How the dark matter halos cluster in Lagrangian space

We investigate the clustering of dark matter halos in Lagrangian space in terms of their two-point correlation function, spanning more than 4 orders of magnitudes of halo masses. Analyzing a set of collisionless scale-free 128^3-particle N-body simulations with spectral indices n = -2,-1, we measure the first two Lagrangian bias parameters b_1 and b_2 relating halo and mass correlations. We find that the Mo & White leading-order formula for b_1 describes the clustering of halos with mass M ~ M_* quite accurately, where M_* indicates the characteristic non-linear mass. 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 b_1 in Lagrangian space.