THE EXCURSION SET THEORY OF HALO MASS FUNCTIONS, HALO CLUSTERING, AND HALO GROWTH

By A. Zentner. 2006

188 citations recorded by the source corpus.

I review the excursion set theory with particular attention toward applications to cold dark matter halo formation and growth, halo abundance, and halo clustering. After a brief introduction to notation and conventions, I begin by recounting the heuristic argument leading to the mass function of bound objects given by Press and Schechter. I then review the more formal derivation of the Press–Schechter halo mass function that makes use of excursion sets of the density field. The excursion set formalism is powerful and can be applied to numerous other problems. I review the excursion set formalism for describing both halo clustering and bias and the properties of void regions. As one of the most enduring legacies of the excursion set approach and one of its most common applications, I spend considerable time reviewing the excursion set theory of halo growth. This section of the review culminates with the description of two Monte Carlo methods for generating ensembles of halo mass accretion histories. In the last section, I emphasize that the standard excursion set approach is the result of several simplifying assumptions. Dropping these assumptions can lead to more faithful predictions and open excursion set theory to new applications. One such assumption is that the height of the barriers that define collapsed objects is a constant function of scale. I illustrate the implementation of the excursion set approach for barriers of arbitrary shape. One such application is the now well-known improvement of the excursion set mass function derived from the "moving" barrier for ellipsoidal collapse. I also emphasize that the statement that halo accretion histories are independent of halo environment in the excursion set approach is not a general prediction of the theory. It is a simplifying assumption. I review the method for constructing correlated random walks of the density field in the more general case. I construct a simple toy model to illustrate that excursion set theory (with a constant barrier height) makes a simple and general prediction for the relation between halo accretion histories and the large-scale environments of halos: regions of high density preferentially contain late-forming halos and conversely for regions of low density. I conclude with a brief discussion of the importance of this prediction relative to recent numerical studies of the environmental dependence of halo properties.

Subfields: Astronomy and Astrophysics, Instrumentation, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/adb12cd8b66c2c515d1998a3bb872a91bb4f9828

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Citations in the corpus

Formation of Galaxy Clusters (2012, background): “…where 〈δ2R〉 ≡ σ2(R) = 1 (2π)3 ∫ P(k)|W̃(k,R)|2d3k, (1) whereW̃(k,R) is the Fourier transform of the window (filter) functionW(r ,R), such that δR(k) = δ(k)W̃(k,R) [see, e.g., Zentner (2007) or Mo, van den Bosch & White (2010) for details on the definition ofP(k) and choices of window function].”
Dynamical friction and galaxy merging time-scales (2007, unknown): “6; Lacey & Cole 1993; Zentner 2007; Fakhouri & Ma 2007, in prep).”
THE HALO MASS FUNCTION FROM EXCURSION SET THEORY. I. GAUSSIAN FLUCTUATIONS WITH NON-MARKOVIAN DEPENDENCE ON THE SMOOTHING SCALE (2009, background): “…set theory (Peacock & Heavens 1990; Bond et al. 1991) are able to reproduce, at least qualitatively, several properties of dark matter halos such as their conditional and un-conditional mass function, halo accretion histories, merger rates and halo bias (see Zentner (2007) for a recent review).”
Lensing is Low: Cosmology, Galaxy Formation, or New Physics? (2016, background): “…by 35 per cent while keeping the bias fixed. addition to halo mass, the strength of halo clustering depends on other properties such as halo age, spin and concentration (Gao, Springel & White 2005; Wechsler et al. 2006; Gao & White 2007; Zentner 2007; Dalal et al. 2008; Lacerna & Padilla 2011).”
Resolving cosmic structure formation with the Millennium-II simulation (2009, background): “The most successful model for dark matter halo formation (Press & Schechter 1974; Bond et al. 1991; Lacey & Cole 1993; Sheth et al. 2001; see Zentner 2007 for a recent review of extended Press-Schechter theory) relates the abundance of halos at mass M and redshift z to the initial power spectrum of…”
Galaxy assembly bias: a significant source of systematic error in the galaxy–halo relationship (2013, background): “Relaxing this assumption, excursion set theory also predicts a correlation between halo formation time and halo environment (e.g., Zentner 2007; Dalal et al. 2008).”
Small-Scale Challenges to the ΛCDM Paradigm (2017, background): “…mass, with the most massive subhalos seen at mmax ∼ 0.2Mhost. et al. 1991; Cole 1991; Sheth, Mo & Tormen 2001), and this extended Press-Schechter (EPS) theory yields abundances of dark matter halos that are perhaps surprisingly accurate (see Zentner 2007 for a comprehensive review of EPS theory).”