Js. Bagla et T. Padmanabhan, A NEW STATISTICAL INDICATOR TO STUDY NONLINEAR GRAVITATIONAL CLUSTERING AND STRUCTURE FORMATION, The Astrophysical journal, 469(2), 1996, pp. 470-479
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.