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Register a new userLensing Constraints on the Mass Profile Shape and the Splashback Radius of Galaxy Clusters
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Keiichi Umetsu
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The lensing signal around galaxy clusters can, in principle, be used to test detailed predictions for their average mass profile from numerical simulations. However, the intrinsic shape of the profiles can be smeared out when a sample that spans a wide range of cluster masses is averaged in physical length units. This effect especially conceals rapid changes in gradient such as the steep drop associated with the splashback radius, a sharp edge corresponding to the outermost caustic in accreting halos. We optimize the extraction of such local features by scaling individual halo profiles to a number of spherical overdensity radii, and apply this method to 16 X-ray-selected high-mass clusters targeted in the Cluster Lensing And Supernova survey with Hubble. By forward-modeling the weak- and strong-lensing data presented by Umetsu et al., we show that, regardless of the scaling overdensity, the projected ensemble density profile is remarkably well described by an NFW or Einasto profile out to $R sim 2.5h^{-1}$Mpc, beyond which the profiles flatten. We constrain the NFW concentration to $c_{200c} = 3.66 pm 0.11$ at $M_{200c} simeq 1.0 times 10^{15}h^{-1}M_odot$, consistent with and improved from previous work that used conventionally stacked lensing profiles, and in excellent agreement with theoretical expectations. Assuming the profile form of Diemer & Kravtsov and generic priors calibrated from numerical simulations, we place a lower limit on the splashback radius of the cluster halos, if it exists, of $R_{sp}/r_{200m} > 0.89$ ($R_{sp} > 1.83h^{-1}$Mpc) at 68% confidence. The corresponding density feature is most pronounced when the cluster profiles are scaled by $r_{200m}$, and smeared out when scaled to higher overdensities.
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We critically examine the methodology behind the claimed observational detection of halo assembly bias using optically selected galaxy clusters by Miyatake et al. (2016) and More et al. (2016). We mimic the optical cluster detection algorithm and apply it to two different mock catalogs generated from the Millennium simulation galaxy catalog, one in which halo assembly bias signal is present, while the other in which the assembly bias signal has been expressly erased. We split each of these cluster samples into two using the average cluster-centric distance of the member galaxies to measure the difference in the clustering strength of the subsamples with respect to each other. We observe that the subsamples split by cluster-centric radii show differences in clustering strength, even in the catalog where the true assembly bias signal was erased. We show that this is a result of contamination of the member galaxy sample from interlopers along the line-of-sight. This undoubtedly shows that the particular methodology adopted in the previous studies cannot be used to claim a detection of the assembly bias signal. We figure out the tell-tale signatures of such contamination, and show that the observational data also shows similar signatures. Furthermore, we also show that projection effects in optical galaxy clusters can bias the inference of the 3-dimensional edges of galaxy clusters (splashback radius), so appropriate care should be taken while interpreting the splashback radius of optical clusters.
Splashback refers to the process of matter that is accreting onto a dark matter halo reaching its first orbital apocenter and turning around in its orbit. The cluster-centric radius at which this process occurs, r_sp, defines a halo boundary that is connected to the dynamics of the cluster. A rapid decline in the halo profile is expected near r_sp. We measure the galaxy number density and weak lensing mass profiles around redMaPPer galaxy clusters in the first year Dark Energy Survey (DES) data. For a cluster sample with mean M_200m mass ~2.5 x 10^14 M_sun, we find strong evidence of a splashback-like steepening of the galaxy density profile and measure r_sp=1.13 +/- 0.07 Mpc/h, consistent with earlier SDSS measurements of More et al. (2016) and Baxter et al. (2017). Moreover, our weak lensing measurement demonstrates for the first time the existence of a splashback-like steepening of the matter profile of galaxy clusters. We measure r_sp=1.34 +/- 0.21 Mpc/h from the weak lensing data, in good agreement with our galaxy density measurements. For different cluster and galaxy samples, we find that consistent with LCDM simulations, r_sp scales with R_200m and does not evolve with redshift over the redshift range of 0.3--0.6. We also find that potential systematic effects associated with the redMaPPer algorithm may impact the location of r_sp. We discuss progress needed to understand the systematic uncertainties and fully exploit forthcoming data from DES and future surveys, emphasizing the importance of more realistic mock catalogs and independent cluster samples.
In the era of large surveys, yielding thousands of galaxy clusters, efficient mass proxies at all scales are necessary in order to fully utilize clusters as cosmological probes. At the cores of strong lensing clusters, the Einstein radius can be turned into a mass estimate. This efficient method has been routinely used in literature, in lieu of detailed mass models; however, its scatter, assumed to be $sim30%$, has not yet been quantified. Here, we assess this method by testing it against ray-traced images of cluster-scale halos from the Outer Rim N-body cosmological simulation. We measure a scatter of $13.9%$ and a positive bias of $8.8%$ in $M(<theta_E)$, with no systematic correlation with total cluster mass, concentration, or lens or source redshifts. We find that increased deviation from spherical symmetry increases the scatter; conversely, where the lens produces arcs that cover a large fraction of its Einstein circle, both the scatter and the bias decrease. While spectroscopic redshifts of the lensed sources are critical for accurate magnifications and time delays, we show that for the purpose of estimating the total enclosed mass, the scatter introduced by source redshift uncertainty is negligible compared to other sources of error. Finally, we derive and apply an empirical correction that eliminates the bias, and reduces the scatter to $10.1%$ without introducing new correlations with mass, redshifts, or concentration. Our analysis provides the first quantitative assessment of the uncertainties in $M(<theta_E)$, and enables its effective use as a core mass estimator of strong lensing galaxy clusters.
We present the direct detection of the splashback feature using the sample of massive galaxy clusters from the Local Cluster Substructure Survey (LoCuSS). This feature is clearly detected (above $5sigma$) in the stacked luminosity density profile obtained using the K-band magnitudes of spectroscopically confirmed cluster members. We obtained the best-fit model by means of Bayesian inference, which ranked models including the splashback feature as more descriptive of the data with respect to models that do not allow for this transition. In addition, we have assessed the impact of the cluster dynamical state on the occurrence of the splashback feature. We exploited the extensive multi-wavelength LoCuSS dataset to test a wide range of proxies for the cluster formation history, finding the most significant dependence of the splashback feature location and scale according to the presence or absence of X-ray emitting galaxy groups in the cluster infall regions. In particular, we report for the first time that clusters that do not show massive infalling groups present the splashback feature at a smaller clustercentric radius $ r_{rm{sp}}/r_{rm{200,m}} = 1.158 pm 0.071$ than clusters that are actively accreting groups $r_{rm{sp}}/r_{rm{200,m}} = 1.291 pm 0.062$. The difference between these two sub-samples is significant at $4.2sigma$, suggesting a correlation between the properties of the cluster potential and its accretion rate and merger history. Similarly, clusters that are classified as old and dynamically inactive present stronger signatures of the splashback feature, with respect to younger, more active clusters. We are directly observing how fundamental dynamical properties of clusters reverberate across vastly different physical scales.
We constrain the scaling relation between optical richness ($lambda$) and halo mass ($M$) for a sample of SDSS redMaPPer galaxy clusters within the context of the {it Planck} cosmological model. We use a forward modeling approach where we model the probability distribution of optical richness for a given mass, $P(ln lambda| M)$. To model the abundance and the stacked lensing profiles, we use an emulator specifically built to interpolate the halo mass function and the stacked lensing profile for an arbitrary set of halo mass and redshift, which is calibrated based on a suite of high-resolution $N$-body simulations. We apply our method to 8,312 SDSS redMaPPer clusters with $20le lambda le 100$ and $0.10le z_{lambda}le0.33$, and show that the log-normal distribution model for $P(lambda|M)$, with four free parameters, well reproduces the measured abundances and lensing profiles simultaneously. The constraints are characterized by the mean relation, $leftlangle ln{lambda}rightrangle(M)=A+Bln(M/M_{rm pivot})$, with $A=3.207^{+0.044}_{-0.046}$ and $B=0.993^{+0.041}_{-0.055}$ (68%~CL), where the pivot mass scale $M_{rm pivot}=3times 10^{14} h^{-1}M_odot$, and the scatter $sigma_{mathrm{lnlambda}|M}=sigma_0+qln(M/M_{rm pivot})$ with $sigma_0=0.456^{+0.047}_{-0.039}$ and $q=-0.169^{+0.035}_{-0.026}$. We find that a large scatter in halo masses is required at the lowest richness bins ($20le lambda lesssim 30$) in order to reproduce the measurements. Without such a large scatter, the model prediction for the lensing profiles tends to overestimate the measured amplitudes. This might imply a possible contamination of intrinsically low-richness clusters due to the projection effects. Such a low-mass halo contribution is significantly reduced when applying our method to the sample of $30le lambda le 100$.
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