One-dimensional self-gravitating sheet model and Lynden-Bell statistics.

Abstract

The Lynden-Bell statistics has been proposed to explain common features among galaxies, which are not in thermal equilibrium. The statistics is not successful to reproduce energy distribution in the one-dimensional self-gravitating sheet model except for initial states near the virial equilibrium. The breakdown is caused by dynamically accelerated high-energy sheets, and hence a modified statistics is examined by focusing on low-energy sheets in order to clarify validity of the basic idea of the Lynden-Bell statistics. The modification improves agreement between the theoretical and numerical energy distributions in a wide interval of the initial virial ratio.