Nonlinear constrained realizations of the large-scale structure

The linear algorithm of the Wiener filter and constrained realizations (CRs) of Gaussian random fields is extended here to perform nonlinear CRs. The procedure consists of (1) using low-resolution data to constrain a high-resolution realization of the underlying held, as if the linear theory were valid; (2) taking the linear CR backward in time, by the linear theory, to set initial conditions for N-body simulations; (3) forwarding the held in time by an N-body code. An intermediate step is introduced to "linearize" the low-resolution data. The nonlinear CR can be applied to any observational data set that is quasi-linearly related to the underlying field. Here it is applied to the IRAS 1.2 Jy catalog using 846 data points within a sphere of 6000 km s(-1), to reconstruct the full nonlinear large-scale structure of our "local" universe. The method is tested against mock IRAS surveys, taken from random nonlinear realizations. A detailed analysis of the reconstructed nonlinear structure is presented.