Nonlocal halo bias with and without massive neutrinos

Understanding the biasing between the clustering properties of halos and the underlying dark matter distribution is important for extracting cosmological information from ongoing and upcoming galaxy surveys. While on sufficiently large scales the halo overdensity is a local function of the mass density fluctuations, on smaller scales the gravitational evolution generates nonlocal terms in the halo density field. We characterize the magnitude of these contributions at third order in perturbation theory by identifying the coefficients of the nonlocal invariant operators, and extend our calculation to include nonlocal (Lagrangian) terms induced by a peak constraint. We apply our results to describe the scale dependence of halo bias in cosmologies with massive neutrinos. The inclusion of gravity-induced nonlocal terms and, especially, a Lagrangian k2 contribution is essential to reproduce the numerical data accurately. We use the peak-background split to derive the numerical values of the various bias coefficients from the excursion set peak mass function. For neutrino masses in the range 0≤ imνi≤0.6eV, we are able to fit the data with a precision of a few percents up to k=0.3hMpc-1 without any free parameter.