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

TL;DR

This paper investigates the microscopic dynamics of a one-dimensional gravitationally interacting sticky gas, revealing the formation of a macroscopic mass and the statistical behavior of fragments, supported by numerical simulations.

Contribution

It provides a rigorous proof of macroscopic mass formation and characterizes the statistical distribution of fragments in a 1D gravitational gas.

Findings

Single macroscopic mass forms at a characteristic time

Fragment statistics follow a Poisson law after shock formation

System remains homogeneous until macroscopic aggregation

Abstract

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 non extensive 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 sqrt(N) of aggregates with masses sqrt(N).