SCALING PROPERTIES OF NONLINEAR GRAVITATIONAL CLUSTERING

Hamilton et al. recently proposed the idea that the growth of density perturbations in an expanding universe is governed by a general scaling law, and showed agreement with existing numerical simulations. We examine the possible origin of this scaling behaviour in more detail. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, h(x, a)= -[v/(ax)], depends on the expansion factor a and comoving coordinate x only through the density contrast <(xi)over bar>(x, a) (the two-point correlation averaged over a sphere of radius x). This leads naturally to the proposed scaling law - the true non-linear density contrast is a universal function of the density contrast <(xi)over bar>(L),(l, a), computed in the linear theory and evaluated at a scale l which is derived to be l=x(1+<(xi)over bar>)(1/3). Apart from basing the proposed scaling form on an explicit dynamical hypothesis, this gives a convenient solution for the scaling function in terms of the input pair velocity. Possibilities for further elaboration of this approach in interpreting simulations of nonlinear gravitational clustering are briefly discussed.