Statistics of Mass Aggregation in a Self-Gravitating One-Dimensional Gas

We study at the microscopic level the dynamics of a one-dimensional, gravitationally interacting sticky gas. Initially, N identical particles of mass m with uncorrelated, randomly distributed velocities fill homogeneously a finite region of space. It is proved that at a characteristic time a single macroscopic mass is formed with certainty, surrounded by a dust of nonextensive fragments. In the continuum limit this corresponds to a single shock creating a singular mass density. The statistics of the remaining fragments obeys the Poisson law at all times following the shock. Numerical simulations indicate that up to the moment of macroscopic aggregation the system remains internally homogeneous. At the short time scale a rapid decrease in the kinetic energy is observed, accompanied by the formation of a number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \sim \sqrt N $$ \end{document} of aggregates with masses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \sim m\sqrt N $$ \end{document}.