Brightest Cluster Galaxy ellipticity as proxy for halo shape: Orientation bias, assembly bias, and potential selection effects in SZ-selected clusters

Abstract

The orientation of triaxial galaxy clusters with respect to the line-of-sight is expected to be one of the prime sources of scatter and potential bias in optical observables (e.g., richness and weak-lensing signal) of galaxy clusters. In this work, we use the observed shape of the central Brightest Cluster Galaxy (BCG) as proxy for the orientation along the line-of-sight for clusters selected via the Sunyaev-Zel'dovich (SZ) effect from the South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) surveys, matched to optically selected clusters from the Dark Energy Survey Year 3 (DES). We construct two samples of clusters that are designed to be identical in SZ mass estimate and redshift but with the roundest vs. the most elliptical BCGs, which we expect to correspond to BCGs (and clusters) with major axes aligned along the line-of-sight vs. in the plane of the sky, respectively. We find that the optical richness of round-BCG clusters is $\sim 10$\% larger than that of elliptical-BCG clusters, in agreement with the expectation from projection effects and presenting the first such detection in data. The density profiles, however, are not in agreement with the expectation from projection effects: the 1-halo term (below $6~h^{-1}\rm{Mpc}$) of both the weak-lensing and galaxy density profiles are the same for the subsamples, contrary to previous studies based on X-ray selected clusters. In the 2-halo regime (above $6~h^{-1}\rm{Mpc}$), we find a significant excess of the elliptical-BCG cluster profiles compared to the round-BCG cluster profiles, which is the opposite of the expectation from numerical simulations. We hypothesize that the intrinsic shape of the BCG reflects not just the orientation angle, but also intrinsic properties of the cluster which can affect both the SZ signal and the amplitude of the 2-halo term.

Figures (22)

• Figure 1: Left: Matching of SPT clusters from the round and elliptical bins selected in BCG axis ratio (q). The black dots represent all the clusters in the SPT data set, the red circles represent clusters with round-BCG (q below the 25th percentile), and the blue ellipses represent clusters with elliptical BCGs (q above the 75th percentile). The pairings (dotted lines) were decided on the basis of proximity in SZ $\rm M_{500}$ mass and redshift (see Section \ref{['Pair matching']}). Right: The same pairing is shown with the axis ratio on the vertical axis. The red and blue shaded regions represent the 25th and 75th percentiles in axis ratio (q) respectively. The shape of each scatter point in the round and elliptical bin is representative of the axis ratio of the respective BCG.
• Figure 2: SZ signal-to-noise ratio, $\hat{\zeta} = \sqrt{\xi^{2} - 3}/\gamma$ vs X-ray gas mass scaling relation for the SPT cluster sample matched to the eRASS1 clusters. Here, the $\gamma$ factor accounts for the varying field depth across the SPT survey. The red points indicate the round-BCG cluster sample, blue indicate the elliptical-BCG cluster sample and the black points are the clusters in between. Also, the fitted scaling relation by Dietrich-J-2019:Scaling is plotted as the orange solid line along with $1\,\sigma$ confidence shown in the shaded bands.
• Figure 3: Left: The ratio of SZ Mass estimate ($M^{\rm SZ}_{500}$) to X-ray gas mass (${ M}^{\rm Xray}_{500}$) normalized with its mean, against the axis ratio, $q$. We plot the eRASS1$\times$SPT data set in red with $1\,\sigma$ errorbars and fit a log-linear relation using MCMC method (blue). Right: similar as the left panel, but for eRASS1$\times$ACT data set. The best-fit ranges are shown with the $1\,\sigma$ and the $2\,\sigma$ confidence bands in light blue. The short vertical gray lines at the top show the values of axis ratio for SZ clusters that were not matched to the X-ray dataset. The blue rings represent the faintest BCGs in the dataset defined as z-band absolute magnitude $M_z> -24.0$ (see Section \ref{['Magnitude gap']} for detailed discussion).
• Figure 4: The posterior contours of the linear fit of the SZ to X-ray mass ratio as a function of axis ratio. There are three free parameters: intercept (c), slope (m) and intrinsic scatter ($\sigma_{\rm{int}}$). We neglect the uncertainties in $q$ for the fitting. We find a positive slope with a 86 % significance and 66 % significance for the SPT$\times$eRASS1 (red) and ACT$\times$eRASS1 (blue) samples respectively, i.e., at most marginal evidence for orientation bias in the SZ selection.
• Figure 5: Top: The distribution of SZ mass $M_{500}$ (left) and the distribution of relative richness (the ratio of the redMaPPer richness to the predicted richness using the scaling relation from Bleem-L-2020:SPTECS, (right) for the combined ACT and SPT sample. Middle: The Quantile-Quantile (QQ) plot for the cluster mass, $M_{500}$, of the round-BCG and the elliptical-BCG samples (left) and that for the relative richness (right). The SPT SZ clusters are plotted in yellow, the ACT SZ clusters in orange and the combined ACT+SPT sample in black. Bottom: The difference between the Round and the elliptical-BCG sample shown in the QQ plots. Note that the relative richness is systematically biased high for the round-BCG clusters (aligned along the LOS) compared to the elliptical-BCG clusters (aligned along the plane-of-sky). Above the top panels, we show a few summary statistics to compare the distributions of the round-BCG sample and the elliptical-BCG sample. We use the Kolmogorov–Smirnov (KS) statistics and a re-shuffling test to rule out the null hypothesis that the two sub-samples follow identical distributions. The KS 2-sample test and the shuffling test confirm the observed discrepancy in the richness distributions for the two samples with significance well above $3\,\sigma$.