A NEW STATISTICAL INDICATOR TO STUDY NONLINEAR GRAVITATIONAL CLUSTERING AND STRUCTURE FORMATION

In an Omega = 1 universe dominated by nonrelativistic matter, the velo city held and the gravitational force field are proportional to each o ther in the linear regime. Neither of these quantities evolves in time , and they can be scaled suitably so that the constant of proportional ity is unity and the velocity and force fields are equal. The Zeldovic h approximation extends this feature beyond the linear regime, until t he formation of pancakes. Nonlinear clustering that takes place after shell crossing breaks this relation, and the mismatch between these tw o vectors increases as the evolution proceeds. We suggest that the dif ference of these two vectors could form the basis for a new indicator of nonlinear clustering. We define an indicator called velocity contra st, study its behavior using N-body simulations, and show that it can be used effectively to delineate the regions where nonlinear clusterin g has taken place. We discuss several features of this statistical ind icator and provide simple analytic models to understand its behavior. Particles with velocity contrast higher than a threshold have a correl ation function that is biased with respect to the original sample. Thi s bias factor is scale dependent and tends to a constant value at larg e scales.