cluster based on the calibrated red-sequence model, as measured from the photometrically identified candidate cluster members.

### Probability of being a cluster member {#sec:clus_mem}

The candidate cluster members are each assigned to a redMaPPer cluster based on a membership probability ($P_{\rm{MEM}}$). $P_{\rm{MEM}}$ indicates the probability of a galaxy being a red-sequence galaxy that belongs to a specific cluster. This follows directly from the method used by the cluster detection algorithm to identify clusters, i.e. looking for overdensities of red-sequence galaxies, with the luminosity cut and radial filtering mentioned above. redMaPPer provides catalogues of (candidate) cluster members for each cluster, based on the galaxies’ individual properties, including $P_{\rm{MEM}}$, and it is these catalogues which we use throughout our analysis.

In Fig. \[fig:PR\_rms\_cuts\_red\_seq\] we show the colour-magnitude diagrams ($g-r$ vs. $m_\mathrm{i}$) of the redMaPPer clusters out to $z=0.35$ (the redshift cut will be explained in the next section). All candidate cluster members and those with $P_{\rm{MEM}} > 0.9$ are shown in grey and green respectively. In each panel it is apparent that members with large $P_{\rm{MEM}}$ values form a tighter sequence, as expected, since these galaxies are more likely to be red-sequence galaxies. We will return to this idea in Section \[sec:fpair\_results\].

