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PLANETARY MIGRATION Review Presented at the Protostars & Planets VI Conference in Heidelberg, September 2013 (Updated)

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PLANETARY MIGRATION Review Presented at the Protostars & Planets VI Conference in Heidelberg, September 2013 (Updated) PLANETARY MIGRATION Review presented at the Protostars & Planets VI conference in Heidelberg, september 2013 (updated). Reference : Baruteau et al. (2014) (arXiv:1312.4293) see also : https://www.youtube.com/watch?v=_HMw4Lh7IOo C. Baruteau, A. Crida, B. Bitsch, J. Guilet, W. Kley, F. Masset, S-J. Paardekooper, R. Nelson, J. Papaloizou INTRODUCTION Planets form in proto-planetary discs. Thus, there must be planet-disc interactions. EvidencesEvidences ofof planet-discplanet-disc interactionsinteractions :: -- hothot JupitersJupiters :: inwardsinwards migrationmigration ?? -- resonantresonant systemssystems :: convergentconvergent migrationmigration ?? -- compact,compact, coplanar,coplanar, low-mass,low-mass, multi-planetmulti-planet systems...systems... IAC winter school 2016 2 / 37 INTRODUCTION The gravity of the planet perturbs the fluid. Spiral pressure wave : the wake, corotating with the planet. Planet on a fixed, circular orbit. White = over density, Dark = under density. Movie by F. Masset IAC winter school 2016 3 / 37 INTRODUCTION Effect of the disc on the planet : Γ Overdensity => Force from the disc => Torque : = dJp / dt 1/2 where Jp=Mp(G M* rp) (orbital angular momentum for a circular orbit, rp=orbital radius) Γ → d rp / dt ~ / Mp The planet feels a force from the disc, its orbit changes. rp This is planetary migration. Rate ? Direction ? What is the value of Γ ? Picture: F. Masset & A. Crida IAC winter school 2016 4 / 37 INTRODUCTION Effects of the planet on the disc : → gap opening ? → cavity opening ? → feedback on migration ? → link with observations ? Picture: F. Masset & A. Crida IAC winter school 2016 5 / 37 TYPE I MIGRATION Γ 2 Σ 4 Ω 2 (Lin & Papaloizou 1980, The torque scales with 0 = (q/h) p rp p Goldreich & Tremaine 1979) q = Mp / M* planet/star mass ratio Σ = gas surface density Ω = angular velocity Ω h = aspect ratio H/r p Xp = X at the planet location. r Σ(MMSN @1AU) => p Σ migration time [years] ≈ 1/q p → 300000 yrs for an Earth , → 20000 yrs for a Neptune ! Picture: F. Masset & A. Crida IAC winter school 2016 : wave torque 7 / 37 TYPE I MIGRATION Γ 2 Σ 4 Ω 2 (Lin & Papaloizou 1980, The torque scales with 0 = (q/h) p rp p Goldreich & Tremaine 1979) The torque due to the wave is, in a 2D adiabatic disc : γΓ Γ β α L / 0 = -2.5 - 1.7 Τ + 0.1 Σ where γ = adiabatic index, Σ ~ r – αΣ , T ~ r – βΤ . (Paardekooper et al. 2010) In general, 0.5<αΣ<1.5 and βΤ≈1 → negative torque, fast inward migration. Picture: F. Masset & A. Crida IAC winter school 2016 : wave torque 8 / 37 TYPE I MIGRATION Around the planetary orbit, the gas corotates with the planet. The streamlines of the velocity field have horseshoe shapes. Picture: C. Baruteau IAC winter school 2016 : corotation torque 9 / 37 TYPE I MIGRATION Around the planetary orbit, the gas corotates with the planet. The streamlines of the velocity field have horseshoe shapes. The torque arising from this «horseshoe region», Γ the corotation torque c, has been widely studied in the last 10 years. Picture: F. Masset IAC winter school 2016 : corotation torque 9 / 37 TYPE I MIGRATION γΓ Γ α ξ/γ ξ β γ α c / 0 = 1.1 ( 3/2 – Σ ) + 7.9 = Τ - ( -1) Σ (Paardekooper et al. 2010) 1st term : barotropic part (e.g.: Ward 1991, Masset 2001, Colder, Paardekooper & Papaloizou 2009) denser plume 2nd term : thermal part, due to the advection of the entropy : ξ = - dlog(entropy) / dlog(r) Hotter, (Paardekooper & Mellema 2008, less Baruteau & Masset 2008) dense plume IAC winter school 2016 : corotation torque 10 / 37 TYPE I MIGRATION γΓ Γ α ξ/γ c / 0 = 1.1 ( 3/2 – Σ ) + 7.9 (Paardekooper et al. 2010) As αΣ < 3/2 and ξ > 0, this torque is generally positive, Γ and can overcome the negative L , → outward migration ! Total torque (assuming γ=1.4) : Γ Γ Γ α β ( L+ c) / 0 = – 0.64 – 2.3 Σ + 2.8 Τ IAC winter school 2016 : total torque 11 / 37 TYPE I MIGRATION γΓ Γ α ξ/γ c,circ,unsaturated / 0 = 1.1 ( 3/2 – Σ ) + 7.9 Γ This is only true on circular orbits. c → 0 for large e . (Bitsch & Kley 2010, Fendyke & Nelson 2013) The corotation torque is γ Γ Γ Γ prone to saturation. ( L+ C,c,u)/ 0 0 The horseshoe region only has Γ / a limited a.m. to exchange. t o Needs to be refreshed, through t Γ Γ γ viscosity, otherwise c → 0 . γ Γ Γ (see Masset & Casoli 2010, L / 0 Paardekooper et al. 2011, 10 – 4 α 10 – 1 Fig: Kley & Nelson 2012, ARAA, 52, 211 ). visc IAC winter school 2016 : total torque 12 / 37 IAC winter IAC total schooltorque 2016 : Planet mass [MEarth] large heatingViscous >< radiative cooling : thus on the disc structure. The total torque depends on β Τ TYPE IMIGRATION , non flared disks, easy outward migration. r [AU] Figurefrom α Σ and Bitsch et al 2013, A&A, 549, A124 549, A&A, Bitsch 2013,al et β Τ , Specific torque 2 Ω 2 [rJup Jup ] 13 / 37 13 IAC winter IAC total schooltorque 2016 : Planet mass [MEarth] smaller Stellar heating irradiation + Viscous >< radiative cooling : thus on the disc structure. The total torque depends on TYPE IMIGRATION β Τ , flared disc, smaller outward migration zone. r [AU] Figurefrom α Σ and Bitsch et al 2013, A&A, 549, A124 549, A&A, Bitsch 2013,al et β Τ , Specific torque 2 Ω 2 [rJup Jup ] 13 / 37 13 TYPE I MIGRATION Conclusion on type I migration : Huge theoretical progresses have been made. Well known The wave torque induces fast inwards migration. The horseshoe drag (mostly its thermal part), NEW! enables outwards migration, but may saturate. Still open Turbulence. Magnetic fields. Amplitude and direction depend on the disc properties... Difficult to provide an a priori, universal scenario. IAC winter school 2016 15 / 37 GAP OPENING The planet exerts also a negative torque on the inner disc → promotes its accretion, a positive torque on the outer disc → repels it away from the star. Competition with pressure y t and viscosity, who tend to i s smooth the gas profile. n e d A gap opens if : Picture: e c W. Kley 1/3 2 a α f P = h/q + 50 /qh < ~1 visc r u (Crida et al. 2006) S α h = 0.05 , visc = 0.004 → gap if q>10-3 . radius IAC winter school 2016 16 / 37 TYPE II MIGRATION Locked inside its gap, the planet must follow the disc accretion onto the star. Migration with viscous time-scale τ 2 ν ν=rp / . (Lin & Papaloizou 1986) Picture: F. Masset & A. Crida IAC winter school 2016 17 / 37 TYPE II MIGRATION Locked inside its gap, the planet must follow the disc accretion onto the star. Migration with viscous time-scale τ 2 ν ν=rp / … as long as the planet is not too massive, otherwise it slows down the disc. In fact, τ τ II = ν disc dominated τ τ II = ν x Mp/Mdisc planet dominated (e.g.: Crida & Morbidelli 2007) Picture: F. Masset & A. Crida IAC winter school 2016 17 / 37 TYPE II MIGRATION Locked inside its gap, the planet must follow the disc accretion onto the star. Migration with viscous time-scale Note : τ 2 ν ν=rp / … This simplified picture is as long as the planet is not too questionned by Dürmann massive, otherwise it slows down & Kley (2015). Some gas the disc. In fact, can cross the gap, and the planets may decouple τ τ II = ν disc dominated from the disc evolution. τ τ Stay tuned... II = ν x Mp/Mdisc planet dominated (e.g.: Crida & Morbidelli 2007) IAC winter school 2016 17 / 37 TYPE I – TYPE II TRANSITION Type I migration can be stopped by the corotation torque up to ~30 MEarth at most. A gap is opened beyond 100 MEarth at least. In between ? Given an accretion rate, and assuming a type I migration rate, one can compute the amount of migration a planet suffers while growing to a gap opening mass. In thin discs with low viscosity, it survives... (Crida & Bitsch 2016) IAC winter school 2016 18 / 37 CAVITY OPENING ? If the planet stops the outer disc, the inner disk still accretes into the star → depletion. Assuming the inner disc disappears, one gets a cavity : nothing in the range 0 < r < ro . Very different from a gap : nothing in ri<r<ro with ro/ri<2 In numerical simulations, there is always gas in the inner disc, and gaps are always narrow. Gas cavities are hard to make ! Picture: F. Masset & A. Crida (Crida 2016, SF2A proceeding) PPVI – Planet-disc interactions: Cavity opening. 19 / 37 OBSERVATIONS Observations of cavities <≠> presence of planet(s) Dust (de)coupled from the gas. Gas 30µm 1mm Accumulates at pressure bumps, ex: outer edge of a gap. (Zhu et al. 2012 ApJ, 455, 6) First observation that really looks like a planetary gap: Debes et al 2013 ApJ 471, 988 -4 x Σ q = 1.18 10 / h = 0.081 Σ δ α -4 visc = 5 x 10 rp = 80 AU PPVI – Planet-disc interactions: Observations. 20 / 37 TYPE III MIGRATION Intermediate mass planets, with a partial gap → positive feedback on s u i the drift of the planet. d a r If the disc is massive enough, runaway of the migration, in either direction : type III migration. π 0 azimuth 2 Planets of Neptune ~Jupiter mass can change their orbit, inwards or outwards, dramatically in a few orbits ! IAC winter school 2016 : type III migration 21 / 37 TYPE III MIGRATION Application: Too massive proto-solar nebula → Jupiter lost.
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