In Fig. 11, we compared the WL-derived masses (MWL) with those derived from the dynamical analysis (Mdyn) and listed in Table 1. The dynamical masses were computed under the assumption of the singular isothermal model and velocity dispersions (Haines et al. 2018). We obtained the WL masses for the four massive clusters (A 3556, A 3558, A 3560, and A 3562) with the MCMC method. On the other hand, we only gave the upper limit of the masses for six out of seven low-mass clusters due to the large shape noise in the WL analysis. In the figure, we labelled the low-mass clusters as black crosses, AS 0726 as black box and the four massive clusters as cyan circles. For AS 0726, we only indicatively adopted the average mass for the low-mass clusters derived using the stacked shear profile. We notice that (i) the masses obtained from the dynamical and WL analysis are consistent within 1σ for all clusters except A 3554, A 3558, and AS 0726; (ii) the dynamical masses turn out to be systematically higher than the WL-derived ones. Previous studies showed that WL masses obtained from the tangential shear fitting were biased low up to 10 per cent with a scatter of ∼25 per cent (Oguri et al. 2005; Sereno & Umetsu 2011; Sereno & Ettori 2015). The main source of the bias are due to substructures and triaxiality. When a cluster whose major axis is perpendicular to the line of sight, i.e elongated in the sky-plane, a mass obtained with the spherical NFW profile is typically underestimated. The presence of substructures around clusters and uncorrelated large-scale structures along the line of sight also generate the biases for the estimation of the WL masses (Meneghetti et al. 2010; Becker & Kravtsov 2011; Giocoli et al. 2012, 2014). In addition, we point out that the dynamical mass of AS 0726 is actually an upper limit since the velocity distribution of member galaxies is strongly bimodal, and certainly not Gaussian (see fig. 14 in Haines et al. 2018). This system probably consists of two groups with velocity dispersions ∼300 km s−1 rather than one single system with σ ∼600 km s−1. This would reduce the mass estimate by a factor of 4. The complex structure of A 3558 and, in general, the dynamical activity in the SSC core (see Bardelli et al. 1998; Ettori et al. 2000; Finoguenov et al. 2004; Rossetti et al. 2007a) may explain the systematic differences between the two mass determinations quoted above, since the virial mass tends to overestimate the mass of unrelaxed clusters. Moreover, Rossetti et al. (2007b) studied A 3558 with an X-ray observation and showed the possibility of the presence of substructures along the line of sight, which interact with the cluster. Since such structures along the line of sight broaden velocity distribution, masses obtained from the dynamical analysis can be overestimated up to 100 per cent (Takizawa, Nagino & Matsushita 2010; Pratt et al. 2019). Fig. 14 in Haines et al. (2018) showed the broad velocity distribution of galaxies for the cluster. This indicates the presence of the substructures along the line of sight and the possibility for overestimating the dynamical mass. A 3554 also shows strong substructures in the velocity distribution diagram.
Citation: Sereno & Umetsu 2011
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