Modeling scale-dependent bias on the baryonic acoustic scale with the
  statistics of peaks of Gaussian random fields
  Models of galaxy and halo clustering commonly assume that the tracers can be
treated as a continuous field locally biased with respect to the underlying
mass distribution. In the peak model pioneered by BBKS, one considers instead
density maxima of the initial, Gaussian mass density field as an approximation
to the formation site of virialized objects. In this paper, the peak model is
extended in two ways to improve its predictive accuracy. Firstly, we derive the
two-point correlation function of initial density peaks up to second order and
demonstrate that a peak-background split approach can be applied to obtain the
k-independent and k-dependent peak bias factors at all orders. Secondly, we
explore the gravitational evolution of the peak correlation function within the
Zel'dovich approximation. We show that the local (Lagrangian) bias approach
emerges as a special case of the peak model, in which all bias parameters are
scale-independent and there is no statistical velocity bias. We apply our
formulae to study how the Lagrangian peak biasing, the diffusion due to large
scale flows and the mode-coupling due to nonlocal interactions affect the scale
dependence of bias from small separations up to the baryon acoustic oscillation
(BAO) scale. For 2-sigma density peaks collapsing at z=0.3, our model predicts
a ~ 5% residual scale-dependent bias around the acoustic scale that arises
mostly from first-order Lagrangian peak biasing (as opposed to second-order
gravity mode-coupling). We also search for a scale dependence of bias in the
large scale auto-correlation of massive halos extracted from a very large
N-body simulation provided by the MICE collaboration. For halos with mass
M>10^{14}Msun/h, our measurements demonstrate a scale-dependent bias across the
BAO feature which is very well reproduced by a prediction based on the peak
model.
