Universal structure of two- and three-dimensional self-gravitating systems in the quasiequilibrium state

We study a universal structure of two- and three-dimensional self-gravitating systems in the quasiequilibrium state. It is shown numerically that the two-dimensional self-gravitating system in the quasiequilibrium state has the same kind of density profile as the three-dimensional one, especially when null virial conditions are fulfilled. It is unveiled why the conditions are necessary for the universal structure by the envelope equation. We develop a phenomenological model to describe this universal structure by using a special Langevin equation with a distinctive random noise to self-gravitating systems. We find that the density profile derived theoretically is very consistent with results of observations and simulations.