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.

We use the kinematics of satellite galaxies that orbit around the central galaxy in a dark matter halo to infer the scaling relations between halo mass and central galaxy properties. Using galaxies from the Sloan Digital Sky Survey, we investigate the halo mass–luminosity relation (MLR) and the halo mass–stellar mass relation (MSR) of central galaxies. In particular, we focus on the dependence of these scaling relations on the colour of the central galaxy. We find that red central galaxies on average occupy more massive haloes than blue central galaxies of the same luminosity. However, at fixed stellar mass there is no appreciable difference in the average halo mass of red and blue centrals, especially for M*≲ 1010.5 h−2 M⊙. This indicates that stellar mass is a better indicator of halo mass than luminosity. Nevertheless, we find that the scatter in halo masses at fixed stellar mass is non‐negligible for both red and blue centrals. It increases as a function of stellar mass for red centrals but shows a fairly constant behaviour for blue centrals. We compare the scaling relations obtained in this paper with results from other independent studies of satellite kinematics, with results from a SDSS galaxy group catalog, from galaxy–galaxy weak lensing measurements and from subhalo abundance matching studies. Overall, these different techniques yield MLRs and MSRs in fairly good agreement with each other (typically within a factor of 2), indicating that we are converging on an accurate and reliable description of the galaxy–dark matter connection. We briefly discuss some of the remaining discrepancies among the various methods.

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.