The mass-concentration relation in lensing clusters: the role of statistical biases and selection effects

The relation between mass and concentration of galaxy clusters traces their formation and evolution. Massive lensing clusters were observed to be overconcentrated and following a steep scaling in tension with predictions from the concordance Lambda cold dark matter (Lambda CDM) paradigm. We critically revise the relation in the CLASH (Cluster Lensing And Supernova survey with Hubble), the SGAS (Sloan Giant Arcs Survey), the LOCUSS (Local Cluster Substructure Survey), and the high-redshift samples of weak lensing clusters. Measurements of mass and concentration are anti-correlated, which can bias the observed relation towards steeper values. We corrected for this bias and compared the measured relation to theoretical predictions accounting for halo triaxiality, adiabatic contraction of the halo, presence of a dominant brightest cluster galaxy, and, mostly, selection effects in the observed sample. The normalization, the slope, and the scatter of the expected relation are strongly sample-dependent. For the considered samples, the predicted slope is much steeper than that of the underlying relation characterizing dark matter-only clusters. We found that the correction for statistical and selection biases in observed relations mostly solve the tension with the Lambda CDM model.