Nonlinear Constrained Realizations of the Large‐Scale Structure

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Abstract
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 field, 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 field 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.

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