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 the 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 years. Kenyon, Stern, Broomley, Weisman, Davis etc…

In situe formation of the KB 3- In 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 (~ 10 2 to 10 3 than usual estimates) Kenyon & Luu, 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 4 th ZONE !!

From Dones et al 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 Starting Size-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 populations cannot 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 & COLLISIONAL evolution 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 10 4 years. Each of 6000 particles holds a full size distribution evolved with a Fragmentation code : : Fragmentation + Craterisation COUPLING DYNAMICAL with COLLISIONAL EVOLUTION A Hybrid approach

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

# 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 r Break Radius ~ 10m # 2 : The initial size distribution is ~ today, but 100 times more massive Consistent with : Dynamical depletion r N Break 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 comets Francis et al « Observed * » : with D> 1km

A too severe collisional evolution due to strong dynamical steering of giant planets Only ~ 10 7 bodies with D>1Km survive in the Scattered Disk. 100 times less than Inferred from the observation of Jupiter Family comets (Duncan & Levison, 1997 ) Initial conditions : mass in small bodies  Collisional grinding senario Scattered Disk *From flux of Jupiter family comets Observed*: ~10 9, D>1km Trujjillo et al.2001 ~4x10 4, R>50 km

CASE 2 The Oort Cloud « Observed * » : with D> 1km Much better mach With the estimated population Of the Oort Cloud

The Scattered Disk Trujjillo et al.2001 ~4x10 4, R>50 km Observed*: ~10 9, D>1km Good match to observartions

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

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 In every scenario, the most severly depleted population is the SCATTERED DISK  Charnoz & Morbidelli 2007, ICARUS In press Reprints :

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 !!)

THE END

The Oort Cloud population Divided into 2 parts : The « visible » or Outer Oort Cloud with a> 10 4 au The Inner Oort Cloud with a<10 4 au Total : ~ 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 Break Radius ~ 10m r N Break 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 for Oort Cloud (4 time less) Scattered Disk (OK)

The outer edge of the Solar System is occupied by 3 populations of small bodies whose dynamical & collisional history is coupled 1.The Kuiper Belt ~ Me 2.The Scattered disk ~ 10 9 with D> 1km Gladman et al. 2005