On the efficiency and reliability of cluster mass estimates based on member galaxies

Abstract

Aims. We study the efficiency and reliability of cluster mass estimators that are based on the projected phase-space distribution of galaxies in a cluster region. Methods. We analyse a data-set of 62 clusters extracted from a concordance ΛCDM cosmological hydrodynamical simulation. We consider both dark matter (DM) particles and simulated galaxies as tracers of the clusters gravitational potential. Two cluster mass estimators are considered: the virial mass estimator, corrected for the surface-pressure term, and a mass estimator (that we call M σ ) based entirely on the velocity dispersion estimate of the cluster. In order to simulate observations, galaxies (or DM particles) are first selected in cylinders of given radius (from 0.5 to 1.5h −1 Mpc) and 200h −1 Mpc length. Cluster members are then identified by applying a suitable interloper removal algorithm. Results. The virial mass estimator overestimates the true mass by 10% on average, for sample sizes of > ∼ 60 cluster members. For similar sample sizes, M σ underestimates the true mass by 15%, on average. For smaller sample sizes, the bias of the virial mass estimator substantially increases, while the M σ estimator becomes essentially unbiased. The dispersion of both mass estimates increases by a factor ∼2 as the number of cluster members decreases from ∼400 to ∼20. It is possible to reduce the bias in the virial mass estimates either by removing clusters with significant evidence for subclustering or by selecting early-type galaxies, which substantially reduces the interloper contamination. Early-type galaxies cannot however be used to improve the M σ estimates since their intrinsic velocity distribution is slightly biased relative to that of the DM particles. Radially-dependent incompleteness can drastically affect the virial mass estimates, but leaves the M σ estimates almost unaffected. Other observational effects, like centering and velocity errors and different observational apertures, have little effect on the mass estimates.

Scaling Relations for Galaxy Clusters: Properties and Evolution

“…In the cluster outskirts, where the virial equilibrium assumption does not hold, the caustic method has yielded promising results for the total cluster masses (e.g., Rines et al 2003;Diaferio et al 2005;Rines et al 2013). The accuracy of dynamical methods was studied in detail by Biviano et al (2006), who found that the virial estimator can recover the virial mass for a galaxy cluster within 10% for samples of at least 60 cluster members. In this sense, the dynamical approach is expensive in terms of telescope time.…”

A pan-chromatic view of the galaxy cluster XMMU J1230.3+1339 atz= 0.975

“…While at local redshifts dynamical mass estimators can provide robust measurements for relaxed clusters even for rather small spectroscopic samples (e.g. Biviano et al 2006), high redshift systems are particularly prone to be affected by potentially significant biases. In the case of XMMU J1230.3+1339 the fairly low velocity dispersion estimate compared to similarly rich and massive local clusters becomes plausible in the light of the large-scale structure and component analysis in Sect.…”

Galaxy Cluster Mass Reconstruction Project – II. Quantifying scatter and bias using contrasting mock catalogues

“…Though these techniques generate an impression of which galaxies are associated with a cluster, deducing which galaxies are true members of the cluster is often problematic due to interloping galaxies. These interlopers are close to but not gravitationally bound to the cluster and their inclusion can lead to strong bias in velocity dispersion based mass estimates (e.g., Lucey 1983;Borgani et al 1997;Cen 1997; Biviano et al 2006;Wojtak et al 2007; Mamon et al 2010). …”