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

We study the evolution of the luminosity-to-halo mass relation of Luminous Red Galaxies (LRGs). We select a sample of 52 000 LOWZ and CMASS LRGs from the Baryon Oscillation Spectroscopic Survey (BOSS) SDSS-DR10 in the ~450 deg^2 that overlaps with imaging data from the second Red-sequence Cluster Survey (RCS2), group them into bins of absolute magnitude and redshift and measure their weak lensing signals. The source redshift distribution has a median of 0.7, which allows us to study the lensing signal as a function of lens redshift. We interpret the lensing signal using a halo model, from which we obtain the halo masses as well as the normalisations of the mass-concentration relations. We find that the concentration of haloes that host LRGs is consistent with dark matter only simulations once we allow for miscentering or satellites in the modelling. The slope of the luminosity-to-halo mass relation has a typical value of 1.4 and does not change with redshift, but we do find evidence for a change in amplitude: the average halo mass of LOWZ galaxies increases by 25_{-14}^{+16} % between z=0.36 and 0.22 to an average value of 6.43+/-0.52 x 10^13 h70^-1 Msun. If we extend the redshift range using the CMASS galaxies and assume that they are the progenitors of the LOWZ sample, we find that the average mass of LRGs increases by 80^{+39}_{-28} % between z=0.6 and 0.2Comment: 20 pages, 11 figures, accepted for publication in A&

Toy Models for Galaxy Formation versus Simulations

We describe simple useful toy models for key processes of galaxy formation in its most active phase, at z > 1, and test the approximate expressions against the typical behaviour in a suite of high-resolution hydro-cosmological simulations of massive galaxies at z = 4-1. We address in particular the evolution of (a) the total mass inflow rate from the cosmic web into galactic haloes based on the EPS approximation, (b) the penetration of baryonic streams into the inner galaxy, (c) the disc size, (d) the implied steady-state gas content and star-formation rate (SFR) in the galaxy subject to mass conservation and a universal star-formation law, (e) the inflow rate within the disc to a central bulge and black hole as derived using energy conservation and self-regulated Q ~ 1 violent disc instability (VDI), and (f) the implied steady state in the disc and bulge. The toy models provide useful approximations for the behaviour of the simulated galaxies. We find that (a) the inflow rate is proportional to mass and to (1+z)^5/2, (b) the penetration to the inner halo is ~50% at z = 4-2, (c) the disc radius is ~5% of the virial radius, (d) the galaxies reach a steady state with the SFR following the accretion rate into the galaxy, (e) there is an intense gas inflow through the disc, comparable to the SFR, following the predictions of VDI, and (f) the galaxies approach a steady state with the bulge mass comparable to the disc mass, where the draining of gas by SFR, outflows and disc inflows is replenished by fresh accretion. Given the agreement with simulations, these toy models are useful for understanding the complex phenomena in simple terms and for back-of-the-envelope predictions.Comment: Resubmitted to MNRAS after responding to referee's comments; Revised figure

On Combining Galaxy Clustering and Weak Lensing to Unveil Galaxy Biasing via the Halo Model

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 b_g and R_{gm}, over the range 0.1 Mpc/h < r_p < 30 Mpc/h, 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 a 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_{gm} = 1, for radii r > 1 - 5 Mpc/h, 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 occupation statistics and to unveil the origin of galaxy biasing we propose the use of the bias function Gamma_{gm}(r_p)=b_g(r_p)/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.Comment: 23 pages, 10 figures, submitted to MNRA

The Canadian Cluster Comparison Project: detailed study of systematics and updated weak lensing masses

Masses of clusters of galaxies from weak gravitational lensing analyses of ever larger samples are increasingly used as the reference to which baryonic scaling relations are compared. In this paper we revisit the analysis of a sample of 50 clusters studied as part of the Canadian Cluster Comparison Project. We examine the key sources of systematic error in cluster masses. We quantify the robustness of our shape measurements and calibrate our algorithm empirically using extensive image simulations. The source redshift distribution is revised using the latest state-of-the-art photometric redshift catalogs that include new deep near-infrared observations. Nonetheless we find that the uncertainty in the determination of photometric redshifts is the largest source of systematic error for our mass estimates. We use our updated masses to determine b, the bias in the hydrostatic mass, for the clusters detected by Planck. Our results suggest 1-b=0.76+-0.05(stat)}+-0.06(syst)}, which does not resolve the tension with the measurements from the primary cosmic microwave background.Comment: resubmitted to MNRAS after review by refere

Satellite Kinematics II: The Halo Mass-Luminosity Relation of Central Galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass-luminosity relation (MLR) of their corresponding central galaxies. In this paper we select a large sample of centrals and satellites from the Sloan Digital Sky Survey (SDSS) and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the $r$-band luminosity of the central galaxies. Using the analytical framework presented in Paper I, we use these data to infer {\it both} the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity, $\sigma_{\log M}$, also increases with increasing luminosity. As we demonstrate, this is consistent with $\sigma_{\log L}$, which reflects the scatter in the conditional probability function $P(L_c|M)$, being independent of halo mass. Our analysis of the satellite kinematics yields $\sigma_{\log L}=0.16\pm0.04$, in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by $\sigma_{\log L}$, is well constrained, is independent of halo mass, and is in good agreement with current models of galaxy formation.Comment: 17 pages, 12 figures, MNRAS submitte

Probing the dynamical state of galaxy clusters

We show how hydrostatic equilibrium in galaxy clusters can be quantitatively probed combining X-ray, SZ, and gravitational-lensing data. Our previously published method for recovering three-dimensional cluster gas distributions avoids the assumption of hydrostatic equilibrium. Independent reconstructions of cumulative total-mass profiles can then be obtained from the gas distribution, assuming hydrostatic equilibrium, and from gravitational lensing, neglecting it. Hydrostatic equilibrium can then be quantified comparing the two. We describe this procedure in detail and show that it performs well on progressively realistic synthetic data. An application to a cluster merger demonstrates how hydrostatic equilibrium is violated and restored as the merger proceeds.Comment: 10 pages, 6 figures, submitted to A&

Combining weak and strong lensing in cluster potential reconstruction

We propose a method for recovering the two-dimensional gravitational potential of galaxy clusters which combines data from weak and strong gravitational lensing. A first estimate of the potential from weak lensing is improved at the approximate locations of critical curves. The method can be fully linearised and does not rely on the existence and identification of multiple images. We use simulations to show that it recovers the surface-mass density profiles and distributions very accurately, even if critical curves are only partially known and if their location is realistically uncertain. We further describe how arcs at different redshifts can be combined, and how deviations from weak lensing can be included.Comment: 9 pages, 5 figures, A&A in press, changes to match the accepted versio

Satellite Kinematics I: A New Method to Constrain the Halo Mass-Luminosity Relation of Central Galaxies

Satellite kinematics can be used to probe the masses of dark matter haloes of central galaxies. In order to measure the kinematics with sufficient signal-to-noise, one uses the satellite galaxies of a large number of central galaxies stacked according to similar properties (e.g., luminosity). However, in general the relation between the luminosity of a central galaxy and the mass of its host halo will have non-zero scatter. Consequently, this stacking results in combining the kinematics of satellite galaxies in haloes of different masses, which complicates the interpretation of the data. In this paper we present an analytical framework to model satellite kinematics, properly accounting for this scatter and for various selection effects. We show that in the presence of scatter in the halo mass-luminosity relation, the commonly used velocity dispersion of satellite galaxies can not be used to infer a unique halo mass-luminosity relation. In particular, we demonstrate that there is a degeneracy between the mean and the scatter of the halo mass-luminosity relation. We present a new technique that can break this degeneracy, and which involves measuring the velocity dispersions using two different weighting schemes: host-weighting (each central galaxy gets the same weight) and satellite-weighting (each central galaxy gets a weight proportional to its number of satellites). The ratio between the velocity dispersions obtained using these two weighting schemes is a strong function of the scatter in the halo mass-luminosity relation, and can thus be used to infer a unique relation between light and mass from the kinematics of satellite galaxies.Comment: 8 pages, 3 figures, MNRAS submitte