We employ a large sample of 20171 optically-selected groups and clusters at 0.15 < z < 0.4 in the SDSS to investigate how the stacked stellar mass fraction varies across a wide range of total mass, $M_{500}$. Our study improves upon previous observat
ional studies in a number of important ways, including having a much larger sample size, an explicit inclusion of the intracluster light (ICL) component, and a thorough examination of the accuracy of our total mass estimates via comparisons to simulations and weak lensing observations. We find that the stellar mass fraction depends only weakly on total mass and that the contribution of ICL to the total stellar mass fraction is significant (typically 20-40 per cent). Both of these findings are in excellent accordance with the predictions of cosmological simulations. Under the assumption of a Chabrier (Salpeter) IMF, the derived star formation efficiency ($f_{star}$/$f_{b}$, where $f_b=Omega_b/Omega_m$) is relatively low at 8 per cent (14 per cent) and is consistent with the global star formation efficiency of semi-analytic models that reproduce the galaxy stellar mass function. When our measured stellar mass fractions are combined with the observed relation between hot gas mass fraction and total mass from X-ray observations, our results imply that galaxy groups have significantly lower baryon fractions than massive clusters. Ejection of gas due to energetic AGN feedback (most likely at high redshift) provides a plausible mechanism for explaining the trends we observe.
We investigate the relationship between the halo mass, M_200, and concentration, c, for a sample of 26 group- and cluster-scale strong gravitational lenses. In contrast with previous results, we find that these systems are only ~ 0.1 dex more over-co
ncentrated than similar-mass halos from dark matter simulations; the concentration of a halo with M_200 = 10^14 M_sun is log c = 0.78pm0.05, while simulations of halos with this mass at similar redshifts (z ~ 0.4) predict log c ~ 0.56 - 0.71. We also find that we are unable to make informative inference on the slope of the M_200-c relation in spite of our large sample size; we note that the steep slopes found in previous studies tend to follow the slope in the covariance between M_200 and c, indicating that these results may be measuring the scatter in the data rather than the intrinsic signal. Furthermore, we conclude that our inability to constrain the M_200-c slope is due to a limited range of halo masses, as determined by explicitly modelling our halo mass distribution, and we suggest that other studies may be producing biased results by using an incorrect distribution for their halo masses.
