Modelling Baryon Acoustic Oscillations with Perturbation Theory and
  Stochastic Halo Biasing
  In this work we investigate the generation of mock halo catalogues based on
perturbation theory and nonlinear stochastic biasing with the novel
PATCHY-code. In particular, we use Augmented Lagrangian Perturbation Theory
(ALPT) to generate a dark matter density field on a mesh starting from Gaussian
fluctuations and to compute the peculiar velocity field. ALPT is based on a
combination of second order LPT (2LPT) on large scales and the spherical
collapse model on smaller scales. We account for the systematic deviation of
perturbative approaches from N-body simulations together with halo biasing
adopting an exponential bias model. We then account for stochastic biasing by
defining three regimes: a low, an intermediate and a high density regime, using
a Poisson distribution in the intermediate regime and the negative binomial
distribution to model over-dispersion in the high density regime. Since we
focus in this study on massive halos, we suppress the generation of halos in
the low density regime. The various nonlinear and stochastic biasing
parameters, and density thresholds (five) are calibrated with the large
BigMultiDark N-body simulation to match the power spectrum of the corresponding
halo population. Our mock catalogues show power spectra, both in real- and
redshift-space, which are compatible with N-body simulations within about 2% up
to k ~ 1 h Mpc^-1 at z = 0.577 for a sample of halos with the typical BOSS
CMASS galaxy number density. The corresponding correlation functions are
compatible down to a few Mpc. We also find that neglecting over-dispersion in
high density regions produces power spectra with deviations of 10% at k ~ 0.4 h
Mpc^-1. These results indicate the need to account for an accurate statistical
description of the galaxy clustering for precise studies of large-scale
surveys.
