PLANETARY MIGRATION in protoplanetary discs and OUTER SOLAR SYSTEM ARCHITECTURE Aurélien CRIDA 1,...

PLANETARY MIGRATIONPLANETARY MIGRATIONin protoplanetary discsin protoplanetary discs

andandOUTER SOLAR SYSTEM OUTER SOLAR SYSTEM

ARCHITECTUREARCHITECTURE

Aurélien CRIDA 1,

A. MORBIDELLI, K. TSIGANIS

H. LEVISON, R. GOMES( 1 Institüt für Astronomie und Astrophysik, Universität Tübingen, GERMANY)

A. Crida et al

Introduction :

Proto-planetary disks :

Planets form in it.

Size : several 100s A.U.

Life time : ~ 3-5 106 years.

Aspect Ratio : H/r ~ 0.05 + flaring

Viscosity : = cs H (10-3<<10-1)

Mass : < M* / 10

Europlanet 2007 2 / 21

Planet-disk interactions :

( Animation by Frédéric Masset (C.E.A),using FARGO (Masset 2000a,b) )

Wake formation :A planet on a fixed circular orbit launches a spiral wake by gravitational perturbation

Angular Momentum exchanges :

Positive torque exerted by the planet on the outer disk.Negative torque on the inner disk.

Net result for the planet :differential Lindblad torque (negative), type I migration.(Ward, 1986, 1997 )

Migration rate ~ planet mass.

Migration time scale :

≈ 105 years for 10 M at 5 AU.

≈ disk life time / 100.

A. Crida et alEuroplanet 2007 3 / 21

( Frédéric Masset again, corotating frame )

Gap formation :


The planet repels the inner disk inward, and the outer disk outward.If the planet is massive enough : Gap opening.

Condition 1 : Planetary torque < viscous torque :q = Mp/M* > 40 / rp²Ωp

Condition 2 : Angular momentum not taken away by the wave : RHill > H

Unified criterion :

3/4 H/RH + 50/ qrp²Ωp < 1( Crida et al, 2006 )


Outer diskInner disk

star

Type II migration :

After gap opening :

The planet is no longer inside the gas disk, it cannot drift with respect to the disk.

The disk global evolution is the key.It drives the giant planet close to the central star.


Locked in the gap, the planet follows the disk viscous evolution(accretion onto the central star and spreading, Lynden-Bell & Pringle, 1974)Migration rate α viscosity ; Migration time scale <~ disk life time.


Type II migration explainsthe hot Jupiters,but not Jupiter !

In the Solar System, no giant planet passedthrthrough the Main Asteroid Belt or the Kuiper Belt.

Jupiter, Saturn, Uranus, Neptune didn’t migrate significantly.

How to explain this ?

Questions and Summary

SUMMARY :

1) Migration of a pair of giant planets (+ 2 ice giants)

2) The « Nice model »

3) The « Nice model », revisited in agreement with 1


Two planets in their own gaps migrate in parallel.Outer diskInner disk

star

Outer diskInner disk

star

Migration of a pair of planets ≠ migration of one planet.Lighter outer planet → outward migration.

(Masset & Snellgrove, 2001, MNRAS)

Two planets in a same gap approach each other → MMR.

If the planets have different masses, the pair of planets is not in equilibrium. → gas passes the gap ; decoupling from disk evolution.

1) Migration of Jupiter & Saturn


Dependence onviscosity :

Start with aSaturn = 1.4 aJupiter,fixed planets (for gap opening).

At t ≈ 500, release the planets.

<10-5 (black, red) : They approach,lock in MMR at t ≈ 1000,and then migrate together.

Low :outward migration rate increases with - Jupiter feels a stronger positive torque (α),- corotation torque increases.

= 2.10-5 : Saturn migrates outward (strong corotation torque), then parallel migration in separated gaps : Mechanism broken.



Dependence onaspect ratio H/r :

Start with aSaturn = 1.4 aJupiter, = 10 -5.5, fixed planets (for gap opening).

At t ≈ 500, release the planets.

They approach,lock in MMR at t ≈ 1000,and then migrate together.

The smaller H/r, the deeper Saturn’s gap, the more Jupiter pushed

outward.

(Morbidelli & Crida, 2007)

H/r = 0.05 : stationary solution.



Dependence onthe masses :

Jupiter and Saturn :stationary solution.

Planets of same mass :slowed down inward migration.

More massive outer planet : accelerated migration.

3 times more massive planets :perturbations, scattering, then 2:1 MMR and migration stopped.

(Morbidelli & Crida, 2007)



Add Uranus below Saturn orbit :

Uranus migrates inward (type I), and is caught in MMR with Saturn (3:2 or 4:3).

Add Neptune :

After inward migration, Neptune is caught in 3:2, 4:3, or 5:4 MMR with Uranus.

The 4 planets in this resonant configuration avoid migration in the disc.

(Morbidelli et al, 2007)

1) Migration of Jupiter, Saturn, Uranus, Neptune

Add Neptune :

After inward migration, Neptune is caught in 3:2, 4:3, or 5:4 MMR with Uranus.

The 4 planets in this resonant configuration avoid migration in the disc.


In this model, the 4 giant planets of the Solar System avoid migration in a disc with reasonable parameters.

→ no perturbation of the inner Solar System nor the MAB.

1) Migration of Jupiter, Saturn, Uranus, Neptune

BUT: This configuration has nothing to do with the present one: BUT: This configuration has nothing to do with the present one: the outer Solar System is fully resonant and too compact.the outer Solar System is fully resonant and too compact.

→→ An other model requires a compact configuration of the An other model requires a compact configuration of the outer SS after de gas disk phase : the “Nice model”…outer SS after de gas disk phase : the “Nice model”…


2) The “Nice model”

Questions :

~650 Myr after Solar System birth, a spike of asteroïd bombardment occured, creating the moon bassins (Late Heavy Bombardment).

The four giant planets, particularly Jupiter and Saturn, have a non negligible eccentricity, while planet formation in a gas disk should lead to circular orbits.

Idea :

A late instability in the planets dynamics excited the planets eccentricities and destabilized a reservoir a of small bodies, leading to the LHB.



The Nice model (Tsiganis et al, Gomes et al, 2005) :

After the gas disk disappearance, the four giant planets were initially- on circular orbits- in a compact configuration (within 17 A.U., with J & S inside their 2:1 MMR)- surrounded by a disk of planetesimals (ancestor of the Kuiper Belt). (a)

Planetesimals scattering makes Neptune, Uranus Saturn move slowly outward, and Jupiter inward (b).

At some point, the 1J:2S is reached, which increases their eccentricity and destabilises the whole system, leading to the LHB (c).

It clears the planetesimal disc and causes a major change of the planets orbits (d).



During the instability,- the planets have close encounters,- migration through planetesimal scattering runs away,- eccentricities are damped by dynamical friction.

Finally, the planets reach their present orbits, while the quantity of small bodies crossing the terrestrial orbit is in good agreement with estimates of the LHB.

This model also explains :- the capture of the Jupiter trojans on inclined orbits (Morbidelli et al 2005),- the orbital distribution of the irregular satellites of Saturn, Uranus, Neptune (Nesvorny et al 2007),- the main properties of the Kuiper Belt models (Levison et al 2007).


It relies on : a compact configuration, stable over hundreds of millions of years in the absence of perturbation, that can lead to instability if perturbed.

The initial condition assumed in the original Nice model is arbitrary and somehow ad hoc. Can the planets form in the disc in this configuration ?

Our goal : bridge the gap between disc phase and early dynamics of the SS (Nice model).


Conclusion on the Nice model :

It explains aIt explains a lot of characteristics of our Solar System,thanks to athanks to a late instability in the outer planets dynamics,

with crossing of the 1J:2S MMR.


3) The “Nice model”, revisited

Through planet-disc simulations, six resonant configurations of the 4 giant planets can be achieved, that prevent migration :

2J:3S - 2S:3U - 2U:3N, 3U:4N, 4U:5N.

2J:3S - 3S:4U - 2U:3N, 3U:4N, 4U:5N.

Test their stability on long term with N-body simulations, after having smoothly removed the disc.

Only two are stable over several hundreds of millions of years :

2J:3S - 2S:3U - 2U:3N2J:3S - 2S:3U - 3U:4N (figure)


(Morbidelli et al 2007)


A first attempt :

Take 2J:3S - 2S:3U - 3U:4N.

Add a random small inclination, and a planetesimal disc close beyond Neptune (50 or 65 M)

→ 24 Initial Conditions.

→ 13 yield to a new stable configuration that resembles closely to the one of the outer planets of the Solar System.

Here, the instability is triggered by the 3J:5S MMR. Then, everything goes like in the Nice model. In particular, Jupiter and Saturn cross their 1:2 MMR, which gives them their present eccentricities.


(Morbidelli et al 2007)


A late instability is required :

Changing the initial setup of the planetesimal disc (that was artificially close to Neptune), the instability can be delayed by 200 million years.

At 140 My, Neptune leaves the 3U:4N.

At 190 My, crossing of the 5U:7N.

Then, crossing of the 3J:5S and global

instability.

(Tsiganis et al, in prep.)



Some work is still needed to improve the Some work is still needed to improve the statisticsstatistics on on the final outcome about the final outcome about aa, , ee, the , the close encountersclose encounters between Saturn (or even Jupiter) and the ice giants…between Saturn (or even Jupiter) and the ice giants…

Check if al the properties of the Nice model are kept. Check if al the properties of the Nice model are kept. ((Tsiganis Tsiganis et alet al, in prep., in prep.))

Note that Note that Thommes Thommes et alet al 2007 2007 also studied fully resonant also studied fully resonant configurations, but with Jupiter and Saturn in the 1:2 (and configurations, but with Jupiter and Saturn in the 1:2 (and without hydro simulations).without hydro simulations).

Fully resonant configurations may be a frequent outcome Fully resonant configurations may be a frequent outcome of the disc phase, and a global instability may be a step of the disc phase, and a global instability may be a step of the evolution of many planetary systems.of the evolution of many planetary systems.


CONCLUSION

Planets migrate in gaseous discs, and then interactPlanets migrate in gaseous discs, and then interact→ They not necessarily formed where they orbit → They not necessarily formed where they orbit now.now.

1) To prevent ty1) To prevent type II migration : use a pair of planets in MMR, with theMMR, with the lighter one out (ex: Jupiter & Saturn).

2) From a compact configuration, slowly perturbed by an outer planetesimal disc, a global instability can arise, explaining the Late Heavy Bombardment, the eccentricities of the giant planets… (Nice model)

3) From a fully resonant configuration, compatible with the gas disc phdisc phase also.


THE ENDTHE END

Thank you for your attention.Thank you for your attention.

ENDEENDE

Danke für Ihre Aufmerksamkeit.Danke für Ihre Aufmerksamkeit.

FINFIN

Merci de votre attention.Merci de votre attention.

PLANETARY MIGRATION in protoplanetary discs and OUTER SOLAR SYSTEM ARCHITECTURE Aurélien CRIDA 1,...

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