PLANET-DISC INTERACTIONS and EARLY EVOLUTION of PLANETARY SYSTEMS

PLANET-DISC INTERACTIONS and EARLY EVOLUTION of PLANETARY SYSTEMS C. Baruteau, A. Crida, B. Bitsch, J. Guilet, W. Kley, F. Masset, R. Nelson, S-J. Paardekooper, J. Papaloizou

INTRODUCTION Planets form in proto-planetary discs. Thus, there must be planet-disc interactions. Evidences of planet-disc interactions : - hot Jupiters : inwards migration? - resonant systems : convergent migration? - compact, coplanar, low-mass, multi-planet systems... PPVI Planet-disc interactions... 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 PPVI Planet-disc interactions... 3 / 37

INTRODUCTION Effect of the disc on the planet : Overdensity => Force from the disc => Torque : Γ = djp / dt where Jp=Mp(G M* rp)1/2 (orbital angular momentum for a circular orbit, rp=orbital radius) d rp / dt ~ Γ / 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 PPVI Planet-disc interactions... 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 PPVI Planet-disc interactions... 5 / 37

OUTLINE 1) Single planets - Small planets: type I migration, latest news. - Giant planets: type II migration, gap and cavity opening. - Intermediate mass planets: type III migration. 2) Pairs of planets - resonance capture, eccentricity raise. - migration rate, stop type II migration. - Solar System : Grand Tack. 3) Comparison with observations - hot & cold Jupiters. - multi planet systems. - planet population synthesis. PPVI Planet-disc interactions... 6 / 37

TYPE I MIGRATION The torque scales with Γ0 = (q/h)2 Σp rp4 Ωp2 (Lin & Papaloizou 1980, Goldreich & Tremaine 1979) q = Mp / M* planet/star mass ratio Σ = gas surface density Ω = angular velocity Ωp h = aspect ratio H/r Xp = X at the planet location. Σ(MMSN @1AU) => migration time [years] 1/q rp Σp 300000 yrs for an Earth, 20000 yrs for a Neptune! Picture: F. Masset & A. Crida PPVI Planet-disc interactions: type I migration. 7 / 37

TYPE I MIGRATION The torque scales with Γ0 = (q/h)2 Σp rp4 Ωp2 (Lin & Papaloizou 1980, Goldreich & Tremaine 1979) The torque due to the wave is, in a 2D adiabatic disc : γγl / Γ0 = -2.5-1.7βΤ + 0.1αΣ 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. PPVI Planet-disc interactions: the wave torque Picture: F. Masset & A. Crida 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 PPVI Planet-disc interactions: 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», the corotation torque Γc, has been widely studied in the last ~7 years. Picture: F. Masset PPVI Planet-disc interactions: corotation torque. 9 / 37

TYPE I MIGRATION γγc / Γ0 = 1.1 ( 3/2 ασ ) + 7.9 ξ/γ ξ = βτ - (γ-1)ασ (Paardekooper et al. 2010) 1st term : barotropic part (e.g.: Ward 1991, Masset 2001, Paardekooper & Papaloizou 2009) PPVI Planet-disc interactions: corotation torque. 10 / 37

TYPE I MIGRATION γγc / Γ0 = 1.1 ( 3/2 ασ ) + 7.9 ξ/γ ξ = βτ - (γ-1)ασ (Paardekooper et al. 2010) 1st term : barotropic part (e.g.: Ward 1991, Masset 2001, Paardekooper & Papaloizou 2009) 2nd term : thermal part, due to the advection of the entropy : ξ = - dlog(entropy) / dlog(r) (Paardekooper & Mellema 2008, Baruteau & Masset 2008) PPVI Planet-disc interactions: corotation torque. Colder, denser plume Hotter, less dense plume 10 / 37

TYPE I MIGRATION γγc / Γ0 = 1.1 ( 3/2 ασ ) + 7.9 ξ/γ (Paardekooper et al. 2010) As ασ < 3/2 and ξ > 0, this torque is generally positive, and can overcome the negative ΓL, outward migration! Total torque (assuming γ=1.4) : (ΓL+Γc) / Γ0 = 0.64 2.3 ασ + 2.8 βτ PPVI Planet-disc interactions: total torque. 11 / 37

TYPE I MIGRATION γγc,circ,unsaturated / Γ0 = 1.1 ( 3/2 ασ ) + 7.9 ξ/γ This is only true on circular orbits. Γc 0 for large e. (Bitsch & Kley 2010, Fendyke & Nelson 2013) The corotation torque is prone to saturation. (see Masset & Casoli 2010, Paardekooper et al. 2011, Fig: Kley & Nelson 2012, ARAA, 52, 211). PPVI Planet-disc interactions: saturation. γ Γtot / Γ0 The horseshoe region only has a limited a.m. to exchange. Needs to be refreshed, through viscosity, otherwise Γc 0. γ(γl+γc,c,u)/γ0 γ ΓL / Γ0 10 4 αvisc 10 1 12 / 37

TYPE I MIGRATION The total torque depends on ασ and βτ, thus on the disc structure. Specific torque [rjup2 ΩJup2] Planet mass [MEarth] Viscous heating >< radiative cooling : large βτ, non flared disks, easy outward migration. r [AU] See Poster #2B037 Figure from Bitsch et al 2013, A&A, 549, A124 PPVI Planet-disc interactions: type I migration. 13 / 37

TYPE I MIGRATION The total torque depends on ασ and βτ, thus on the disc structure. Specific torque [rjup2 ΩJup2] Planet mass [MEarth] Stellar irradiation + Viscous heating >< radiative cooling : smaller βτ, flared disc, smaller outward migration zone. r [AU] See Poster #2B037 Figure from Bitsch et al 2013, A&A, 549, A124 PPVI Planet-disc interactions: type I migration. 13 / 37

TYPE I MIGRATION What about magnetic fields? MRI turbulence (if it exists!) desaturates the corotation torque (e.g.: Baruteau et al. 2011, Uribe et al. 2011). Random walk on short term only ; Time averaged wave torque unaffected. (Nelson & Papaloizou 2004, Laughlin et al. 2004, Adams & Bloch, 2009, Baruteau & Lin 2010). New component of the corotation torque, even for small field Poster #2G001 (Guilet et al. 2013, instantaneous δσ azimuth Baruteau et al. 2011) radius Strong field : MHD waves instead of corotation torque (Terquem 2003, Fromang et al. 2005). PPVI Planet-disc interactions: magnetic fields. 14 / 37

TYPE I MIGRATION What about magnetic fields? MRI turbulence (if it exists!) desaturates the corotation torque (e.g.: Baruteau et al. 2011, Uribe et al. 2011). Random walk on short term only ; Time averaged wave torque unaffected. (Nelson & Papaloizou 2004, Laughlin et al. 2004, Adams & Bloch, 2009, Baruteau & Lin 2010). New component of the corotation torque, even for small field Poster #2G001 (Guilet et al. 2013, time-averaged δσ azimuth Baruteau et al. 2011) radius Strong field : MHD waves instead of corotation torque (Terquem 2003, Fromang et al. 2005). PPVI Planet-disc interactions: magnetic fields. 14 / 37

TYPE I MIGRATION Conclusion on type I migration : Huge theoretical progresses have been made. Well known NEW! Still open The wave torque induces fast inwards migration. The horseshoe drag (mostly its thermal part), enables outwards migration, but may saturate. Turbulence. Magnetic fields. Amplitude and direction depend on the disc properties... Difficult to provide an a priori, universal scenario. PPVI Planet-disc interactions: Type I migration. 15 / 37

GAP OPENING Competition with pressure and viscosity, who tend to smooth the gas profile. A gap opens if : P = h/q1/3 + 50αvisc/qh2 < ~1 (Crida et al. 2006) Surface density 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. Picture: W. Kley h = 0.05, αvisc = 0.004 gap if q>10-3. radius PPVI Planet-disc interactions: Gap opening. 17 / 37

TYPE II MIGRATION Locked inside its gap, the planet must follow the disc accretion onto the star. Migration with viscous time-scale τν=rp2 / ν. (Lin & Papaloizou 1986) Picture: F. Masset & A. Crida PPVI Planet-disc interactions: type II migration. 18 / 37

TYPE II MIGRATION Locked inside its gap, the planet must follow the disc accretion onto the star. Migration with viscous time-scale τν=rp2 / ν as long as the planet is not too massive, otherwise it slows down the disc. In fact, τii = τν disc dominated τii = τν x Mp/Mdisc planet dominated (e.g.: Crida & Morbidelli 2007) PPVI Planet-disc interactions: type II migration. Picture: F. Masset & A. Crida 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 PPVI Planet-disc interactions: Cavity opening. 19 / 37

OBSERVATIONS Observations of cavities < > presence of planet(s) Dust (de)coupled from the gas. Accumulates at pressure bumps, ex: outer edge of a gap. Poster (Zhu et al. 2012 ApJ, 455, 6 ; Fouchet et al. 2010) Gas 30µm 1mm #2H055 First observation that really looks like a planetary gap: Debes et al. 2013 q = 1.18 x 10-4 h = 0.081 αvisc = 5 x 10-4 rp = 80 AU δσ / Σ ApJ 471, 988 (also Quanz et al. 2013) PPVI Planet-disc interactions: Observations. 20 / 37

TYPE III MIGRATION positive feedback on the drift of the planet. If the disc is massive enough, runaway of the migration, in either direction : type III migration. radius Intermediate mass planets, with a partial gap 0 azimuth 2π Planets of Neptune ~Jupiter mass can change their orbit, inwards or outwards, dramatically in a few orbits! PPVI Planet-disc interactions: type III migration 21 / 37

TYPE III MIGRATION Application: U 12 8 Massive disc (Desch 2007) S J 4 0 N 0 time [year] 104 Semi major axis [AU] Too massive proto-solar nebula Jupiter lost. (Crida 2009, ApJ, 698, 606-614). Minimum Mass 30 Solar Nebula N U (Hayashi 1981) S J 0 PPVI Planet-disc interactions: type III migration??? time [year] 20 10 105 0 22 / 37

See F. Masset 2000a,b COMMERCIAL BREAK Have you always dreamt of making hydrodynamical simulations of planet-disc interactions??? Download FARGO for free from http://fargo.in2p3.fr! Great game for PhD students! (not for children under 36 months) «I used FARGO during my PhD, it was good fun! And the service is amazing.» A. Crida «Its multiple extensions make FARGO a tool of choice for any study.» C. Baruteau

PAIRS OF PLANETS Two planets migrate at a different rate. M2 Their period ratio varies, and crosses simple fractions. (p+q)ω2 pω1 = 0 P2/P1 = (p+q)/p where p,q are integers. a1 ; a 2 If they approach each other slowly enough, they get captured in Mean Motion Resonance : Then, what happens? P2 /P1 Pierens & Nelson 2008, A&A 482, 333-340 2 1.5 PPVI Planet-disc interactions: Capture in resonance. time [year] time 24 / 37

PAIRS OF PLANETS Eccentricities are excited by the resonance forcing, and damped by the gas disc. reach non zero equilibrium value. Ex: reproduction of the observed orbital parameters of the GJ876 system (Lee & Peale 2002, Kley et al. 2005, Figure from: Crida et al. 2008, A&A 483, 325-327). PPVI Planet-disc interactions: Eccentricity excitation. 25 / 37

PAIRS OF PLANETS Eccentricities are excited by the resonance forcing, and damped by the gas disc. reach non zero equilibrium value. Possibility of close encounters, in particular if 3 planets. Then, scattering and e and i increase. (Marzari et al. 2010, Juric & Tremaine 2008, Chatterjee et al. 2008, Lega et al. 2013) But the disc damps e and i of an isolated planet. (Xiang-Gruess & Papaloizou 2013, Bitsch et al. 2013) Poster #2H015 Scattering should take place as the disc dissipates in order to explain the observed high e of exoplanets. Unikely fine tuning of the timing (Lega et al. 2013). PPVI Planet-disc interactions: Scattering. 26 / 37

PAIRS OF PLANETS Migration scheme changes if the two planets open a common gap. Standard type II : inner disc outer disc Common gap + resonance locking case : inner disc outer disc M2<M1 => smaller negative torque from outer disk than positive torque from inner disc (Masset & Snellgrove 2001). The pair goes outwards, even if the disc goes inwards. PPVI Planet-disc interactions: Outward migration. 27 / 37

PAIRS OF PLANETS Jupiter migrates in type II. Saturn enters type III. Capture in 3:2 MMR, then outwards migration. (Morbidelli & Crida 2007, Pierens & Nelson 2008, Walsh et al. 2011, Pierens & Raymond 2011). Semi major axis [AU] Application to the Jupiter-Saturn case : the Grand Tack model (See S. Raymond's talk.) PPVI Planet-disc interactions: Solar System Image courtesy: K. Walsh time 28 / 37

EXO-PLANETS Planet mass [Mjup] 10 1 0.1 0.01 0.01 0.1 1 10 Semi major axis [AU] PPVI Planet-disc interactions : Exoplanets. 100 30 / 37

HOT JUPITERS Local formation is impossible (for 99% of the theorists). Giant planets should form beyond the ice line. Many hot Jupiters are on eccentric or inclined orbits. only scattering or Kozai pumping + more or less tidal cirularization / alignment? (Albrecht et al. 2012, Triaud et al. 2010) No more type II migration??? Wait... a) Scattering is induced by convergent migration. b) Tidal realignment without infalling into the star => as many aligned prograde as retrograde orbits (Rogers & Lin 2013). Not observed. PPVI Planet-disc interactions : Hot Jupiters. 31 / 37

HOT JUPITERS c) The past midplane of the proto-planetary disc could be misaligned with the present stellar equator (ex: Bate et al. 2010, Batygin 2012). delivery of misaligned hot Jupiters by type II migration. Many warm giant planets on circular, coplanar, prograde orbits, very compatible with type II migration, even at P>6-10 days, where stellar tides are inefficient. For them, type II migration is a natural mechanism. Why not also for the circular, coplanar, prograde hot Jupiters? Eccentricitic exo-planets: probably planet-planet interactions. PPVI Planet-disc interactions : Hot Jupiters. 32 / 37

COLD JUPITERS Giant planets have been seen at few dozens of AUs from their star (e.g. Marois et al. 2010, Nature, 468, 1080). HR8799 PPVI Planet-disc interactions : Cold Jupiters. 33 / 37

COLD JUPITERS Giant planets have been seen at few dozens of AUs from their star (e.g. Marois et al. 2010, Nature, 468, 1080). Local formation by gravitational instability? Possible, but fast migration of the clumps... Outward migration of a planet pair may go far, under specific conditions. Scattering (after convergent migration). Semi major axis [AU] (Voroboyov & Basu 2010, Baruteau et al. 2011, Zhu et al. 2011) HR8799 PPVI Planet-disc interactions : Cold Jupiters. 80 60 40 (Fig: Crida et al. 2009 ApJL, 705, 148) 20 0 0 time [years] 6x105 33 / 37

SYSTEMS Resonant systems smoking gun of convergent migration! Coplanar, multi-resonant systems (Kepler 50, 55...) : even better. PPVI Planet-disc interactions : Systems. 34 / 37

SYSTEMS Resonant systems smoking gun of convergent migration! Coplanar, multi-resonant systems (Kepler 50, 55...) : even better. But there are non resonant, or close to resonant systems... Does migration fail? No. Resonances can be broken after the disc dissipates (stellar tides) or due to planet-disc interactions: - stochastic torques due to turbulence (Rein 2012, Pierens et al. 2012) - interaction between a planet and the wake of a companion (Podlewska-Gaca et al. 12, Baruteau & Papaloizou '13) Figures from our coming chapter in PPVI. PPVI Planet-disc interactions : Systems. 34 / 37

SYNTHESIS Any statistic relies on the distribution of the parameters. Planet Population Synthesis (see next talk...) Past results concerning migration: - only wave torque loss of all planets. - need of a small cavity to stop type II migration of hot Jupiters. Possible improvements of the models: - Effects of the corotation torque (implemented). - Planet-planet interactions during migration (in progress). - Disc structure and evolution. PPVI Planet-disc interactions : Synthesis. 35 / 37

THE FUTURE Theory of Migration : - role of magnetic fields - effect of turbulence Disc properties : - Turbulence : which nature, which properties? - Density and temperature profiles ALMA, ALMA, ALMA, AL Observations : - Disc structures: decouple gas and dust. - Exo-planets statistics: understand the observed distribution. PPVI Planet-disc interactions... 36 / 37

CONCLUSION Planets do migrate. It's a fact. Gap Cavity Type I migration (small mass planets) : Can be outwards, depends on the disc's local properties ασ, βτ, γ, ν, h. Migration = a key ingredient of planet formation and evolution. resonant or not systems hot Jupiters (not all of them) possibly cold Jupiters Not all structures are created by 1 planet. PPVI Planet-disc interactions... 37 / 37

PLANET-DISC INTERACTIONS and EARLY EVOLUTION of PLANETARY SYSTEMS C. Baruteau (P.I.), A. Crida (speaker), B. Bitsch, J. Guilet, W. Kley, F. Masset, R. Nelson, S-J. Paardekooper, J. Papaloizou