Galaxy clustering and galaxy-galaxy lensing: a promising union to constrain cosmological parameters

Abstract

Galaxy clustering and galaxy–galaxy lensing probe the connection between galaxies and their dark matter haloes in complementary ways. Since the clustering of dark matter haloes depends on cosmology, the halo occupation statistics inferred from the observed clustering properties of galaxies are degenerate with the adopted cosmology. Consequently, different cosmologies imply different mass‐to‐light ratios for dark matter haloes. Galaxy–galaxy lensing, which yields direct constraints on the actual mass‐to‐light ratios, can therefore be used to break this degeneracy, and thus to constrain cosmological parameters. In this paper, we establish the link between galaxy luminosity and dark matter halo mass using the conditional luminosity function (CLF), Φ(L|M) dL, which gives the number of galaxies with luminosities in the range L± dL/2 that reside in a halo of mass M. We constrain the CLF parameters using the galaxy luminosity function and the luminosity dependence of the correlation lengths of galaxies. The resulting CLF models are used to predict the galaxy–galaxy lensing signal. For a cosmology that agrees with constraints from the cosmic microwave background, i.e. (Ωm, σ8) = (0.238, 0.734), the model accurately fits the galaxy–galaxy lensing data obtained from the Sloan Digital Sky Survey. For a comparison cosmology with (Ωm, σ8) = (0.3, 0.9), however, we can accurately fit the luminosity function and clustering properties of the galaxy population, but the model predicts mass‐to‐light ratios that are too high, resulting in a strong overprediction of the galaxy–galaxy lensing signal. We conclude that the combination of galaxy clustering and galaxy–galaxy lensing is a powerful probe of the galaxy–dark matter connection, with the potential to yield tight constraints on cosmological parameters. Since this method mainly probes the mass distribution on relatively small (non‐linear) scales, it is complementary to constraints obtained from the galaxy power spectrum, which mainly probes the large‐scale (linear) matter distribution.

Galaxy-galaxy lensing constraints on the relation between baryons and dark matter in galaxies in the Red Sequence Cluster Survey 2

“…When we fit a halo mass to the stacked shear signal of galaxies within a luminosity bin, the resulting mass is not equal to the mean halo mass, nor to the central mass of the original distribution (Tasitsiomi et al 2004;Mandelbaum et al 2005b;Cacciato et al 2009;Leauthaud et al 2010) because the distribution in halo mass is not uniform (in addition, the NFW profile itself depends on mass). It is useful to convert the measured lensing mass to the mean halo mass to allow comparison with simulations.…”

“…Different approaches to halo exclusion have been used in the literature. For example, Cacciato et al (2009) set the two-halo correlation function to zero below r 180 , which leads to a sharp truncation in the halo models. We follow the approach of Tinker et al (2005), which leads to a more natural smooth cut-off: the integral in Eq.…”

Evolution of the luminosity-to-halo mass relation of LRGs from a combined analysis of SDSS-DR10+RCS2

“…The halo model provides a useful framework in which to describe the stacked weak-lensing signal around galaxies (see e.g. Mandelbaum et al 2006b;Cacciato et al 2009Cacciato et al , 2014Miyatake et al 2015). It is based on a statistical description of dark matter properties, such as their average density profile, their abundance, and their large-scale bias, complemented with a statistical description of the way galaxies of a given luminosity populate dark matter haloes of different masses (also known as halo occupation statistics).…”

“…The three-dimensional comoving distance r is related to ω through r 2 = ω 2 l + ω 2 − 2ω l ω cos θ, with ω l the comoving distance to the lens and θ = R/D l the angular separation between lens and source (see Fig. 1 in Cacciato et al 2009). Note that the cross-correlation of galaxy to dark matter is evaluated at the average redshift of the lens galaxies.…”

Simultaneous measurement of cosmology and intrinsic alignments using joint cosmic shear and galaxy number density correlations

“…In doing so we incorporate several cosmological signals which have been considered before as promising probes of cosmology themselves, including galaxy clustering from photometric redshift surveys (Blake & Bridle 2005;Dolney et al 2006;Zhan 2006;Blake et al 2007;Padmanabhan et al 2007) galaxy-galaxy lensing (e.g. Schneider & Rix 1997;Guzik & Seljak 2001Seljak 2002;Seljak et al 2005;Yoo et al 2006;Johnston et al 2007;Cacciato et al 2009) and lensing magnification (Broadhurst et al 1995;Zhang & Pen 2005, 2006van Waerbeke 2010). We follow the ansatz outlined in Bernstein (2009) and extend the investigation by Bridle & King (2007) who considered the residual information content in galaxy shape correlations after marginalising over the parameters of two loglinear grid models representing the II and GI terms.…”