AGGREGATION DYNAMICS IN A SELF-GRAVITATING ONE-DIMENSIONAL GAS

Aggregation of mass by perfectly inelastic collisions in a one-dimensi onal self-gravitating gas is studied. The binary collisions are subjec t to the laws of mass and momentum conservation. A method to obtain an exact probabilistic description of aggregation is presented. Since th e one-dimensional gravitational attraction is confining, all particles will eventually form a single body. The detailed analysis of the prob ability P-n(t) of such a complete merging before time t is performed f or initial states of n equidistant identical particles with uncorrelat ed velocities. It is found that for a macroscopic amount of matter (n --> infinity), this probability vanishes before a characteristic lime t. In the limit of a continuous initial mass distribution the exact a nalytic form of P-n(t) is derived. The analysis of collisions leading to the time-variation of P-n(t) reveals that in fact the merging into macroscopic bodies always occurs in the immediate vicinity of t. For t > t, and n large, P-n(t) describes events corresponding to the fina l aggregation of remaining microscopic fragments.