Evidence of Halo Assembly Bias in Massive Clusters

We present significant evidence of halo assembly bias for SDSS redMaPPer galaxy clusters in the redshift range [0.1, 0.33]. By dividing the 8,648 clusters into two subsamples based on the average member galaxy separation from the cluster center, we first show that the two subsamples have very similar halo mass of $M_{200\mathit{m}}\simeq 1.9\times {10}^{14}{h}^{-1}{M}_{\odot }$ based on the weak lensing signals at small radii $R\lesssim 10h^{-1}\mathrm{Mpc}$. However, their halo bias inferred from both the large-scale weak lensing and the projected autocorrelation functions differs by a factor of $\sim 1.5$, which is a signature of assembly bias. The same bias hypothesis for the two subsamples is excluded at $2.5\sigma$ in the weak lensing and $4.4\sigma$ in the autocorrelation data, respectively. This result could bring a significant impact on both galaxy evolution and precision cosmology.

Figure 1

Halo mass consistency and assembly bias from the WL signal. The data points with error bars in the top and middle panels show the excess surface mass density profile as a function of the cluster-centric projected radius (in comoving units), obtained from the WL measurements for the large- and small-$⟨R_{\text{mem}}⟩$ subsamples of redMaPPer clusters [see Eq. (1)], respectively. The points from the top panel are reproduced in semitransparent color in the middle panel for comparison. The mass profiles at small radii $R\lesssim 10h^{-1}\mathrm{Mpc}$ appear to have similar amplitudes with slightly different shapes, but show a difference in amplitude at $R\gtrsim 10h^{-1}\mathrm{Mpc}$, as expected from assembly bias. The bold solid line shows the best-fit halo model, the thin solid line is the centered 1-halo term, the dashed line is the off-centered 1-halo term, while the dotted line corresponds to the stellar mass contribution from the central galaxy. Comparison between the dot-dashed lines in the two panels implies that the 2-halo term contributions, which arise from the average mass distribution surrounding the clusters, are different by a factor of 1.6. The bottom panel shows the ratios of the lensing signals, highlighting a clear deviation from unity at $R\gtrsim 15\mathrm{Mpc}/h$.

Figure 2

The posterior distributions of halo model parameters given the WL signals for each of the two cluster subsamples shown in Fig. 1. The distributions include marginalization over nuisance parameters which correspond to off-centering effects and stellar mass contribution from the central galaxy (see text for details). The parameters $M_{200\mathit{m}}$ and $c_{200\mathit{m}}$ are the halo mass and concentration parameters that specify the average NFW profile of the clusters (1-halo term), while $b$ is the linear halo bias of the cluster subsample. The posterior distributions show the large- and small-$⟨R_{\text{mem}}⟩$ subsamples have similar halo mass, but display a significant difference in their bias parameters.

Figure 3

Halo assembly bias from the projected clustering signal: The projected autocorrelation function of clusters for each of the large- and small-$⟨R_{\text{mem}}⟩$ subsamples, relative to that of the full sample (i.e., all clusters). The clustering signals at large separations, $R\gtrsim 2h^{-1}\mathrm{Mpc}$, show a significant difference, which is consistent with the WL measurements in Fig. 1 as shown by the shaded regions.