Non-linear 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 non-linear CRs. The procedure consists of: (1) Using low resolution data to constrain a high resolution realization of the underlying field, as if the linear theory is valid; (2) Taking the linear CR backwards in time, by the linear theory, to set initial conditions for N-body simulations; (3) Forwarding the field in time by an N-body code. An intermediate step is introduced to `linearize' the low resolution data. The non-linear 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 1.2Jy catalog using 846 data points within a sphere of 6000 km/s, to reconstruct the full non-linear large scale structure of our `local' universe. The method is tested against mock IRAS surveys, taken from random non-linear realizations. A detaile analysis of the reconstructed non-linear structure is presented.