How 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. 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 MgtrsimM\\ (where Msstarf 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.