The halo bias b(M,x) as a function of σ(M), at distance x = 50   h^-1Mpc, for halos defined by the nonlinear density contrast δ_∗ = 200. We plot our results at redshifts z = 0 (left panel), z = 1.25 (middle panel), and z = 2.5 (right panel). The black solid line, “δ_L ∗ ”, is the theoretical prediction (24), the red dashed line, “s = x”, corresponds to the approximation where halo motions are neglected, and the green dot-dashed line, “δ_c”, corresponds to the use of δ_c = 1.686 instead of δ_L ∗ . The blue dashed line, “SMT”, is the fit from Sheth et al. (2001), and the points are the results from numerical simulations of Tinker et al. (2010).