Dark matter halo assembly bias: environmental dependence in the non-Markovian excursion set theory

Abstract

In the standard excursion set model for the growth of structure, the statistical properties of halos are governed by the halo mass and are independent of the larger scale environment in which the halos reside. Numerical simulations, however, have found the spatial distributions of halos to depend not only on their mass but also on the details of their assembly history and environment. Here we present a theoretical framework for incorporating this "assembly bias" into the excursion set model. Our derivations are based on modifications of the path integral approach of Maggiore & Riotto (2010) that models halo formation as a non-Markovian random walk process. The perturbed density field is assumed to evolve stochastically with the smoothing scale and exhibits correlated walks in the presence of a density barrier. We write down conditional probabilities for multiple barrier crossings, and derive from them analytic expressions for descendant and progenitor halo mass functions and halo merger rates as a function of both halo mass and the linear overdensity of the larger-scale environment of the halo. Our results predict a higher halo merger rate and higher progenitor halo mass function in regions of higher overdensity, consistent with the behavior seen in N-body simulations.

13 pages, 1 figure, ApJ in press

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Cited by in corpus (7)

• The Impact of Assembly Bias on the Galaxy Content of Dark Matter Halos
• Elucidating Galaxy Assembly Bias in SDSS
• The effects of assembly bias on cosmological inference from galaxy-galaxy lensing and galaxy clusters
• Statistics of Dark Matter Halos in the Excursion Set Peak Framework
• Voids and Halos in Voids statistics as a probe of the Expansion History of the Universe
• Accurate halo mass functions from the simplest excursion set theory
• Assembly bias in quadratic bias parameters of dark matter halos from forward modeling