BAM: bias assignment method to generate mock catalogues

We present BAM: a novel Bias Assignment Method envisaged to generate mock catalogs by linking the continuous cosmic dark matter field to a discrete population of tracers, such as dark matter halos or galaxies. Using a reference high resolution cosmological N-body simulation to extract a biasing scheme we can generate halo catalogues starting from much coarser density fields calculated from downsampled initial conditions using efficient structure formation solvers. We characterize the halo-bias relation as a function of a number of properties (e.g. local densiy, cosmic web type) to the dark matter density field defined on a mesh of a 3 Mpc/h cell side resolution, derived from the fast structure formation solvers. In this way our bias description automatically includes stochastic, deterministic, local and non-local components directly extracted from full $N$-body simulations. We sample the halo density field according to the observed halo bias, such that the two-point statistics of the mock halo catalog follows the same statistics as the reference. By construction, our approach reaches percentage accuracy, 1%, in the majority of the k-range up to the Nyquist frequency without systematic deviations for power spectra (about k~ 1 h/Mpc) using either particle mesh or Lagrangian perturbation theory based solvers. When using phase-space mapping to compensate the low resolution of the approximate gravity solvers, our method is able to reproduce the bispectra of the reference within 10% precision studying configurations tracing the quasi-nonlinear regime. Therefore BAM promises to become a standard technique to produce mock halo and galaxy catalogs for future galaxy surveys and cosmological studies being highly accurate, efficient and parameter free.