Large scale bias and the inaccuracy of the peak-background split

The peak-background split argument is commonly used to relate the abundance of dark matter halos to their spatial clustering. Testing this argument requires an accurate determination of the halo mass function. We present a Maximum Likelihood method for fitting parametric functional forms to halo abundances which differs from previous work because it does not require binned counts. Our conclusions do not depend on whether we use our method or more conventional ones. In addition, halo abundances depend on how halos are defined; our conclusions do not depend on the choice of link length associated with the friends-of-friends halo-finder. The large scale halo bias measured from the matter-halo cross spectrum b× and the halo autocorrelation function bξ (on scales k ∼ 0.03h Mpc−1 and r ∼ 50h−1Mpc) can differ by as much as 5 percent for halos that are significantly more massive than the characteristic mass M∗. At these large masses, the peak background split estimate of the linear bias factor b1 is 5% smaller than bξ, which is 5% smaller than b×. We discuss the origin of these discrepancies: deterministic nonlinear local bias, with parameters determined by the peak-background split argument, is unable to account for the discrepancies we see. A simple linear but nonlocal bias model, motivated by peaks theory, may also be difficult to reconcile with our measurements. More work on such nonlocal bias models may be needed to understand the nature of halo bias at this level of precision.