Halo occupation distribution of the most massive galaxies
The plot shows the mean number of the most massive galaxies at z=0.3, depending on the mass of the halo they live in. The black solid line shows the result from one of the Magneticum Simulations, while the red line shows the corresponding fit to this distribution. Our simulation agrees very well with the observations from Zehavi+11. Our cut-off is sharper then in the observations because we take the most massive galaxies, while in the observations only luminous red galaxies (LRGs) are considered.
The black dashed and dotted lines show the simulation result split up into central galaxies and substructures. The slope for the substructures is 1.15.
This is getting interesting when you compare it to AGN (plot from April 2016). Here the slope is much smaller, i.e. 0.57. This automatically means that AGN are not just random events and that (at least some of them) must be triggered by certain physical conditions.