Perturbative analysis of high virial multi-specie self gravitating one dimensional systems in the collisionless regime

Abstract

One dimensional gravitational gases (1DGGs) are simple models for studying the evolution of many body systems with long range interactions. Though their link with real systems is tenuous, 1DGGs continue to attract attention as the simpler equations governing their dynamics plus the absence of escape and singular interparticle interactions, in contrast to their higher dimensional counterparts, allow for very long time dynamical simulations with little loss of accuracy.
The practicability of long time dynamical simulations for IDGG has made it possible to test mumerous theories of dynamical relaxation. For instance, early predictions that the macroscopic relaxation time for self gravitating one dimensional systems (OGS) made up of identical masses is approximately t_equil ≈ N²t_c, where N is the number of masses in the system and t_c is a typical time to transverse the system, were later found inconsistent with dynamical simulations tending to show that, if the system relaxes at all, t_equil ≫ N²t_c. In contrast, a recent dynamical simulation of a two-mass-specie OGS clearly demonstrated energy equipartition and mass segregation after approximately 10⁷ system crossing times.
These prompt the question: "How else are multimass-specie IDGGs different from single-mass-specie 1DGGs?"
In this paper the behavior of high-virial multi-specie OGS's in the collisionless regime is studied. In particular, this paper will atempt to determine whether or not density pulses, previously observed in single-specie 1DGGs with either Dirac delta or Heaviside type initial density discontinuites, are manifested in multi-specie 1DGGs.