Halo model analysis of cluster statistics

Eduardo Rozo, Scott Dodelson, Joshua A. Frieman

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass-tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass-tracer is chosen to be the number of satellite galaxies assigned to a cluster. Such a survey can strongly constrain σ<inf>8</inf> (Δσ<inf>8</inf> ≈ 0.05), the power law index α where 〈N<inf>gal</inf>|m〉 = (m/M<inf>1</inf>) <sup>α</sup> (Δα ≈ 0.03), and perhaps even the Hubble parameter (Δh ≈ 0.07). We find cluster abundances and bias are not well suited for constraining Ω<inf>m</inf> or the amplitude M<inf>1</inf>. We also find that without bias information σ<inf>8</inf> and α are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass-tracer used in the survey.

Original languageEnglish (US)
Article number083008
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume70
Issue number8
DOIs
StatePublished - 2004
Externally publishedYes

Fingerprint

Model Analysis
halos
statistics
Statistics
tracers
Scatter
formalism
scaling
Scaling Relations
Correlation Matrix
Galaxies
completeness
Degeneracy
stems
Completeness
Power Law
purity
Scaling
galaxies
Dependent

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics
  • Mathematical Physics

Cite this

Halo model analysis of cluster statistics. / Rozo, Eduardo; Dodelson, Scott; Frieman, Joshua A.

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 70, No. 8, 083008, 2004.

Research output: Contribution to journalArticle

@article{fa6f728cde5c4b68b7d3abde7f16afae,
title = "Halo model analysis of cluster statistics",
abstract = "We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass-tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass-tracer is chosen to be the number of satellite galaxies assigned to a cluster. Such a survey can strongly constrain σ8 (Δσ8 ≈ 0.05), the power law index α where 〈Ngal|m〉 = (m/M1) α (Δα ≈ 0.03), and perhaps even the Hubble parameter (Δh ≈ 0.07). We find cluster abundances and bias are not well suited for constraining Ωm or the amplitude M1. We also find that without bias information σ8 and α are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass-tracer used in the survey.",
author = "Eduardo Rozo and Scott Dodelson and Frieman, {Joshua A.}",
year = "2004",
doi = "10.1103/PhysRevD.70.083008",
language = "English (US)",
volume = "70",
journal = "Physical review D: Particles and fields",
issn = "0556-2821",
publisher = "American Institute of Physics",
number = "8",

}

TY - JOUR

T1 - Halo model analysis of cluster statistics

AU - Rozo, Eduardo

AU - Dodelson, Scott

AU - Frieman, Joshua A.

PY - 2004

Y1 - 2004

N2 - We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass-tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass-tracer is chosen to be the number of satellite galaxies assigned to a cluster. Such a survey can strongly constrain σ8 (Δσ8 ≈ 0.05), the power law index α where 〈Ngal|m〉 = (m/M1) α (Δα ≈ 0.03), and perhaps even the Hubble parameter (Δh ≈ 0.07). We find cluster abundances and bias are not well suited for constraining Ωm or the amplitude M1. We also find that without bias information σ8 and α are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass-tracer used in the survey.

AB - We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass-tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass-tracer is chosen to be the number of satellite galaxies assigned to a cluster. Such a survey can strongly constrain σ8 (Δσ8 ≈ 0.05), the power law index α where 〈Ngal|m〉 = (m/M1) α (Δα ≈ 0.03), and perhaps even the Hubble parameter (Δh ≈ 0.07). We find cluster abundances and bias are not well suited for constraining Ωm or the amplitude M1. We also find that without bias information σ8 and α are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass-tracer used in the survey.

UR - http://www.scopus.com/inward/record.url?scp=84927743509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927743509&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.70.083008

DO - 10.1103/PhysRevD.70.083008

M3 - Article

AN - SCOPUS:84927743509

VL - 70

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

M1 - 083008

ER -