Constraining the halo bispectrum in real and redshift space from
  perturbation theory and non-linear stochastic bias
  We present a method to produce mock galaxy catalogues with efficient
perturbation theory schemes, which match the number density, power spectra and
bispectra in real and in redshift space from N-body simulations. The essential
contribution of this work is the way in which we constrain the bias parameters
in the PATCHY-code. In addition of aiming at reproducing the two-point
statistics, we seek the set of bias parameters, which constrain the univariate
halo probability distribution function (PDF) encoding higher-order correlation
functions. We demonstrate that halo catalogues based on the same underlying
dark matter field with a fix halo number density, and accurately matching the
power spectrum (within 2%), can lead to very different bispectra depending on
the adopted halo bias model. A model ignoring the shape of the halo PDF can
lead to deviations up to factors of 2. The catalogues obtained additionally
constraining the shape of the halo PDF can significantly lower the discrepancy
in the three-point statistics, yielding closely unbiased bispectra both in real
and in redshift space; which are in general compatible with those corresponding
to an N-body simulation within 10% (deviating at most up to 20%). Our
calculations show that the constant linear bias of ~2 for Luminous Red Galaxy
(LRG) like galaxies seen in the power spectrum, mainly comes from sampling
halos in high density peaks, choosing a high density threshold rather than from
a factor multiplying the dark matter density field. Our method contributes
towards an efficient modelling of the halo/galaxy distribution required to
estimate uncertainties in the clustering measurements from galaxy redshift
surveys. We have also demonstrated that it represents a powerful tool to test
various bias models.
