Change in mass and energy of galaxies through mutual encounters

We present the result of a systematic study of the evolution of galaxies th rough their encounters. We performed a series of numerical experiments of e ncounters of two galaxies and determined how the change of mass and binding energy depends on galaxy models and collision parameters. Using both numer ical experiments and analytic theory, we found that the relation between th e relative change of energy delta(E) and that of mass delta(M) of one galax y per unit time is expressed as delta(E) similar or equal to 1.5 delta(M) i f the evolution is solely due to encounters. This result suggests that when galaxies in a cluster evolve mainly through frequent encounters with each other, a relation sigma(4) similar to M devel ops between the mass M and the velocity dispersion sigma of the galaxies. I f we assume that M/L is constant, this relation is equivalent to the Faber- Jackson relation, sigma(4) similar to L, which is observed for elliptical g alaxies in a cluster of galaxies. This agreement with observations suggests that the encounters of galaxies play an important role in the evolution of galaxies in clusters.