Long-Range Correlations in Self-Gravitating N-Body Systems
  Observed self-gravitating systems reveal often fragmented non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations and a better understanding of self-gravitating $N$-body systems appears necessary. Because unstable gravitating systems are sensitive to non-gravitational perturbations we study the effect of different dissipative factors as well as different small and large scale boundary conditions on idealized $N$-body systems. We find, in the interval of negative specific heat, equilibrium properties differing from theoretical predictions made for gravo-thermal systems, substantiating the importance of microscopic physics and the lack of consistent theoretical tools to describe self-gravitating gas. Also, in the interval of negative specific heat, yet outside of equilibrium, unforced systems fragment and establish transient long-range correlations. The strength of these correlations depends on the degree of granularity, suggesting to make the resolution of mass and force coherent. Finally, persistent correlations appear in model systems subject to an energy flow. 
Daniel Huber & Daniel Pfenniger