Statistical Mechanics of 1d Self-Gravitating Systems: The Core-Halo Distribution

We study, using both theory and simulations, a system of self-gravitating sheets. A new statistical mechanics theory - free of any adjustable parameters - is derived to quantitatively predict the final stationary state achieved by this system after the process of collisionless relaxation is completed. The theory shows a very good agreement with the numerical simulations. The model sheds new light on the general mechanism of relaxation of self-gravitating systems and may help us to understand cold matter distribution in the Universe.