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Galaxy Populations in the 26 most massive Galaxy Clusters in the South Pole Telescope SZE Survey

We present a study of the optical properties of the 26 most massive galaxy clusters selected within the SPT-SZ 2500 deg$^2$ survey. This Sunyaev-Zel'dovich effect selected sample spans a redshift range of 0.10 < z < 1.13. We measure the galaxy radial profile, the luminosity function (LF), and the halo occupation number (HON) using optical data with a typical depth of $m^*$ + 2. The stacked radial profiles are consistent with a NFW profile with a concentration of $2.84^{+0.40}_{-0.37}$ for the red sequence (RS) and $2.36^{+0.38}_{-0.35}$ for the total population. Stacking the data in multiple redshift bins shows a hint of redshift evolution in the concentration when both the total population is used, and when only RS galaxies are used (at 2.1$σ$ and 2.8$σ$, respectively). The stacked LF shows a faint end slope $α= -1.06^{+0.04}_{-0.03}$ for the total and $α= -0.80^{+0.04}_{-0.03}$ for the RS population. The redshift evolution of $m^*$ is found to be consistent with a passively evolving Composite Stellar Population (CSP) model. By adopting the CSP model predictions, we explore the redshift evolution of the schechter parameters $α$ and $ϕ^*$. We find $α$ for the total population to be consistent with no evolution (0.3$σ$), while evidence of evolution for the red galaxies is mildly significant (1.1-2.1$σ$). The data show that the density $ϕ^*$/E$^2$(z) decreases with redshift, in tension with the self-similar expectation at a 2.4$σ$ level for the total population. The measured HON-mass relation has a lower normalization than previous studies at low redshift. Finally, our data support HON redshift evolution at a 2.1$σ$ level, with clusters at higher redshift containing fewer galaxies per unit mass to $m^*$ + 3 than their low-z counterparts [abridged].