Large-scale bias of dark matter halos

We build a simple analytical model for the bias of dark matter halos that applies to objects defined by an arbitrary density threshold, $200\leq\deltas\leq 1600$, and that provides accurate predictions from low-mass to high-mass halos. We point out that it is possible to build simple and efficient models, with no free parameter for the halo bias, by using integral constraints that govern the behavior of low-mass and typical halos, whereas the properties of rare massive halos are derived through explicit asymptotic approaches. We also describe how to take into account the impact of halo motions on their bias, using their linear displacement field. We obtain a good agreement with numerical simulations for the halo mass functions and large-scale bias at redshifts $0\leq z \leq 2.5$, for halos defined by a nonlinear density threshold $200\leq\deltas\leq 1600$. We also evaluate the impact on the halo bias of two common approximations, i) neglecting halo motions, and ii) linearizing the halo two-point correlation.