M 1= 0.75 M 2= 0.70 M 3= 0.014 t=140.4 No collisions Collisions with shear ε=0.3 Scaling to Kuiper belt gives twice as large planetesimals (Johansen, Youdin, & Lithwick 2012) Explains why Kuiper belt objects are larger than asteroids Largest planetesimals can grow to cores by pebble accretion N=9 M bound= 1.42 M 1= 0.45 M 2= 0.33 M 9= 0.012 N=7 M bound= 1.37 M 1= 0.54 M 2= 0.31 M 7= 52 N=6 M bound= 1.46 M 1= 0.63 M 2= 0.59 M 6= 0.021 N=3 M bound= 1.44 M 1= 0.63 M 2= 0.59 M 3= 0.22 Collisions without shear ε=0.3 Collisions with shear ε=1.0 9 / 11
Formation of icy pebbles Pebbles are observed in abundance in nearby protoplanetary discs (e.g. Testi et al. 2003; Wilner et al. 2005) How do pebbles form so efficiently? Near ice lines pebbles can form like hail stones Efficient formation of cm-dm sized icy pebbles near ice lines (Ros & Johansen, in preparation; poster by Katrin Ros) 10 / 11
Summary of talk Dust Pebbles Planetesimals Ice condensation Gravitational instability Pebble accretion Cores 1 Ice condensation leads to efficient formation of pebbles near ice lines (Ros & Johansen, in preparation; poster by Katrin Ros) 2 Streaming instabilities form large planetesimals ( Ceres or Pluto) (Johansen, Youdin, & Lithwick 2012) 3 Large planetesimals grow rapidly by pebble accretion, explaining the giants of the solar system as well as gas giants in wide orbits (Lambrechts & Johansen, submitted; poster by Michiel Lambrechts) Icy pebbles may play important role in planet formation Planet formation can be probed and constrained through observations of water vapour and pebbles 11 / 11