Surviving memory in violently relaxing systems

Abstract

The collapse of a spherical collisionless system of particles is studied. The initial conditions are consinstent with the scenario of galaxy formation from small initial density perturbations. An investigation of the effects of violent relaxation on wiping out the memory of initial conditions is presented. The final distribution of energies of individual particles depends on the radial profile of the initial density perturbation. When this profile becomes steeper, the spectrum of the times scales, in which collapsing of various shells occurs, broadens. The correlation found between the final and the initial distribution of energies is almost linear and the mean slope of this correlation depends on how wide the spectrum of the above time scales is. This slope can be a measure of the surviving memory of initial conditions in the system. The surviving memory is larger in the case when the collapse occurs gradually during a wider range of time scales. If the collapse is completed in a short time interval the relaxation occurs more violently, and the surviving memory is less. Moreover, an estimation of the collapse factors is made by calculating their dependence of the final radius of several fractions of the system's mass, reached at the relaxation. As a consequence, a better fitting of the final radial density profile is made, comparing with the one predicted by the “similarity solution”.