RECOVERY OF THE COSMOLOGICAL PECULIAR VELOCITY FROM THE DENSITY FIELDIN THE WEAKLY NONLINEAR REGIME

Using third-order perturbation theory, we derive a relation between th e divergence of the peculiar velocity and the density. Specifically, w e compute the expectation value of the divergence given density. Our c alculations assume Gaussian initial conditions and are valid for Gauss ian filtering of the evolved density and velocity fields. The mean vel ocity divergence turns out to be a third-order polynomial in the densi ty contrast. We test the power-spectrum dependence of the coefficients of the polynomial for scale-free and standard CDM spectra and find it rather weak. Over scales larger than about 5 h(-1) Mpc, the scatter i n the relation is small compared with that introduced by random errors in the observed density and velocity fields; The relation can be usef ul for recovering the peculiar velocity from the associated density fi eld, and also for non-linear analyses of the anisotropies of structure in redshift surveys.