A new statistical indicator to study nonlinear gravitational clustering and structure formation

Abstract

In an Ω = 1 universe dominated by nonrelativistic matter, the velocity field and the gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolves in time, and they can be scaled suitably so that the constant of proportionality is unity and the velocity and force fields are equal. The Zeldovich approximation extends this feature beyond the linear regime, until the formation of pancakes. Nonlinear clustering that takes place after shell crossing breaks this relation, and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a new indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behavior using N-body simulations, and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place. We discuss several features of this statistical indicator and provide simple analytic models to understand its behavior. Particles with velocity contrast higher than a threshold have a correlation function that is biased with respect to the original sample. This bias factor is scale dependent and tends to a constant value at large scales.