How Dark Matter Halos Cluster in Lagrangian Space

We investigate the clustering of dark matter halos in Lagrangian space interms of their two-point correlation function, spanning more than 4 orders ofmagnitudes of halo masses. Analyzing a set of collisionless scale-free128^3-particle N-body simulations with spectral indices n = -2,-1, we measurethe first two Lagrangian bias parameters b_1 and b_2 relating halo and masscorrelations. We find that the Mo & White leading-order formula for b_1describes the clustering of halos with mass M ~ M_* quite accurately, where M_*indicates the characteristic non-linear mass. Smaller halos turn out to be lessclustered in Lagrangian space than predicted by Mo & White. Our findings areconsistent with the recent results of Jing for the clustering of halopopulations in Eulerian space, demonstrating that the discrepancies between theN-body and analytical Mo & White prediction for the bias exist already inLagrangian space. This shows that a more refined theoretical algorithm forselecting halos in the initial conditions needs to be developed. Finally, wepresent a very accurate fitting formula for the linear halo bias factor b_1 inLagrangian space.Comment: 4 pages, Latex (included emulateapj.sty and psfig.tex), 2 figures. Submitted to ApJ Letter