Detecting clusters of galaxies in the sloan digital sky survey. I. Monte Carlo comparison of cluster detection algorithms

We present a comparison of three cluster-finding algorithms from imaging data using Monte Carlo simulations of clusters embedded in a 25 deg² region of Sloan Digital Sky Survey (SDSS) imaging data: the matched filter (MF; Postman et al., published in 1996), the adaptive matched filter (AMF; Kepner et al., published in 1999), and a color-magnitude filtered Voronoi tessellation technique (VTT). Among the two matched filters, we find that the MF is more efficient in detecting faint clusters, whereas the AMF evaluates the redshifts and richnesses more accurately, therefore suggesting a hybrid method (HMF) that combines the two. The HMF outperforms the VTT when using a background that is uniform, but it is more sensitive to the presence of a nonuniform galaxy background than is the VTT; this is due to the assumption of a uniform background in the HMF model. We thus find that for the detection thresholds we determine to be appropriate for the SDSS data, the performance of both algorithms are similar; we present the selection function for each method evaluated with these thresholds as a function of redshift and richness. For simulated clusters generated with a Schechter luminosity function (M _r* = -21.5 and α = -1.1), both algorithms are complete for Abell richness ≳1 clusters up to z ∼ 0.4 for a sample magnitude limited to r = 21. While the cluster parameter evaluation shows a mild correlation with the local background density, the detection efficiency is not significantly affected by the background fluctuations, unlike previous shallower surveys.