Coupling dynamical and collisional evolution of small bodies: an application to the early ejection of planetesimals from the Jupiter-Saturn region

Abstract We present a new algorithm designed to compute the collisional erosion of a population of small bodies undergoing a complex and rapid dynamical evolution induced by strong gravitational perturbations. Usual particle-in-a-box models have been extensively and successfully used to study the evolution of asteroids or KBOs. However, they cannot track the evolution of small bodies in rapid dynamical evolution, due to their oversimplified description of the dynamics. Our code is based on both (1) a direct simulation of the dynamical evolution which is used to compute local encounter rates and (2) a classical fragmentation model. Such a code may be used to track the erosional evolution of the planetesimal disk under the action of newly formed giant-planets, a passing star or a population of massive planetary-embryos. We present here an application to a problem related to the formation of the Oort cloud. The usually accepted formation scenario is that planetesimals, originally formed in the giant planet region, have been transported to the Oort cloud by gravitational scattering. However, it has been suggested that, during the initial transport phase, the mutual large encounter velocities might have induced a rapid and intense collisional evolution of the planetesimal population, potentially causing a significant reduction of the Oort cloud formation process. This mechanism is explored with our new algorithm. Because the advantages of our new approach are better highlighted for a population undergoing a violent dynamical evolution, we concentrate in this paper on the planetesimals originally in the Jupiter–Saturn region, although it is known that they are only minor contributors to the final Oort cloud population. A wide range of parameters is explored (mass of the particle disk, initial size-distribution, material strength): depending upon the assumed parameter values, we find that from 15 to 90% of the mass contained in bodies larger than 1 km survives the collisional process; for our preferred choice of the parameters this fraction is ∼70%. It is also found that the majority of planetesimals larger than 1–10 km are pristine, and not fragments. We show also that collisional damping may not prevent planetesimals from being ejected to the outer Solar System. Thus, although the collisional activity is high during the scattering by Jupiter and Saturn, collisional grinding does not lower by orders of magnitude the mass contained in bodies larger than 1 km, originally in the Jupiter–Saturn region. These conclusions seem to support the classical collisionless scenario of Oort cloud formation, at least for the Jupiter–Saturn region.