Coupling the dynamical and collisional evolution of the Kuiper Belt, the Scattered Disk & the Oort Cloud

S. CharnozA. Morbidelli

Equipe AIMEquipe AIMUniversité Paris 7 / CEA SaclayUniversité Paris 7 / CEA Saclay

A big mistery of the Kuiper Belt : The mass deficit

A popular scenario to explain the mass deficit isthe Collisional Griding of the KB over the age of the Solar System

We explore here some consequences of this scenario.

Collisional Grinding Scenario

Start , dn/dr r-4.5

From Kenyon & Bromley 2004

end

Initial Conditions :

Steep size distribution +Only a few Plutos

Consequences :Strong erosion after 4 109 years.

Kenyon, Stern, Broomley, Weisman, Davis etc…

3- In situe formation of the KBIn situe formation of the KB: Accretion + destruction occurs at the same place

The « recipe » of the today’s kuiper belt

2- KBO must have a very low material strength (~ 102 to 103 than usual estimates)

Kenyon & Luu, 1999

4- The system is described as a statistical set of particles at thermodynamical equilibrium(Particle in a Box) => Collisional griding occurs over the age of the Solar System=> Coarse description of the dynamics

1- The mass must be contained in small bodies that are naturally easy to break ( steep initial distrution (q~ -4.5) down to R~10m)

BUT Other scenarios reproduce the KB size distribution : Dynamical depletion of the belt (see presentation by Morby)

=> Need very low collisonal evolution, initial SD= today’s SD

In short : All models seem to ~ reproduce the today’s size

distribution of the Kuiper Belt !!

How to be more discriminent ?

We should broaden the problem and take into account ….

THE 4th ZONE !!

From Dones et al. 2004

Broadening the problem : the Oort and the Scattered Disk

SD Objects KB

All 3 populations (KB, SD, OC) have their origin approximately in the same region

=> Similar StartingSize-distribution

What are the consequences of the KB formation scenario for the evolution

Implication of steep-size distributions for the evolution of :

- Scattered Disk- Oort Cloud

The origin of the 3 populationscannot be studied separately

IDEA: Test the collisional griding scenario for bodies of - Kuiper Belt- Oort Cloud - Scattered Disk

DIFFICULTY : To couple properly both the DYNAMICAL & COLLISIONALevolution of bodies: « Particle in a box » method cannot achieve this properly

ALGORITHM : Use of a new hybrid approach (Charnoz & Morbidelli Icarus 2004)that was used to compute evolution of bodies ejected by Jupiter and Saturn.

Dynamical code : Integration of 6000 particles with J,S,U,N

Compute collision frequencies and velocities for all pairs of particles, with steps 104 years.

Each of 6000 particles holds a full size distributionevolved with a Fragmentation code :: Fragmentation + Craterisation

COUPLING DYNAMICAL with COLLISIONAL EVOLUTIONA Hybrid approach

A REALISTIC DYNAMICALEVOLUTION

6000 independant size distributions evolved conjointlysame time

At the end of the Simulation~ 700 particles in the KB~ 10 particles in the SC~250 particles in the OC

# 1 : The initial size distribution

is very steep, consistent with what is needed In the scenario : a few plutos, R_break~100m

Consistent with : Collisional griding scenarior

-4.5

-3.5Break Radius ~ 10m

# 2 : The initial size distribution is ~ today, but 100 times more massive

Consistent with : Dynamical depletion

r

NBreak Radius ~ 100 km

Investigation of 2 scenarios

Evolution of the Kuiper Belt

Initial conditions : mass in small bodies Collisional grinding senario

Q=Benz &Asphaug 1999

CASE 1

~ 20 times less massive than expected

=> As argued in Stern & Weissman (2001)

BUT big observational uncertainties exist for the Oort Cloud !!

Oort Cloud

Initial conditions : mass in small bodies

Collisional

grinding senario•From Flux of Long period cometsFrancis et al. 2005

« Observed* » : 4 1011 with D> 1km

A too severe collisional evolution due to strong dynamical steeringof giant planets

Only ~ 107 bodies with D>1Km survive in the Scattered Disk.100 times less than Inferred from the observationof Jupiter Family comets(Duncan & Levison, 1997 )

Initial conditions : mass in small bodies

Collisional

grinding senario

Scattered Disk

*From flux of Jupiter family comets

Observed*: ~109 , D>1km

Trujjillo et al.2001~4x104, R>50 km

CASE 2

The Oort Cloud

« Observed* » : 4 1011 with D> 1km

Much better machWith the estimated populationOf the Oort Cloud

The Scattered Disk

Trujjillo et al.2001~4x104, R>50 km

Observed*: ~109 , D>1km

Good match toobservartions

The Kuiper Belt

Good shape of the S.D.

But to get the right (low) mass onlythe scenario of dynamicalImplantation seem to work

SUMMARY-Using a new and hybrid approach to couple collisional and dynamical evolution, we show that :

3- Dynamical depletion, not collisional erosion, should be responsible for the mass deficit of the KB

2- The collisional griding of the KB has severe problems :

- The Oort Cloud is too severly depleted by a factor of ~ 20- The Scattered Disk is too severely depleted by a factor of 100

1- In every scenario, the most severly depleted population is the SCATTERED DISK

Charnoz & Morbidelli 2007, ICARUS In press Reprints : charnoz@cea.fr

SUGGESTIONS FOR NEW HORIZONS

- Observation of the surface moderately big objects (>50 and < 200 km) Kuiper Belt objects may help to determine the Cratering rate and the constrain the flux of impactors over the age of the Solar System

-Observation of small (<10 km) Kuiper belt objects may help detrmine if they arePristine or not (difficult !!) . * scattered disk bodies are better here*

Such data may be critical to better constrain the formation scenario of the KB Region and may help to decide which « story » is the right one :Collisional erosion ? Dynamical Depletion ?

(A. Stern may have a preference for the first !!)

THE END

The Oort Cloud population

Divided into 2 parts :

The « visible » or Outer Oort Cloud with a> 104 au

The Inner Oort Cloudwith a<104 au

Total : ~ 4 1011 bodies with D>1km

CLEAR OPPOSITION BETWEEN 2 MODELS OF KUIPER BELT ORIGIN

Collisional Griding Dynamical erosion

Mass in small bodies

Steep S.D.

A few plutos

Mass in big bodies

shallow S.D.

A few 100 plutos

N

r

-4.5

-3.5Break Radius ~ 10m

r

NBreak Radius ~ 100 km

?How to get out of the dilemna ?

Other Scenario : mass in big bodies Dynamical depletion

The size distribution almost does not evolve under collisions

Reasonable results forOort Cloud (4 time less)Scattered Disk (OK)

The outer edge of the Solar System is occupied by 3 populationsof small bodies whose dynamical & collisional history is coupled

1. The Kuiper Belt

~ 0.01-0.1 Me

2. The Scattered disk

~ 109 with D> 1km

Gladman et al. 2005