The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth

Abstract

I review the excursion set theory (EST) of dark matter halo formation and clustering. I recount the Press-Schechter argument for the mass function of bound objects and review the derivation of the Press-Schechter mass function in EST. The EST formalism is powerful and can be applied to numerous problems. I review the EST of halo bias and the properties of void regions. I spend considerable time reviewing halo growth in the EST. This section culminates with descriptions of two Monte Carlo methods for generating halo mass accretion histories. In the final section, I emphasize that the standard EST approach is the result of several simplifying assumptions. Dropping these assumptions can lead to more faithful predictions and a more versatile formalism. One such assumption is the constant height of the barrier for nonlinear collapse. I review implementations of the excursion set approach with arbitrary barrier shapes. An application of this is the now well-known improvement to standard EST that follows from the ellipsoidal-collapse barrier. Additionally, I emphasize that the statement that halo accretion histories are independent of halo environments is a simplifying assumption, rather than a prediction of the theory. I review the method for constructing correlated random walks of the density field in more general cases. I construct a simple toy model with correlated walks and I show that excursion set theory makes a qualitatively simple and general prediction for the relation between halo accretion histories and halo environments: regions of high density preferentially contain late-forming halos and conversely for regions of low density. I conclude with a brief discussion of this prediction in the context of recent numerical studies of the environmental dependence of halo properties. (Abridged)

62 pages, 19 figures. Review article based on lectures given at the Sixth Summer School of the Helmholtz Institute for Supercomputational Physics. Accepted for Publication in IJMPD. Comments Welcome

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