planetary migration - a review richard nelson queen mary, university of london collaborators: paul...

Planetary migration - a review

Richard NelsonQueen Mary, University of London

Collaborators: Paul Cresswell (QMUL),Martyn Fogg (QMUL), Arnaud Pierens QMUL), Sebastien

Fromang (CEA), John Papaloizou (DAMTP)

Talk Outline • Type I migration in laminar discs• The role of corotation torques(non linear effects; planet traps; non isothermal effects)

• Multiple low mass planets • Protoplanets in turbulent discs:

Low mass planets Planetesimals

High mass planets

• Terrestrial planet formation during/after giant planet migration

• Conclusions and future directions

Low mass planets - type I migration

• Planet generates spiral waves in disc at Lindblad resonances

• Gravitational interaction between planet and spiral wakes causes exchange of angular momentum

• Wake in outer disc is dominant (pressure support shifts resonant locations) - drives inward migration

• Corotation torque generated by material in horseshoe region- exerts positive torque, but weaker thanLindblad torques

• Migration time scale ~ 70,000 yr for mp=10 Mearth

• Giant planet formation time 1 Myr

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Pollack et al. (1996)

Tanaka, Takeuchi & Ward (2002)• Low mass protoplanets migrate rapidly < 105 yr• Gas accretion onto solid core requires > 1 Myr - Difficult to form gas giant planets - Reducing dust opacity speeds up gas accretion but migration is always more rapid (e.g. Papaloizou & Nelson 2005, Lissauer et al 2006)

Evidence for type I migration• Short-period low mass planets:

20 planets with m sini < 40 Mearth

(e.g. HD69830 Lovis et al 2006, Gl581 Udry et al 2007, GJ436 Butler et al 2005)- but 45 candidates…

• Disc models agree T > 1500 K within 0.1AU- dust sublimates

• Mass of solids inside 1 AU~ 5 Earth masses for MMSN

• Type I migration does occur !- but probably more slowly than predicted by basic theory

…….10 Earth mass…….

Stopping/slowing type I migration• MHD Turbulence (see later)

• Planet-planet scattering (Cresswell & Nelson 2006) - migration stops if e > H/r

• Corotation torques may slow/stop planetmigration (Masset et al 2006)

• Planet enters cavity due to transition from ‘dead-zone’ to ‘live zone’ - planet trap (Masset et al. 2005)

• Corotation torque in optically thick discs(Pardekooper & Mellema 2007)

• Strong magnetic field (Terquem 2002; Fromang, Terquem & Nelson 2005)

• Opacity variations: sharp transition in density and temperature (Menou & Goodman 2002)

• Eccentric disks (Papaloizou 2002)

Can corotation torques slow type I migration ?

(Masset, D’Angelo & Kley 2006)

Basic idea - corotation region widens with planet mass and can boost corotation torqueFor = const. corotation torque can cause migration reversal for mp>10 ME

3D simulations with evolving planets

= constantH/r=0.05=0.005

= constantH/r=0.05=0.0

Questions: Dead-zones ? Does corotation torque operate in turbulent disc ?

m=10 Mearth

m=20 Mearth

m=30 Mearth

m=10 Mearth

m=20 Mearth

m=30 Mearth

Viscous discs Inviscid discs

Surface density transitions as planet traps

• Regions where surface density gradient is positive cause strongpositive corotation torque(Masset, Morbidelli & Crida 2005)

• Planets migrate into planet trapand migration is halted

Planet stops here

Gap formation by giant planet formsplanet trap for mp < 30 Mearth

Very low mass planets cannot formmean motion resonances withinterior giants (Pierens & Nelson 2008)

Corotation torques in optically thick discs

• Corotation torque can exceed Lindblad torques in optically thick discs(Paardekooper & Mellema 2007; Baruteau & Masset 2008; Pardekooper & Papaloizou 2008)

• Effect is due to warm gas being advected from inside to outside orbit of planet- and vice versa

• Pressure equilibrium leads to modification of density structure in horseshoe region

• High density region leads planet, low density region trails it - net positive torque - which saturates

Models with viscous heating and radiative cooling showsustained outward migration (Kley & Crida 2008)

Thermal time scale ~ horseshoe libration time scale

Now have a problem of rapid outward type I migration…

Low mass planetary swarms• Consider swarm consisting of

between 5 - 20 low mass interacting planets

• Question: can interaction within swarm maintain eccentric population and prevent type I migration ?

• Answer: No !• Outcomes:

Initial burst of gravitational scatteringCollisons (~ 1 per run)“Stacked” mean motion resonancesInward migration in lockstepExotic planet configurations:Horseshoe and tadpole systems(sometimes in MMR with each other)

Coorbital planets stable even duringsignificant mass growth - giant coorbital planets canremain stable(Cresswell &Nelson 2008) .

May be detected byCOROT, KEPLER,or RV surveys

High mass protoplanets• When planets grow to ~ Jovian mass they open gaps:

(i) The waves they excite become shock waves when RHill > H

(ii) Planet tidal torques exceed viscous torques

• Inward migration occurs on viscous evolution time scale of the disk





• Inward migration occurs on time scale of ~ few x 105 year • Jovian mass planets remain on ~ circular orbits• Heavier planets migrate more slowly than viscous rate due to their inertia• A 1 MJ planet accretes additional 2 – 3 MJ during migration time of ~ few x 105 yr

Eccentricity Evolution• Disc interaction can cause both

growth and damping of e due tointeraction at ELRs, CRs, and COLRs

• For Mp > 5 MJup can get disc eccentricity growth- planet eccentricity growth ?(Kley & Dirksen 2005)

• Most simulations show e dampingfor Jovian mass planets- but D’Angelo et al (2006) findmost e growth

• Origin of exoplanet eccentricities:planet-planet scattering ?(Rasio & Ford; Papaloizou & Terquem 2003; Laughlin & Adams 2004; Juric & Tremaine 2007)

Evidence for type II migration

• Existence of short period planets (Hot Jupiters)

• Resonant multiplanet systems: GJ876 – 2:1 HD82943 – 2:1 55 Cnc – 3:1 HD73526 - 2:1 HD128311 - 2:1

Planets in turbulent discs

0/ <Ω dRd

• Magnetorotational instability vigorous turbulence in discs (Balbus & Hawley 1991; Hawley, Gammie & Balbus 1996, etc…)

• Necessary ingredients: (i) Weak magnetic field (ii) (iii) Sufficient ionisation: X(e-) ~ 10-12

(iv) Rem > 100

Dust free disc ~ 50 % of matter turbulent Dusty disc ~ 1 % of matter turbulent

Ilgner & Nelson (2006a,b,c)

Obtain a basic core-halo structure:Dense MRI-unstable disc near midplane, surrounded by magneticallydominant corona (see also Miller & Stone 2000)

Stratified disc models• H/R=0.07 and H/R=0.1 discs computed

• Locally isothermal equation of state• ~ 9 vertical scale heights

πφ

4BB

mrT = φδρδ vvT rR .=

=

PTT mR−=

Stratified global model

H/R=0.1, mp=10 mearth

Nr x N x N = 464 x 280 x 1200

Local view – turbulent fluctuations ≥ spiral wakes



• Planet in laminar disc shows expected inward migration

• Planet in turbulent discundergoes stochastic migration

T ~ 20 x type I torque for mp=10 Earth mass ttype 1 ~ 400 tcorr

T ~ 200 x type I torque for mp=20 Earth massttype 1 ~ 40,000 tcorr

Run times currently achievable ~ 200 orbits

tTT

+>=<

Can treat stochastic migration asa signal to noise problem(assume linear superposition oftype I + stochastic torques)

Calculate time scale over whichtype I torque dominates random walk

Results show exampleswhere stochastic torques (and migration)contain long-termsignal…

This is apparently due to persistent featuresdeveloping in the flow(transient and looselydefined vortices)

This example:mp=1 EarthH/R=0.1

This example:mp=10 EarthH/R=0.07

Planetesimals in stratified, turbulent discs

• Gas in pressure supported disc orbits with sub-Keplerian velocity• Solid bodies orbit with Keplerian velocity Planetesimals experience head wind (Weidenschilling 1977) • Gas drag induces inward drift & efficient eccentricity damping

Consider evolution of 1m, 10m, 100m and 1km planetesimalssubject to gas drag and stochastic gravitational forcing

Aim: Calculate velocity dispersion assuming bodies orbit at ~ 5 AU

For runaway growth require planetesimal velocity dispersionto be much smaller than escape velocity from largest accretingobjects:

For 10 km sized bodies with ρ=2 g/cm3 escape velocity=10 m/s

Collisional break-up occurs for impact velocities 15 - 30 m/sfor bodies in size range 100m - 1km (Benz & Asphaug 1999)

1m-sized bodies stronglycoupled to gas.Velocity dispersion ~ turbulent velocities

10m bodies have<v> ~ few x 10 m/s - gas drag efficient atdamping random velocities

100m - 1km sizedbodies excited by turbulent density fluctuations<v> ~ 50-100 m/s

Larger planetesimals prevented from undergoing runaway growthPlanetesimal-planetesimal collisions likely to lead to break-up

Need dead-zones to form planets rapidly ? Or leap-frog this phase with gravitational instability ? Or can a relatively small number of bodies avoid catastrophic collisions and grow ?

High mass planets in turbulent discs

• mp=30 mearth accretes gas andforms gap

• Migrates inward on viscous time scale ~ 105 yr

• Gas accretion rate enhanced due to magnetic torques

Terrestrial Planet Formation During Giant

Planet Migration• N-body simulations performed (Fogg & Nelson 2005, 2006, 2007)

• Initial conditions: inner disk of planetesimals+protoplanets undergoing different stages of `oligarchic growth’ within a viscously evolving gas disc

• Giant planet is introduced which migrates through inner planet-forming disc

• General outcomes:(i) massive terrestrial planets can form interior to migrating giant(ii) significant outer disk forms from scattered planetesimals and embryos(iii) water-rich terrestrial planets can form in outer disc

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Continued accretion in the scattered disk. Initial condition.

Continued accretion in the scattered disk. t + 1 Myr.

Continued accretion in the scattered disk. t + 6 Myr.

Compositional Mixing. Before.

Compositional Mixing. After.

Ocean PlanetsOcean Planetspredictedpredicted

A case where an inner super-earth forms…

Conclusions and Future Directions

• Low mass planets migrate rapidly in laminar discs- but this remains an active research area

• Multiple low mass planet systems display:inward resonant migration, horseshoe and trojan systems - observable by COROT or KEPLER ?

• Turbulence modifies type I migration and may prevent large-scale inward migration for some planets

• Turbulence increases velocity dispersion of planetesimals and may lead to destructive collisions and quenching of runaway growth

• Stochastic forces experienced by planets in vertically stratified discs lower in amplitude due to finite disc thickness - work in progress

• Water-rich terrestrial planets probably form in “hot Jupiter” systems

GJ876: Already known to have 2 planets in 2:1 resonance Velocity residuals showed periodic variation - 3rd planet with mass ~ 7.5 Earth masses

Gl436 - 22 Earth mass transiting planet lightcurve suggests it is just like Neptune & Uranus

Gl581 - Short-period 5 Earth mass planet detected by radial velocity

System Age = 1.5 Myr:

t = 80,000 years

t = 20,000 years

154,700 years

Power spectrum – shows torques have temporal variations ~ run time of simulations

Stochastic torques may overcome type I torques over significant time scales for some planetsRequire longer simulations…

Torque distributions σ

tTT

+>=<

Naïve application suggests inward migration should be obtained for mp=10

Planetesimals in laminar discs• Gas in pressure supported

disc orbits with sub-Keplerian velocity• Solid bodies orbit with Keplerian velocity Planetesimals experience head wind (Weidenschilling 1977) • Gas drag induces inward drift & efficient eccentricity damping

Planetesimals in turbulent discs

• Evolution of 100 - 1000 planetesimals calculated to examine inward drift and velocity dispersion

• Planetesimal treated as particlesthat experience gas drag and gravitational force due to disc andcentral star

• Sizes: 1m – 1km

1 metre sized planetesimals

1 metre sized objects migrate inward within ~ 30 orbits (300 years)1m sized boulders become trapped in long-lived vortices - about 50% of particles trappedTight coupling to gas causes large eccentricities – potentially destructivevelocity dispersion ?Neighbouring planetesimals appear to be on very similar orbits

Mp = 10 Earth masses

Mp = 1 Earth mass


• Most 10 m size boulders drift inward on time scale of ~ few thousand years – a few drift in more slowly• Velocity dispersion remains quite small – coupling too weak to allow individual fluctuations in gas velocity to determine velocity dispersion • Danger of destructive collisions: e=0.01 <v> ~ 0.12 km/s at 5 AU• Icy 10 m sized bodies fragment with <v> ~ 20 m/s (Benz & Asphaug 1999)

1 km sized planetesimals

• Results similar to 100 metre sized objects

• Large velocity dispersion prevents runaway growth of planetesimals to form planetary embryos

Stopping type II migration

• Fortuitous disk removal – form planets late on ?

• Overlap gaps of ‘Jupiter’ and ‘Saturn’ ?• Roche lobe overflow – only works close-in• Magnetospheric cavity – only works close-in• Switch viscosity off ? – difficult to explain observed distribution of exoplanets – or observed accretion rates onto T Tauri stars

Planets in turbulent discs

0/ <Ω dRd

• Magnetorotational instability vigorous turbulence in discs (Balbus & Hawley 1991; Hawley, Gammie & Balbus 1996, etc…)

• Necessary ingredients: (i) Weak magnetic field (ii) (iii) Sufficient ionisation: X(e-) ~ 10-12

(iv) Rem > 100

Dust free disc ~ 50 % of matter turbulent Dusty disc ~ 3 % of matter turbulent

Ilgner & Nelson (2006a)

πφ

4BB

mrT = φδρδ vvT rR .=

=

PTT mR−=

Low mass planets

• Consider orbital evolution of: mp=1, 3, 5, 10, 30 Earth mass planets

• Question: what is effect of turbulence on type I migration ?

(Nelson & Papaloizou 2004; Nelson 2005; Laughlin, Adams & Steinaker 2004)

Fluctuating torques – suggest stochastic migration

Mp = 10 Earth masses

Power spectrum – shows torques have temporal variations ~ run time of simulations

Stochastic torques may overcome type I torques over significant time scales for some planetsRequire longer simulations…

Torque distributions σ

tTT

+>=<

Naïve application suggests inward migration should be obtained for mp=10

Planetesimals in laminar discs• Gas in pressure supported

disc orbits with sub-Keplerian velocity• Solid bodies orbit with Keplerian velocity Planetesimals experience head wind (Weidenschilling 1977) • Gas drag induces inward drift & efficient eccentricity damping

Planetesimals in turbulent discs

• Evolution of 100 - 1000 planetesimals calculated to examine inward drift and velocity dispersion

• Planetesimal treated as particlesthat experience gas drag and gravitational force due to disc andcentral star

• Sizes: 1m – 1km


1 metre sized objects migrate inward within ~ 30 orbits (300 years)1m sized boulders become trapped in long-lived vortices - about 50% of particles trappedTight coupling to gas causes large eccentricities – potentially destructivevelocity dispersion ?Neighbouring planetesimals appear to be on very similar orbits


• Most 10 m size boulders drift inward on time scale of ~ few thousand years – a few drift in more slowly• Velocity dispersion remains quite small – coupling too weak to allow individual fluctuations in gas velocity to determine velocity dispersion • Danger of destructive collisions: e=0.01 <v> ~ 0.12 km/s at 5 AU• Icy 10 m sized bodies fragment with <v> ~ 20 m/s (Benz & Asphaug 1999)


• 100 m sized objects dominated by fluctuations in disc gravity• Instead of inward drift undergo `random walk’ on time scales ~ 100 orbits• Icy 100m sized objects fragment if <v> ~ 14 m/s• <v> ~ 0.24 km/s for e=0.02 at 5 AU • Destructive collisions likely as neighbouring orbits randomly orientated

1 km sized planetesimals

• Results similar to 100 metre sized objects

• Large velocity dispersion prevents runaway growth of planetesimals to form planetary embryos

Migration in optically thick discs• Corotation torque can

exceed Lindblad torques inoptically thick discs(Paardekooper & Mellema 2007)

• Effect is due to warm gasbeing advected from insideto outside orbit of planetand vice versa

• Pressure equilibrium leads to modification of density structure

• High density region leads planet, low density region trails it - positive torque

planetary migration - a review richard nelson queen mary, university of london collaborators: paul...

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