Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

Abstract

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 Bardeen et al. (1986), 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 2σ 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 M⊙/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.

Halo profile evolution and velocity bias

“…there is initial velocity bias, large scale gravitational evolution will naturally drive the galaxy velocity field to that of the dark matter [14,23]. On the other hand, the peak model predicts that the velocity bias persists and remains constant at late time [24]. This result seems to be favoured by the recent simulation results, which suggest that the halo velocity bias at late time is nonnegligible at k ∼ 0.…”

“…these k 2 corrections can be derived from the peak model [26]. In [24], Zel'dovich approximation was used to displace the peaks to the Eulerian space, and they found that the velocity bias remains constant over time. The numerical measurement seemed to be in favour of the peak model result [15].…”

“…We note that our approach also has rather different interpretation for the generation of velocity bias from that in [15,[24][25][26]. In peak theory, although the smoothing window is an important ingredient, the window function is usually assumed to be static.…”

Covariance matrices for halo number counts and correlation functions

“…This approximation of scale-independent halo bias is valid to better than 10% on scales 20 < r < 130 h −1 Mpc (Manera & Gaztanaga 2011), with a small feature on the baryon acoustic scale (r ∼ 100 h −1 Mpc) of amplitude of 5% (Desjacques et al 2010). Throughout most of this paper we assume that correlations are negligible over cosmological distances (of order c/H 0 ), so that the redshift z on the right-hand side of Eq.…”

Imprint of primordial non-Gaussianity on dark matter halo profiles

“…To constrain primordial non-Gaussianity (PNG) from large-scale structure, we need to identify a signature that can be produced only by primordial non-Gaussianity and not by gravitational instability. One that has emerged in recent years is scale-dependent bias [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In this paper we investigate whether primordial non-Gaussianity leaves a distinctive imprint in a different arena, on the profile of dark matter halos.…”