Mass functions and bias of dark matter halos

Abstract

We report on some results on the mass function and the bias of dark matter halos. Focusing on the limit of rare massive halos, we point out that exact analytical results can be obtained for the large‐mass tail of the halo mass function. This is most easily seen from a steepest‐descent approach, that becomes asymptotically exact for rare events. We also revisit the traditional derivation of the bias of massive halos, associated with overdense regions in the primordial density field, paying attention to the Lagrangian‐Eulerian mapping (i.e. corrections associated with the motions of halos). This allows us to improve the standard analytical formula for the bias of massive halos without introducing any free parameter. Next, we briefly note that this approach can be extended to non‐Gaussian initial conditions. We again obtain a good agreement with numerical simulations. Moreover, the nonlinear real‐space expression we obtain for the halo correlation clearly shows how the baryon acoustic oscillation at ∼100 h−1 Mpc is amplified by the bias of massive halos and modified by primordial non‐Gaussianity. At smaller scales, 30<x<90 h−1 Mpc, we find that the correction to the real‐space bias roughly scales as fNLbM(fNL = 0)x2.