On the level of cluster assembly bias in SDSS

Recently, several studies have discovered a strong discrepancy between the large-scale clustering biases of two subsamples of galaxy clusters at the same halo mass, split by their average projected membership distances < R-mem >. The level of this discrepancy significantly exceeds the maximum halo assembly bias predicted by Lambda cold dark matter (Lambda CDM). We explore whether some of the large-scale bias differences could be caused by projection effects in < R-mem > due to other systems along the line of sight. We thoroughly investigate the assembly bias of the redMaPPer clusters in Sloan Digital Sky Survey (SDSS), by defining a new variant of the average membership distance estimator (R) over tilde (mem) that is robust against projection effects in the cluster membership identification. Using the angular mark correlation functions, we show that the large-scale bias differences when splitting by < R-mem > can be mostly attributed to projection effects. After splitting by (R) over tilde (mem), the anomalously large signal is reduced, giving a ratio of 1.02 +/- 0.14 between the two clustering biases as measured from weak lensing. Using a realistic mock cluster catalogue, we predict that the bias ratio between two (R) over tilde (mem)-split subsamples should be similar or equal to 1.10, which is >60 per cent weaker than the maximum halo assembly bias (1.24) when split by halo concentration. Therefore, our results demonstrate that the level of halo assembly bias exhibited by clusters in SDSS is consistent with the Lambda CDM prediction. With a 10-fold increase in cluster numbers, deeper ongoing surveys will enable a more robust detection of halo assembly bias. Our findings also have important implications for quantifying the impact of projection effects on cosmological constraints using photometrically selected clusters.