ALBERT

Description: We present a study of the optical properties of the 26 most massive galaxy clusters within the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) 2500 deg 2 survey spanning the redshift range 0.10 〈  z  〈 1.13. We measure the radial profiles, the luminosity functions (LFs), and the halo occupation numbers (HONs) using optical data of typical depth m * + 2. The stacked radial profiles are consistent with a Navarro–Frenk–White profile of concentration $2.84^{+0.40}_{-0.37}$ for the red sequence (RS) and $2.36^{+0.38}_{-0.35}$ for the total population. Stacking the data in multiple redshift bins shows slight redshift evolution in the concentration when both the total population is used, and when only RS galaxies are used (at 2.1 and 2.8, respectively). The stacked LF shows a faint end slope $\alpha = -1.06^{+0.04}_{-0.03}$ for the total and $\alpha = -0.80^{+0.04}_{-0.03}$ for the RS population. The redshift evolution of m * is consistent with a passively evolving composite stellar population (CSP) model. Adopting the CSP model predictions, we explore the redshift evolution of the Schechter parameters α and *. We find α for the total population to be consistent with no evolution (0.3), and mildly significant evidence of evolution for the red galaxies (1.1–2.1). The data show that the density */ E 2 ( z ) decreases with redshift, in tension with the self-similar expectation at a 2.4 level for the total population. The measured HON–mass relation has a lower normalization than previous low redshift studies. Finally, our data support HON redshift evolution at a 2.1 level, with clusters at higher redshift containing fewer galaxies than their low- z counterparts.