Evolution of protoplanetary discs

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1 Evolution of protoplanetary discs and why it is important for planet formation Bertram Bitsch Lund Observatory April 2015 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

2 Observations of planets How can we explain this diversity? Data from exoplanet.org Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

3 Outline Introduction Protoplanetary disc structure Planet growth and migration Planet formation in evolving protoplanetary discs Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

4 Planetary system evolution (a) Collapse of interstellar cloud (b) Formation of protostar with protoplanetary disc made out of dust and gas (c) Small particles stick and form bigger objects (c)-(e) Formation of planetesimals and planetary embryos (f) Formation of planets, clearing of gas in disc in 10 Myr Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

5 Protoplanetary discs in the Orion Nebula Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

6 Observations of protoplanetary discs Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

7 Composition of the disc The inner regions of the disc are hotter than the outer regions: Icy particles only in the outer parts of the disc! Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

8 The four steps of planet formation 1 Dust to pebbles µm dm: contact forces during collision lead to sticking 2 Pebbles to planetesimals dm km: gravitational collapse of pebble clouds form planetesimals 3 Planetesimals to protoplanets km 1,000 km: gravity (run-away accretion) 4 Protoplanets to planets Gas giants: 10 M core accretes gas (< 10 7 years) Terrestrial planets: protoplanets collide ( years) Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

9 Time-scale to build gas giants Mamajek (2009) Giant planet formation has to happen within the disc s lifetime of a few Myr! Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

10 Important quantities in the disc Temperature T Viscosity ν = αh 2 Ω K with: H is the thickness of the disc Ω K is the Keplerian frequency, Ω K = GM /r 3 α Gas density ρ g and gas surface density Σ g : Σ g = ρ g H 2π z in [a Jup ] r [a Jup ] 7e-11 6e-11 5e-11 4e-11 3e-11 2e-11 1e-11 ρ in g/cm 3 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

11 Importance of the disc structure Growth and formation of planets relies on the disc structure: Growth of dust particles to pebbles (Zsom et al., 2010; Birnstiel et al., 2012) Movements of pebbles inside the gas disc (Brauer et al., 2008) Formation of planetesimals via streaming instability (Johansen & Youdin, 2007) Formation of planetary cores from embryos and planetesimals (Levison et al., 2010) or pebble accretion (Lambrechts & Johansen, 2012) Migration of planetary cores in the disc (Ward, 1997; Paardekooper & Mellema, 2006; Kley et al., 2009) Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

12 Radial drift of dust particles v Kep (1 η) F G F P Disc is hotter and denser close to the star Radial pressure gradient force mimics decreased gravity gas orbits slower than Keplerian: η = 1 ( ) 2 H ln(p) 2 r ln(r) Particles do not feel the pressure gradient force and want to orbit Keplerian Headwind from sub-keplerian gas drains angular momentum from particles, so they spiral in through the disc Particles sublimate when reaching higher temperatures close to the star Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

13 Streaming instability: planetesimal formation Gas orbits slightly slower than Keplerian Particles lose angular momentum due to headwind Particle clumps locally reduce headwind and are fed by isolated particles v Kep (1 η) F G F P Streaming instabilities feed on velocity difference between two components (gas and particles) at the same location Interested in details of the S.I.? Ask Anders Johansen or Chao-Chin Yang! Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

14 Streaming instability: lots of literature! This is just a tiny example of literature to the streaming instabilty! Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

15 Streaming instability: a movie (Johansen et al. 2011) Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

16 Protoplanetary disc structure Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

17 The Minimum Mass Solar Nebula - MMSN Spread appropriate mass of solids around the orbit of each planet in the solar system and multiply by 100 (add gas) Power law through data (Hayashi (1981), Weidenschilling (1977)): ( r ) 3/2 Σ g (r) = 1700 g/cm 2 1AU The planets accreted all solids (hence Minimum ) The planets formed on their present orbits and did not move Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

18 Constraints from Observations Σ R γ with γ = Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

19 Time evolution of the star and the disc Accretion rate Ṁ ( Σ g ) changes with time (Hartmann et al., 1998) Accretion rate changes by a factor of 100 in 5Myr! Star changes luminosity in time (Baraffe et al., 1998) Stellar luminosity changes by a factor of 3 in 5Myr! 2 LṀ L in L Ṁ in M /yr t in Myr The disc is subject to massive changes in its lifetime! Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

20 Disc Model 2D hydrodynamical disc model with viscous heating, radiative cooling and stellar irradiation with S L : z in [a Jup ] r [a Jup ] log ( ρ in g/cm 3 ) Bitsch et al., 2013 Mass flux through disc: Ṁ constant at each r with α viscosity: Ṁ = 3πνΣ = 3παH 2 Ω K Σ Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

21 Influence of opacity on cooling Cooling of the disc: F = λc ρκ R E R Grey area marks transition in opacity at the ice line Change of opacity: change of cooling Change of cooling: change in T (r) log (κ in cm 2 /g) T in K Transition κ R = κ P κ* T in K Transition Ṁ = M /yr MMSN r [AU] Bitsch et al., 2015 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

22 Influence of viscosity and Ṁ 0.08 Hydrostatic equilibrium: T = ( ) H 2 GM µ r r R bump in T : bump in H/r Ṁ disc: Ṁ = 3πνΣ = 3παH 2 Ω K Σ Ṁ constant at each r: dip in Σ Σ in g/cm 2 H/r Ṁ = M /yr MMSN Ṁ = M /yr MMSN r [AU] Bitsch et al., 2015 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

23 Importance for the streaming instability Streaming instabilities feed on velocity difference between two components (gas and particles) at the same location, caused by a reduction of the effective gravitational force by the radially outwards pointing force of the radial pressure gradient: H/r Ṁ = M /yr MMSN = η v K = 1 H ln(p) c s 2 r ln(r) Reduced helps the formation of large clumps via streaming instability (Bai & Stone, 2010b) Ṁ = M /yr MMSN r [AU] Bitsch et al., 2015 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

24 Change of Ṁ in time T in K Transition Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = H/r r [AU] Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = Ṁ decreases with decreasing Σ Ṁ = 3πνΣ = 3παH 2 Ω K Σ Inner disc dominated by viscous heating for high Ṁ, dominated by stellar heating for low Ṁ ΣG in g/cm Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = r [AU] Bitsch et al., 2015 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

25 Time evolution of the disc Evolution in time follows Hartmann et al equation: ( ) ( Ṁ tdisc ) yr log = log M /yr 10 6 yr. T in K Transition Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = Ṁ = r [AU] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

26 Planet growth and migration Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

27 Pebble accretion Small pebbles (τ f < 1) can be easily accreted by planetesimals (Lambrechts & Johansen, 2012) Stokes number τ f and friction time t f : τ f = t f Ω K = ρ R Ω K = ρ R ρ G c s ρ G H Pebbles are weakly enough bound to the gas to feel the gravitational pull from the core, but strongly enough to deposit their kinetic energy through drag forces, when passing the core. Lambrechts & Johansen, 2012 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

28 Scaling of pebble accretion Core growth via pebbles (Lambrechts & Johansen, 2014): ( τf ) 2/3 Ṁ c = 2 rh v H Σ Peb 0.1 Growth faster in inner regions of the disc Red dots mark pebble isolation mass: Pebble accretion does not continue forever! Lambrechts & Johansen, 2014 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

29 Pebble isolation mass Pebble isolation mass: ( ) H/r 3 M iso = 20 M Earth 0.05 After pebble isolation mass is reached, gas accretion can start! Lambrechts et al., 2014 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

30 Gas accretion M c M env M tot M [M E ] t [yr] Phase 1: accretion of solid core until pebble isolation ( yr) Phase 2: envelope contraction ( yr, following Piso & Youdin, 2014), when M c > M env Phase 3: rapid accretion of gas onto core when M c < M env (Machida et al. 2010) Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

31 Planets in discs Planet embedded in a disc creates a wake Wake directed forwards in inner disc and backwards in outer disc Planet pushes inner (outer) disc inwards (outwards), inner (outer) disc pushes planet outwards (inwards) Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

32 Type-II-migration High mass planets (M P > M Jup ) open gaps in discs (Crida et al. 2007): P = h/q 1/3 + 50α/qh 2 < 1 with h = H/r Planet is locked in the disc Planet moves with disc on accretion timescale : τ ν = rp/ν 2 (up to a few Myrs) It is called Type-II-migration Σ in g/cm initial 200 Orbits r [a Jup ] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

33 Type-I-migration Planet fully embedded in the disc, free to migrate with respect to the gas Waves carry energy and angular momentum Torque calculated through Lindblad Resonances (e.g. Goldreich & Tremaine, 1980) ILR: positive torque, OLR: negative torque OLR stronger than ILR: inward migration (ȧ q) Σ in g/cm initial 200 Orbits r [a Jup ] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

34 Migration map Paardekooper et al. (2011): Analytic torque estimate of embedded low mass planets using gradients in the disc (Σ r α Σ; T r β T) ( q ) 2 γγ tot /Γ 0 = α Σ β T Γ 0 = ΣP r 4 h PΩ 2 K Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

35 Planet formation in evolving protoplanetary discs Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

36 Evolution track starting at t 0 = 2 Myr M [M E ] r 0 = 4 AU r 0 = 10 AU r = 20 AU r 0 = 30 AU r 0 = 40 AU t D =3.0Myr r [AU] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

37 Planet formation at all orbital distances r 0 at t 0 = 2 Myr M core M env M tot r f r M [M E ] r f [AU] r 0 [AU] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

38 t Planet disc = 3.0Myr formation at all orbital distances r 0 at t 0 = 2 Myr H/r t disc = 2.0Myr r [AU] M core M env M tot r f r M [M E ] r f [AU] r 0 [AU] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

39 Planet formation in evolving disc Everything below blue line: pebble isolation reached Everything above white line: M core > M env 3.0x x t 0 [yr] 2.0x x M P in M E 1.0x x r 0 [AU] Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

40 Power law disc: MMSN 3.0x x x t 0 [yr] 1.5x M P in M E 1.0x x r 0 [AU] 0.1 Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

41 Schematic view of planet formation Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41

42 Summary Protoplanetary discs evolve in time and change their properties (Σ, T, H), which matters for all processes inside the disc! Resulting planetary systems depend crucially on the underlying disc structure Early planet formation produces mainly gas giants Giant planets form far out in the disc: no in-situ formation Smaller planets can form in-situ, but form late Late formation scenario preferred: larger diversity of planetary types as predicted by observations Bertram Bitsch (Lund) Evolution of protoplanetary discs April / 41