On the environmental dependence of halo formation

By R. Sheth, Giuseppe Tormen Pittsburgh, Padova. 2004

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ABSTRACT A generic prediction of hierarchical gravitationalclustering models is that the distribu-tion of halo formation times should depend relatively strongly on halo mass, massivehaloes forming more recently, and depend only weakly, if at all, on the large scaleenvironment of the haloes. We present a novel test of this assumption which uses thestatistics of weighted or ‘marked’ correlations, which prove to be particularly well-suited to detecting and quantifying weak correlations with environment. We ﬁnd thatclose pairs of haloes form at slightly higher redshifts than do more widely separatedhalo pairs, suggesting that haloes in dense regions form at slightly earlier times thando haloes of the same mass in less dense regions. The environmental trends we ﬁndare useful for models which relate the properties of galaxies to the formation historiesof the haloes which surround them.Key words: galaxies: clustering – cosmology: theory – dark matter. 1 INTRODUCTIONThe excursion set model of hierarchical clustering (Epstein1983; Bond et al. 1991) has been remarkably successful. Itprovides useful analytic approximations for the abundanceof haloes of mass m at time t (Bond et al. 1991; Sheth,Mo & Tormen 2001), for the conditional mass function ofm haloes at t which are later (at T > t) in more massivehaloes M > m (Bond et al. 1991; Lacey & Cole 1993; Sheth& Tormen 2002), for the abundance of haloes as a functionof the larger scale environment (Mo & White 1996; Lemson& Kauﬀmann 1999; Sheth & Tormen 2002) for the distribu-tion of halo formation times (Lacey & Cole 1993) and masses(Nusser & Sheth 1999; Sheth & Tormen 2004). Here, forma-tion is typically deﬁned as that time when the most massiveprogenitor contains at least half the ﬁnal mass.In the simplest and most used approximation, this ap-proach ignores most correlations between diﬀerent spatialscales. In this approximation, the approach predicts thatthere should be no correlation between halo formation andthe large scale environment in which the halo sits (White1996). This is because, in the model, formation refers toa smaller mass than the ﬁnal virial mass, and hence toa smaller spatial scale than that associated with the La-grangian radius of an object, whereas the larger scale envi-ronment, by deﬁnition, refers to scales which are larger thanthat of the halo.Lemson & Kauﬀmann (1999) presented evidence frommeasurements in numerical simulations of clustering thathalo formation times were indeed independent of environ-ment. They interpreted this as evidence that the excursionset neglect of correlations was justiﬁed. (Lemson & Kauﬀ-mann also presented evidence that a number of other physi-cal properties of haloes were also independent of environ-ment, and this evidence has been used to justify an as-sumption which enormously simpliﬁes semi-analytic mod-els of galaxy formation: that the properties of galaxies aredetermined by the haloes in which they form, and not bythe surrounding larger-scale environment.) Their conclusionis somewhat surprising for the following reason. It is quitewell established that the ratio of massive to low mass haloesis larger in dense regions, and that the excursion set modelis able to quantify this dependence quite well (see the refer-ences given earlier). It is also well established that, on aver-age, low mass haloes form at higher redshifts (see referencesgiven earlier). Together, these suggest that if one averagesover the entire range of halo masses in any given region,then the mean formation time in dense regions should beshifted to lower redshifts, simply because these regions con-tain more massive haloes which, on average, form later. InFigure 4 of their paper, Lemson & Kauﬀmann averaged overthe entire range of halo masses accessible to them in theirsimulations, and found no dependence of formation time onenvironement; at face value, this is inconsistent with thesimplest excursion set prediction!The main goal of this paper is to repeat the test for envi-ronmental eﬀects on halo formation. Section 2 shows that asimple plot of formation time versus local density does notshow strong trends, suggesting that the excursion set ap-proximation is rather accurate. But then, Section 3 presents

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Citations in the corpus

Halo Assembly Bias in Hierarchical Structure Formation (2008, background): “…2006; Bett et al. 2007; Wetzel et al. 2007; Jing, Suto & Mo 2007; Gao & White 2007; Angulo, Baugh & Lacey 2008) Using a marked correlation function, Sheth & Tormen (2004) found that close halo pairs tend to have earlier formation times than more distant pairs, work which was extended and…”
A primer on hierarchical galaxy formation: the semi-analytical approach (2006, result): “However, some of these results have recently been reanalysed and found to show evidence in favour of an environmental dependence of halo properties (Sheth & Tormen 2004).”
THE SPIN AND ORIENTATION OF DARK MATTER HALOS WITHIN COSMIC FILAMENTS (2009, background): “In a recent study, using high-resolution N-body simulations, Gao et al. (2005) found that the halo clustering strength not only depends on the masses of the halos but also on their formation times (see also Sheth & Tormen 2004; Wang et al. 2007; Dalal et al. 2008; Hahn et al. 2009).”
Statistics of Physical Properties of Dark Matter Clusters (2005, background): “As demonstrated by Sheth & Tormen (2004), halos in dense regions accumulate their mass earlier than their counterparts in lower density regions.”
The evolution of dark matter halo properties in clusters, filaments, sheets and voids (2007, background): “In detail, us- ⋆ E-mail: hahn@phys.ethz.ch ing marked statistics, Sheth & Tormen (2004) find evidence that haloes of a given mass form earlier in dense regions.”
Formation and Evolution of Galaxy Dark Matter Halos and Their Substructure (2007, background): “Such correlations have indeed been quantified recently in terms of stronger clustering of early forming sub-M∗ halos (Gao et al. 2005) and as earlier median formation times in high density environments (Sheth & Tormen 2004; Harker et al. 2006).”
The Luminosity and Color Dependence of the Galaxy Correlation Function (2004, background): “HOD 23 We implicitly assume that halos of the samemass in different environments have, on average, the same galaxy populations, as expected on the basis of fairly general theoretical arguments (Lemson & Kauffmann 1999; Berlind et al. 2003; Sheth & Tormen 2004).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey:a large sample of mock galaxy catalogues (2012, background): “We also did not include assembly bias effects (Sheth & Tormen 2004, Croft et al. 2011) in our mocks, but kept the concentration parameter and HOD independent of the environment.”
Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, background): “In particular, numerical simulations show that the concentrations, c, for haloes of mass M at redshift z follow a log-normal distribution P (c|M, z) dc = 1√ 2π σlnc exp [ − (ln c− ln c̄) 2 2σ2lnc ] dc c , (88) where c̄ = c̄(M, z) is the median halo concentration for a halo of mass M at redshift z, a”
GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY (2010, background): “…depends on large-scale environment as well as halo mass, since halo concentrations and assembly histories show some environmental correlations (Sheth & Tormen 2004; Gao, Springel & White 2005; Harker et al. 2006; Wechsler et al. 2006; Zhu et al. 2006; Croton, Gao & White 2007; Jing, Suto, &…”
Building merger trees from cosmological N-body simulations. Towards improving galaxy formation model (2009, background): “Monte-Carlo merging trees not only do not contain position information but they also fail to describe environment effects on low mass halo assembly (Sheth & Tormen 2004; Wechsler et al. 2006; Reed et al. 2007; Zhu et al. 2006).”
GALAXIES IN ΛCDM WITH HALO ABUNDANCE MATCHING: LUMINOSITY–VELOCITY RELATION, BARYONIC MASS–VELOCITY RELATION, VELOCITY FUNCTION, AND CLUSTERING (2010, background): “…can reproduce some basic environmen tal relations such as the morphology–density relation and the dependence of galaxy clustering on the luminosity of galaxies (e.g., Conroy et al. 2006) because of the correlation of environ ment with the average halo mass (Sheth et al. 2001; Sheth & Tormen 2004).”
Halo assembly bias and its effects on galaxy clustering (2006, methodology): “Earlier studies had missed the strength of this dependence (e.g. Lemson & Kauffmann 1999; Sheth & Tormen 2004), apparently because they were based on simulations of insufficient size and resolution to reliably reach the relevant regime.”
The Dependence of Halo Clustering on Halo Formation History, Concentration, and Occupation (2005, background): “Sheth & Tormen (2004), Gao et al. (2005), and Harker et al. (2006) have emphasized that the trend with formation time indicates that using the halo model to estimate clustering can be problematic.”
The age dependence of halo clustering (2005, result): “A formation time dependence was seen, however, in the mark correlation analysis of Sheth & Tormen (2004), although these authors characterised the effect as “slight”.”
Properties of dark matter haloes in clusters, filaments, sheets and voids (2006, background): “Using marked statistics, Sheth & Tormen (2004) found evidence that haloes of a given mass form earlier in dense regions.”
Concentration, spin and shape of dark matter haloes: Scatter and the dependence on mass and environment (2006, methodology): “All these results seem to overrule the finding by LK99, and seem to suggest that dark matter properties depend rather sensitively on their large-scale environment.”
A marked correlation function analysis of halo formation times in the Millennium Simulation (2005, methodology): “…(1999) in which no signal is apparent, despite the simulation being the same as the one which showed evidence of environmental dependence in the marked correlation function analysis of Sheth & Tormen (2004): both studies used th GIF simulations (Jenkins et al. 1998; Kauffmann et al. 1999).”