Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions

By Chung-Pei Ma, J. Fry. 2000

289 citations recorded by the source corpus.

We present an analytic model for the fully nonlinear two- and three-point correlation functions of the cosmological mass density field, and their Fourier transforms, the mass power spectrum and bispectrum. The model is based on physical properties of dark matter halos, with the three main model inputs being analytic halo density profiles, halo mass functions, and halo-halo spatial correlations, each of which has been well studied in the literature. We demonstrate that this new model can reproduce the power spectrum and bispectrum computed from cosmological simulations of both an n = -2 scale-free model and a low-density cold dark matter model. To enhance the dynamic range of these large simulations, we use the synthetic-halo replacement technique of Ma & Fry, in which the original halos with numerically softened cores are replaced by synthetic halos of realistic density profiles. At high wavenumbers, our model predicts a slope for the nonlinear power spectrum different from the often-used fitting formulas in the literature based on the stable-clustering assumption. Our model also predicts a three-point amplitude, Q, that is scale dependent, in contrast to the popular hierarchical clustering assumption. This model provides a rapid way to compute the mass power spectrum and bispectrum over all length scales where the input halo properties are valid. It also provides a physical interpretation of the clustering properties of matter in the universe.

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

View Paper: https://www.semanticscholar.org/paper/d87d4cfd0b340448bc83ec9918bf5adf70fdef71

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Citations in the corpus

Cosmology with massive neutrinos I: towards a realistic modeling of the relation between matter, haloes and galaxies (2013, methodology): “The HOD is a framework used to link the distribution of galaxies to that of dark matter haloes [59–65].”
The Intermediate-Scale Clustering of Luminous Red Galaxies (2004, background): “…the clustering of galaxies within single halos and the clustering between halos (Kauffmann et al. 1997, 1999; Jing et al. 1998; Benson et al. 2000; Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Berlind et al. 2003; Magliocchetti & Porciani…”
The Halo Occupation Distribution and the Physics of Galaxy Formation (2002, methodology): “…these studies have utilized the power of the HOD formalism and the related ‘‘ halo model ’’ of dark matter clustering as a tool for analytic calculations (Ma & Fry 2000; Seljak 2000; Benson 2001; Scoccimarro et al. 2001; Sheth et al. 2001a; White 2001; Cooray & Sheth 2002), drawing on methods…”
GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY (2010, methodology): “…of galaxy clustering has been enhanced through development of the Halo Occupation Distribution (HOD) framework (e.g., Jing, Mo, & Börner 1998; Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Cooray & Sheth 2002; Yang, Mo, & van den Bosch…”
The Luminosity and Color Dependence of the Galaxy Correlation Function (2004, methodology): “Three-point correlations probe the high-mass regime of P(N |M ) (Ma & Fry 2000; Scoccimarro et al. 2001; LUMINOSITY AND COLOR DEPENDENCE 25No. 1, 2005 Takada & Jain 2003), and they provide a diagnostic for the amplitude of dark matter fluctuations (Fry 1994; Feldman et al. 2001; Verde et al. 2002).”
Constraining galaxy formation and cosmology with the conditional luminosity function of galaxies (2002, unknown): “The Fourier transform of the one-halo term is given by P 1hdm(k) = ∫ ∞ 0 n(M) [ δ̂(M ; k) ]2 dM, (31) where δ̂(M ; k) = ∫ ∞ 0 ρ(r) ρ̄ e−ik·rd3r (32) is the Fourier transform of the halo density profile ρ(r) (e.g. Neyman & Scott 1952; McClelland & Silk 1977; Ma & Fry 2000).”
Constraining primordial non-Gaussianity with future galaxy surveys (2011, methodology): “We compute the non-linear mass power spectrum using the halo model developed by Ma & Fry (2000); Seljak (2000) based on an original idea by McClelland & Silk (1977).”
REVISING THE HALOFIT MODEL FOR THE NONLINEAR MATTER POWER SPECTRUM (2012, methodology): “Smith et al. (2003, hereafter S03) proposed a new model of P (k), the so-called halofit model, which is based on a halo model of structure formation (e.g., Ma & Fry 2000; Seljak 2000; Cooray & Sheth 2002).”
Detailed cluster lensing profiles at large radii and the impact on cluster weak lensing studies (2011, methodology): “The Fourier transform of a dark halo density profile constitute an important ingredient of the so-called halo model approach (e.g., Seljak 2000; Ma & Fry 2000; Scoccimarro et al. 2001).”
Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, methodology): “This is a well known effect that has already been discussed in numerous studies of the halo model (e.g., e.g., Ma & Fry 2000; Seljak 2000; Scoccimarro et al. 2001; Smith et al. 2003; Cole et al. 2005; Hayashi & White 2008).”
Weak Gravitational Lensing (2012, unknown): “[51, 52, 78, 19]).”
Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies (2004, methodology): “The Halo Occupation Distribution (HOD) has emerged as a powerful framework for describing galaxy bias and modeling galaxy clustering (e.g., Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002).”
On Departures from a Power Law in the Galaxy Correlation Function (2003, methodology): “…relation between galaxies and mass, we adopt the general framework of the ‘‘halo occupation distribution’’ (HOD) and use a modified form of the calculational methods introduced by Ma & Fry (2000), Peacock & Smith (2000), Seljak (2000), Scoccimarro et al. (2001), and Berlind & Weinberg (2002).”
How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering (2000, background): “(53) This generalizes the derivation in Ma & Fry (2000b) for galaxies.”
The Dark Side of the Halo Occupation Distribution (2003, background): “The description of different elements of the halo model can be found in several recent papers (e.g., Seljak 2000; Ma & Fry 2000; Peacock & Smith 2000; Scoccimarro et al. 2001; Sheth et al. 2001a, 2001b; Berlind & Weinberg 2002; Cooray & Sheth 2002; Yang et al. 2003).”
Galaxy Clustering in Early Sloan Digital Sky Survey Redshift Data (2002, unknown): “A ‘‘ halo occupation ’’ analysis of galaxy clustering (see, e.g., Benson et al. 1999; Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Berlind & Weinberg 2001; Scoccimarro et al. 2001) implies that the correlation function at submegaparsec scales is dominated by pairs of galaxies that reside in the”
Linking early‐ and late‐type galaxies to their dark matter haloes (2002, background): “…k2 sin kr kr ∫ ∞ 0 dM n(M) [ δ̂(M ; k) ]2 (A4) where δ̂(M ; k) = ∫ rv 0 ρ(r) ρ̄ e−ik·rd3r (A5) is the Fourier transform of the halo density profile ρ(r), truncated at the virial radius rv (e.g., Neyman & Scott 1952; McClelland & Silk 1977; Seljak 2000; Ma & Fry 2000; Scoccimarro et al. 2001).”
There's no place like home? Statistics of Milky Way-mass dark matter haloes (2009, background): “This scatter is also a fundamental input parameter for halo occupation distribution (HOD) models (e.g., Ma & Fry 2000; Peacock & Smith 2000; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002).”