Local bias approach to the clustering of discrete density peaks

Vincent Desjacques
Phys. Rev. D 87, 043505 – Published 4 February 2013

Abstract

Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering statistics of discrete density peaks are difficult to evaluate. For this reason, local bias schemes have received considerably more attention in the literature thus far. In this paper, we show that the two-point correlation function of maxima of a homogeneous and isotropic Gaussian random field can be thought of, up to second order at least, as arising from a local bias expansion formulated in terms of rotationally invariant variables. This expansion relies on a unique smoothing scale, which is the Lagrangian radius of dark matter halos. The great advantage of this local bias approach is that it circumvents the difficult computation of joint probability distributions. We demonstrate that the bias factors associated with these rotational invariants can be computed using a peak-background split argument, in which the background perturbation shifts the corresponding probability distribution functions. Consequently, the bias factors are orthogonal polynomials averaged over those spatial locations that satisfy the peak constraint. In particular, asphericity in the peak profile contributes to the clustering at quadratic and higher order, with bias factors given by generalized Laguerre polynomials. We speculate that our approach remains valid at all orders, and that it can be extended to describe clustering statistics of any point process of a Gaussian random field. Our results will be very useful to model the clustering of discrete tracers with more realistic collapse prescriptions involving the tidal shear for instance.

  • Figure
  • Received 22 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.043505

© 2013 American Physical Society

Authors & Affiliations

Vincent Desjacques*

  • Département de Physique Théorique and Center for Astroparticle Physics (CAP), Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Switzerland

  • *Vincent.Desjacques@unige.ch

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Vol. 87, Iss. 4 — 15 February 2013

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