NONLOCAL AND COLLECTIVE RELAXATION IN STELLAR-SYSTEMS

Using both analytic theory and n-body simulation, this paper considers the modal response of stellar systems to fluctuations at large scales. As the system size approaches its Jeans length, the maximum amplitude of the large-scale low-order modes dramatically increases, enhancing the relaxation by factors of 10-100. However, we show that the stochastic excitation of these modes significantly increases the relaxation rate even for a system moderately far from instability. The effects of large-scale fluctuations are apparent in n-body simulations which are designed to suppress relaxation at small scales. In these cases, the linear theory developed here predicts that relaxation will be dominated by large-scale modes; thus there should be little advantage to either softened particle or truncated expansion codes vis-a-vis relaxation. These predictions are verified in n-body simulations performed here and provide insight into similar results reported by others. In addition, the theory predicts that the large-scale fluctuations will be largest for marginally bound systems, such as forming star clusters and associations. This additional relaxation will act like violent relaxation by causing acceleration independent of particle mass but will occur for near-equilibrium systems. The importance to the early evolution of these systems remains to be investigated.