The Effects of the Peak‐Peak Correlation on the Peak Model of Hierarchical Clustering

Manrique, Alberto; Raig, A.; Solanes, J. M.; González-Casado, Guillermo; Stein, Petra; Salvador-Solé, E.

doi:10.1086/305662

Cited by 29 publications

(39 citation statements)

References 14 publications

(8 reference statements)

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“…At smaller ν, however, this expression differs from equation (12). If the initial spectrum of density fluctuations was a power law, P(k) ∝ k n , then equation (14) for the mass function associated with peaks becomes Note that this expression explicitly depends on the shape of the power spectrum.…”

Section: Peaks In Gaussian Random Fieldsmentioning

confidence: 96%

“…Modifying the peaks mass function to include the effects of ellipsoidal collapse can be done by using the mass dependent δ ec ( m ) when identifying peaks; this is relatively straightforward and the results are not shown here. Extending the peaks model to provide a description of the forest of merger histories remains an open problem (but see Manrique et al [14] for an initial attempt to do this). Also, I have not seen any discussion of how one might include a mass dependent δ ec ( m ) into the Smoluchowski binary merger model of the mass function.…”

Section: The Mass Function and Merger Histories Of Collapsed Objectsmentioning

confidence: 99%

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A Random Walk through Models of Nonlinear Clustering

Sheth

2001

Annals of the New York Academy of Sciences

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Section: Peaks In Gaussian Random Fieldsmentioning

confidence: 96%

Section: The Mass Function and Merger Histories Of Collapsed Objectsmentioning

confidence: 99%

A Random Walk through Models of Nonlinear Clustering

Sheth

2001

Annals of the New York Academy of Sciences

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“…Since these do not explicitly use the properties of random walks, we did not include them in the list above. Quite different approaches to estimating the mass function (Manrique & Salvador‐Sole 1995, 1996; Lee & Shandarin 1998) and the merger rate (Manrique et al 1998; Hanami 2001) have also been presented in the literature, but we will not describe them further here.…”

Section: Introductionmentioning

confidence: 99%

An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier

Sheth

Tormen

2002

Monthly Notices of the Royal Astronomical Society

916

1,210

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The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the non-linear processes of collapse and virialization are modelled. We present simple analytic approximations that allow us to compare the excursion set predictions associated with spherical and ellipsoidal collapse. In particular, we present formulae for the universal unconditional mass function of bound objects and the conditional mass function which describes the mass function of the progenitors of haloes in a given mass range today. We show that the ellipsoidal collapse based moving barrier model provides a better description of what we measure in the numerical simulations than the spherical collapse based constant barrier model, although the agreement between model and simulations is better at large lookback times. Our results for the conditional mass function can be used to compute accurate approximations to the local-density mass function, which quantifies the tendency for massive haloes to populate denser regions than less massive haloes. This happens because low-density regions can be thought of as being collapsed haloes viewed at large lookback times, whereas high-density regions are collapsed haloes viewed at small lookback times. Although we have applied our analytic formulae only to two simple barrier shapes, we show that they are, in fact, accurate for a wide variety of moving barriers. We suggest how they can be used to study the case in which the initial dark matter distribution is not completely cold

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“…[62][63][64], for numerical studies of this association). Peak abundances, profiles, and correlation functions in real and redshift space have been studied in the literature [36,[65][66][67][68][69][70][71][72][73][74][75]. Some of these results have been used to interpret the abundance and clustering of rich clusters [42,[76][77][78][79][80], constrain the power spectrum of mass fluctuations [81,82], and study evolution bias [83] and assembly bias [84].…”

Section: Introductionmentioning

confidence: 99%

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

2010

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Models of galaxy and halo clustering commonly assume that the tracers can be treated as a continuous field locally biased with respect to the underlying mass distribution. In the peak model pioneered by Bardeen et al. (1986), one considers instead density maxima of the initial, Gaussian mass density field as an approximation to the formation site of virialized objects. In this paper, the peak model is extended in two ways to improve its predictive accuracy. Firstly, we derive the two-point correlation function of initial density peaks up to second order and demonstrate that a peak-background split approach can be applied to obtain the k-independent and k-dependent peak bias factors at all orders. Secondly, we explore the gravitational evolution of the peak correlation function within the Zel'dovich approximation. We show that the local (Lagrangian) bias approach emerges as a special case of the peak model, in which all bias parameters are scale-independent and there is no statistical velocity bias. We apply our formulae to study how the Lagrangian peak biasing, the diffusion due to large scale flows and the mode-coupling due to nonlocal interactions affect the scale dependence of bias from small separations up to the baryon acoustic oscillation (BAO) scale. For 2σ density peaks collapsing at z = 0.3, our model predicts a ∼5% residual scale-dependent bias around the acoustic scale that arises mostly from first-order Lagrangian peak biasing (as opposed to second-order gravity mode-coupling). We also search for a scale dependence of bias in the large scale auto-correlation of massive halos extracted from a very large N-body simulation provided by the MICE collaboration. For halos with mass M 10 14 M⊙/h, our measurements demonstrate a scale-dependent bias across the BAO feature which is very well reproduced by a prediction based on the peak model.

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The Effects of the Peak‐Peak Correlation on the Peak Model of Hierarchical Clustering

Cited by 29 publications

References 14 publications

A Random Walk through Models of Nonlinear Clustering

A Random Walk through Models of Nonlinear Clustering

An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

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