Dynamical evolution of the Oort cloud: II. A theoretical approach

We investigate the dynamical evolution of a cloud of comets created by stellar perturbations. We first show the respective advantages of numerical simulations and of studies of more theoretical character. Then we investigate the probability distribution of the velocity changes imparted to comets by passing stars. This distribution is shown to be different from a Maxwellian distribution, mainly because of pronounced tails. The number of fairly large impulses is thus more important than it would be in the case of a Maxwellian distribution. Finally we estimate the probability for a comet to be ejected from the Solar System. About 10% of the cloud population is lost through this mechanism over the age of the Solar System. Taking advantage of the velocity change distribution, we study the random walk of semimajor axes of comets as a function of time. We derive the probability that a comet is lost into interstellar space as a function of its initial semimajor axis.