On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

M. Cacciato; O. Lahav; F. C. van den Bosch; H. Hoekstra; A. Dekel

On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

M. Cacciato^*, O. Lahav, F. C. van den Bosch, H. Hoekstra, A. Dekel

^*Corresponding author for this work

Racah Institute of Physics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Galaxies are (biased) tracers of the dark matter in the Universe. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, b_g(r_p), and the galaxy-dark matter cross-correlation function, R_gm(r_p), where r_p is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and Rgm, over the range 0.1 ≤ r_p ≤ 30 h^-1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with R_g = 1, for radii r = 1-5 h^-1 Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function γ_gm(r_p) = b_g(rp)/R_gm(r_p). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.

Original language	English
Title of host publication	Relativity in Fundamental Astronomy
Subtitle of host publication	Dynamics, Reference Frames, and Data Analysis
Editors	Sergei A. Klioner, Michael H. Soffel, P. Kenneth Seidelmann
Pages	566-587
Number of pages	22
Edition	S261
State	Published - Apr 2009

Publication series

Name	Proceedings of the International Astronomical Union
Number	S261
Volume	5
ISSN (Print)	1743-9213
ISSN (Electronic)	1743-9221

Keywords

Haloes - dark matter - large-scale structure of Universe
Methods
Statistical - galaxies

Cite this

Cacciato, M., Lahav, O., van den Bosch, F. C., Hoekstra, H., & Dekel, A. (2009). On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model. In S. A. Klioner, M. H. Soffel, & P. K. Seidelmann (Eds.), Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis (S261 ed., pp. 566-587). (Proceedings of the International Astronomical Union; Vol. 5, No. S261).

Cacciato, M. ; Lahav, O. ; van den Bosch, F. C. et al. / On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model. Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. editor / Sergei A. Klioner ; Michael H. Soffel ; P. Kenneth Seidelmann. S261. ed. 2009. pp. 566-587 (Proceedings of the International Astronomical Union; S261).

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title = "On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model",

abstract = "Galaxies are (biased) tracers of the dark matter in the Universe. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, bg(rp), and the galaxy-dark matter cross-correlation function, Rgm(rp), where rp is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and Rgm, over the range 0.1 ≤ rp ≤ 30 h-1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with Rg = 1, for radii r = 1-5 h-1 Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function γgm(rp) = bg(rp)/Rgm(rp). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.",

keywords = "Haloes - dark matter - large-scale structure of Universe, Methods, Statistical - galaxies",

author = "M. Cacciato and O. Lahav and {van den Bosch}, {F. C.} and H. Hoekstra and A. Dekel",

year = "2009",

month = apr,

language = "אנגלית",

isbn = "9780521764810",

series = "Proceedings of the International Astronomical Union",

number = "S261",

pages = "566--587",

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Cacciato, M, Lahav, O, van den Bosch, FC, Hoekstra, H & Dekel, A 2009, On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model. in SA Klioner, MH Soffel & PK Seidelmann (eds), Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. S261 edn, Proceedings of the International Astronomical Union, no. S261, vol. 5, pp. 566-587.

On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model. / Cacciato, M.; Lahav, O.; van den Bosch, F. C. et al.
Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. ed. / Sergei A. Klioner; Michael H. Soffel; P. Kenneth Seidelmann. S261. ed. 2009. p. 566-587 (Proceedings of the International Astronomical Union; Vol. 5, No. S261).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

AU - Cacciato, M.

AU - Lahav, O.

AU - van den Bosch, F. C.

AU - Hoekstra, H.

AU - Dekel, A.

PY - 2009/4

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N2 - Galaxies are (biased) tracers of the dark matter in the Universe. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, bg(rp), and the galaxy-dark matter cross-correlation function, Rgm(rp), where rp is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and Rgm, over the range 0.1 ≤ rp ≤ 30 h-1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with Rg = 1, for radii r = 1-5 h-1 Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function γgm(rp) = bg(rp)/Rgm(rp). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.

AB - Galaxies are (biased) tracers of the dark matter in the Universe. This mapping can be conveniently divided into two parts: the connection between galaxies and dark matter haloes (halo occupation statistics) and the relation between haloes and the underlying matter distribution. The former is the focus of this paper in which we formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, bg(rp), and the galaxy-dark matter cross-correlation function, Rgm(rp), where rp is the projected distance. We use the analytical halo model to predict how the scale dependence of bg and Rgm, over the range 0.1 ≤ rp ≤ 30 h-1 Mpc, depends on the non-linearity and stochasticity in halo occupation models. In particular, we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo and the Poisson character of the probability to have a certain number of satellite galaxies in the halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real space, we find that galaxy bias becomes scale independent, with Rg = 1, for radii r = 1-5 h-1 Mpc, depending on luminosity. However, galaxy bias is scale dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo model and to unveil the origin of galaxy biasing, we propose the use of the bias function γgm(rp) = bg(rp)/Rgm(rp). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.

KW - Haloes - dark matter - large-scale structure of Universe

KW - Methods

KW - Statistical - galaxies

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A2 - Soffel, Michael H.

A2 - Seidelmann, P. Kenneth

ER -

Cacciato M, Lahav O, van den Bosch FC, Hoekstra H, Dekel A. On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model. In Klioner SA, Soffel MH, Seidelmann PK, editors, Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. S261 ed. 2009. p. 566-587. (Proceedings of the International Astronomical Union; S261).

On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model

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