Weak-lensing mass calibration of the Sunyaev–Zel’dovich effect using APEX-SZ galaxy clusters

Abstract

The use of galaxy clusters as precision cosmological probes relies on an accurate determination of their masses. However, inferring the relationship between cluster mass and observables from direct observations is difficult and prone to sample selection biases. In this work, we use weak lensing as the best possible proxy for cluster mass to calibrate the Sunyaev-Zel'dovich (SZ) effect measurements from the APEX-SZ experiment. For a well-defined (ROSAT) X-ray complete cluster sample, we calibrate the integrated Comptonization parameter, Y SZ , to the weak-lensing derived total cluster mass, M 500 . We employ a novel Bayesian approach to account for the selection effects by jointly fitting both the SZ Comptonization, Y SZ -M 500 , and the X-ray luminosity, L x -M 500 , scaling relations. We also account for a possible correlation between the intrinsic (log-normal) scatter of L x and Y SZ at fixed mass. We find the corresponding correlation coefficient to be r = 0.47 +0.24 −0.35 , and at the current precision level our constraints on the scaling relations are consistent with previous works. For our APEX-SZ sample, we find that ignoring the covariance between the SZ and X-ray observables biases the normalization of the Y SZ -M 500 scaling high by 1-2σ and the slope low by ∼ 1σ, even when the SZ effect plays no role in the sample selection. We conclude that for higher-precision data and larger cluster samples, as anticipated from on-going and near-future cluster cosmology experiments, similar biases (due to intrinsic covariances of cluster observables) in the scaling relations will dominate the cosmological error budget if not accounted for correctly.

Weak lensing measurements of the APEX-SZ galaxy cluster sample

“…This goal was achieved with the only exception of a cluster at z = 0.98, resulting in a complete sample up to z = 0.83. The follow-up observations also includes clusters that were only observed but not detected by APEX-SZ, in order to ensure the completeness of an X-ray selected subsample (Nagarajan et al 2018). To illustrate the data analysis we select three clusters as examples.…”

“…In order to obtain cluster masses from our shear measurements we are again following a similar approach as described in Israel et al (2010) and model the tangential ellipticity profile ε t (θ) of a cluster with the reduced shear profile g(θ, Σ crit ; r 200 , c 200 ) (Bartelmann 1996;Wright & Brainerd 2000) of a NFW (Navarro et al 1995(Navarro et al , 1996(Navarro et al , 1997) density profile. In contrast to Israel et al (2010) we do not assume a source sheet with common Σ crit .…”

“…Weak-lensing mass estimation have been actively pursued for numerous galaxy cluster samples (e.g., Applegate et al 2014;Postman et al 2012) of typical sample size of ∼ 20 to 50 clusters. In this paper, we present the weak gravitational lensing analysis of the APEX-SZ galaxy cluster sample (Bender et al 2016;Nagarajan et al 2018) comprising of 39 galaxy clusters in the redshift range of z = 0.1 to z = 0.83. Most of these clusters are X-ray selected.…”

“…Most of these clusters are X-ray selected. A sub-sample of 27 clusters form a complete galaxy cluster sample in X-ray luminosity and redshift space (see Nagarajan et al (2018) for details). One of the main purposes of measuring the cluster masses for this sample is to obtain reasonable constraints on mass-observable scaling relations.…”

“…One of the main purposes of measuring the cluster masses for this sample is to obtain reasonable constraints on mass-observable scaling relations. In particular, the subject matter of measuring the scaling between the Sunyaev-Zel'dovich effect and the cluster mass is studied in a companion paper by Nagarajan et al (2018). Here, we describe the weak-lensing analysis adopted for the cluster mass measurements that form the basis for such work.…”