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Coupling the dynamical and collisional evolution of the Kuiper Belt, the Scattered Disk & the Oort Cloud. S. Charnoz A. Morbidelli. Equipe AIM Université Paris 7 / CEA Saclay. A big mistery of the Kuiper Belt : The mass deficit. A popular scenario to explain the mass deficit is

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slide1

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

S. Charnoz

A. Morbidelli

Equipe AIM

Université Paris 7 / CEA Saclay

slide2

A big mistery of the Kuiper Belt : The mass deficit

A popular scenario to explain the mass deficit is

the Collisional Griding of the KB over the age of the Solar System

We explore here some consequences of this scenario.

slide3

Collisional Grinding Scenario

Start , dn/dr r-4.5

Initial Conditions :

Steep size distribution

+

Only a few Plutos

end

Consequences :

Strong erosion after

4 109 years.

From Kenyon & Bromley 2004

Kenyon, Stern, Broomley, Weisman, Davis etc…

slide4

Kenyon & Luu, 1999

The « recipe » of the today’s kuiper belt

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)

2- KBO must have a very low material strength

(~ 102 to 103 than usual estimates)

3- In situe formation of the KB:

Accretion + destruction occurs at the same place

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

slide5

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 ….

slide7

Broadening the problem : the Oort and the Scattered Disk

All 3 populations (KB,

SD, OC) have their

origin approximately in

the same region

=> Similar Starting

Size-distribution

SD Objects KB

From Dones et al. 2004

slide8

The origin of the 3 populations

cannot be studied separately

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

slide9

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.

slide10

COUPLING DYNAMICAL with COLLISIONAL EVOLUTION

A Hybrid approach

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 distribution

evolved with a Fragmentation code :

: Fragmentation + Craterisation

slide11

A REALISTIC DYNAMICAL

  • EVOLUTION
  • 6000 independant size

distributions evolved conjointly

same time

At the end of the Simulation

~ 700 particles in the KB

~ 10 particles in the SC

~250 particles in the OC

slide12

-3.5

Break Radius ~ 10m

Break Radius ~ 100 km

N

-4.5

r

r

Investigation of 2 scenarios

# 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 scenario

# 2: The initial size distribution is

~ today, but 100 times more massive

Consistent with : Dynamical depletion

slide13

CASE 1

Evolution of the Kuiper Belt

Initial conditions : mass in small bodies

Collisional

grinding senario

Q=Benz &Asphaug 1999

slide14

« Observed* » : 4 1011with D> 1km

Oort Cloud

~ 20 times less

massive than expected

=> As argued in Stern & Weissman (2001)

Initial conditions : mass in small bodies

Collisional

grinding senario

BUT big observational uncertainties

exist for the Oort Cloud !!

  • From Flux of Long period cometsFrancis et al. 2005
slide15

Observed*: ~109 , D>1km

Trujjillo et al.2001

~4x104, R>50 km

Scattered Disk

A too severe collisional evolution

due to strong dynamical steering

of giant planets

*From flux of Jupiter family

comets

Initial conditions : mass in small bodies

Collisional

grinding senario

Only ~ 107 bodies with D>1Km survive in the Scattered Disk.

100 times less than Inferred from the observation

of Jupiter Family comets

(Duncan & Levison, 1997 )

slide16

« Observed* » : 4 1011with D> 1km

CASE 2

The Oort Cloud

Much better mach

With the estimated population

Of the Oort Cloud

slide17

Observed*: ~109 , D>1km

Trujjillo et al.2001

~4x104, R>50 km

The Scattered Disk

Good match to

observartions

slide18

The Kuiper Belt

Good shape of the S.D.

But to get the right (low) mass only

the scenario of dynamical

Implantation seem to work

slide19

SUMMARY

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

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

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

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

 Charnoz & Morbidelli 2007, ICARUS In press

Reprints : charnoz@cea.fr

slide20

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 are
  • Pristine 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 !!)

slide22

The Oort Cloud population

Divided into 2 parts :

The « visible » or

Outer Oort Cloud

with a> 104 au

The Inner Oort Cloud

with a<104 au

Total : ~ 4 1011

bodies with D>1km

slide23

-3.5

Break Radius ~ 10m

Break Radius ~ 100 km

N

-4.5

r

r

CLEAR OPPOSITION BETWEEN 2 MODELS OF KUIPER BELT ORIGIN

Collisional Griding

Dynamical erosion

Mass in big bodies

shallow S.D.

A few 100 plutos

Mass in small bodies

Steep S.D.

A few plutos

N

?

How to get out of the dilemna ?

slide24

Other Scenario : mass in big bodies  Dynamical depletion

The size distribution almost

does not evolve under collisions

Reasonable results for

Oort Cloud (4 time less)

Scattered Disk (OK)

slide25

The outer edge of the Solar System is occupied by 3 populations

of small bodies whose dynamical & collisional history is coupled

  • The Kuiper Belt
  • ~ 0.01-0.1 Me
  • The Scattered disk
  • ~ 109 with D> 1km

Gladman et al. 2005