How Dark Matter Halos Cluster in Lagrangian Space

Abstract

We investigate the clustering of dark matter halos in Lagrangian space in terms of their two-point correlation function. Analyzing a set of collisionless scale-free 1283 particle N-body simulations with spectral indices n=-2, -1, we measure the first two Lagrangian bias parameters b1 and b2 relating halo and mass correlations. We find that the Mo & White leading-order formula for b1 describes the clustering of halos with mass M≳M (where M⋆ indicates the characteristic nonlinear mass) quite accurately. Smaller halos turn out to be less clustered in Lagrangian space than predicted by Mo & White. Our findings are consistent with the recent results of Jing for the clustering of halo populations in Eulerian space, demonstrating that the discrepancies between the N-body and analytical Mo & White prediction for the bias exist already in Lagrangian space. This shows that a more refined theoretical algorithm for selecting halos in the initial conditions needs to be developed. Finally, we present a very accurate fitting formula for the linear halo bias factor b1 in Lagrangian space.