Measuring nonlocal Lagrangian peak bias

In the Lagrangian approach to halo clustering, nonlocal bias can be generated either in the initial conditions or by the subsequent gravitational motions. Here, we investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We reformulate this approach in order to explicitly take into account the variable describing the crossing of the collapse barrier. This enables us to write down a bias expansion which includes all the bias terms, including the nonlocal ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we extend the 1-point cross-correlation technique of Musso, Paranjape & Sheth (2012) to bias contributions that are chi-squared distributed. We validate the method with numerical realizations of peaks of Gaussian random fields before applying it to N-body simulations. We focus on the lowest (quadratic) order nonlocal bias factors predicted by the excursion set peaks approach. While the measurements are qualitatively consistent with the theoretical predictions, they point to the need for a refined description of the Lagrangian patches that collapse into haloes.

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Date added: Tue, 8 Oct 13