Aggregation dynamics in a self-gravitating one-dimensional gas

Abstract

Aggregation of mass by perfectly inelastic collisions in a one-dimensional self-gravitating gas is studied. The binary collisions are subject to the laws of mass and momentum conservation. A method to obtain an exact probabilistic description of aggregation is presented. Since the one-dimensional gravitational attraction is confining, all particles will eventually form a single body. The detailed analysis of the probabilityP n (t) of such a complete merging before timet is performed for initial states ofn equidistant identical particles with uncorrelated velocities. It is found that for a macroscopic amount of matter (n→∞), this probability vanishes before a characteristic timet*. In the limit of a continuous initial mass distribution the exact analytic form ofP n (t) is derived. The analysis of collisions leading to the time-variation ofP n (t), reveals that in fact the merging into macroscopic bodies always occurs in the immediate vicinity oft*. Fort>t*, andn large,P n (t) describes events corresponding to the final aggregation of remaining microscopic fragments.