Dynamical mass estimates of Sunyaev-Zel'dovich E_ect selected galaxy clusters in the millennium gas simulations.

Abstract

Abstract To extract and make estimates of the cosmological parameters requires knowledge of the cluster mass. Cluster mass is not directly observable but can be predicted by numerical simulations of structure formation and can be inferred from observable proxies for mass. One way to nd a cluster is by the Sunyaev-Zel'dovich (SZ) e ect, caused by the inverse Compton scattering of photons from the cosmic microwave background (CMB) by hot gas in clusters. The observable SZ e ect signal (Y , the integrated Comptonisation parameter) does correlate well with cluster dynamical mass. The cluster mass can be estimated from measuring the one dimensional (1D) line-of-sight (LOS) velocity dispersion ( v) of galaxies in clusters, however, depending on the type of galaxies selected, such measurements may be subject to biases. We investigate this issue using simulated cluster and galaxy catalogues produced by the Millennium Gas Simulations Project. We aim to design an optimal observing strategy which is important for future dynamical mass measurements of Atacama Cosmology Telescope (ACT) clusters that aim to use the Southern African Large Telescope (SALT) for much larger studies of dynamical mass measurements (M500). We describe the methods used to make mock cluster catalogues by following the same procedure used in multi-object spectroscopic observations with the Robert Stobie Spectroi graph. In our case we applied a di erent number of slits masks for targeting the galaxy clusters and investigate the impact it has on the recovered v and estimated M500. We do this for both an idealized case (100% redshift z completeness), and for a realistic case, where redshift completeness decreases for fainter objects. We calculate the velocity dispersion ( v) of each cluster at z = 0.3 using galaxies selected as members only, and then use galaxy cluster scaling relations derived from N-body/hydrodynamic simulations to estimate the cluster dynamical mass M500. The recovered velocity dispersion is almost unbiased (1.5􀀀2%) but with much bigger scatter (12􀀀18%). We found that the bias of the estimated M500 for 100% z completeness is less than that for the realistic z incompleteness, which is as expected. For realistic redshift completeness, the bias in recovered M500 ranges from 11􀀀30%. The ultimate goal for this project is to determine how many masks we need to use per cluster, and how many clusters in total we need, to make a reasonable measurement of the Y500D2A 􀀀 v relation, since the observing time on a queue-scheduled telescope such as SALT is quantized by how many masks are allocated to each cluster. Using a Markov Chain Monte Carlo (MCMC) method to t the Y500D2A 􀀀 v relation, we found that the recovered slope of the relation has less bias when using a large sample of clusters with poor quality v measurements, as compared to a smaller sample of clusters with high quality v measurements.