Biases in galaxy cluster velocity dispersion and mass estimates in the small number of galaxies regime

Abstract

We present a study of the statistical properties of three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime ($N_{\mathrm{gal}}\le 75$). Using a set of 73 numerically simulated galaxy clusters, we characterise the statistical bias and the variance for the three estimators, both in the determination of the velocity dispersion and the dynamical mass of the clusters via the $\sigma -M$ relation. The results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases with a minimal increase of the associated variance. The numerical simulations are also used to characterise the impact of velocity segregation in the selection of cluster members, and the impact of using cluster members within different physical radii from the cluster centre. The standard deviation is found to be the lowest variance estimator. The selection of galaxies within the sub-sample of the most massive galaxies in the cluster introduces a $2$\% bias in the velocity dispersion estimate when calculated using a quarter of the most massive cluster members. We also find a dependence of the velocity dispersion estimate on the aperture radius as a fraction of $R_{200}$, consistent with previous results. The proposed set of unbiased estimators effectively provides a correction of the velocity dispersion and mass estimates from all those effects in the small number of cluster members regime. This is tested by applying the new estimators to a subset of simulated observations. Although for a single galaxy cluster the statistical and physical effects discussed here are comparable or slightly smaller than the bias introduced by interlopers, they will be of relevance when dealing with ensemble properties and scaling relations for large cluster samples (Abridged).

arXiv commentaccepted for publication in A&A

References in corpus (37)

• Galactic Stellar and Substellar Initial Mass Function
• GADGET: A code for collisionless and gasdynamical cosmological simulations
• Cosmological Parameters from Observations of Galaxy Clusters
• Substructures in hydrodynamical cluster simulations
• The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and the Y_SZ-M_500 relation
• The effect of photo-ionization on the cooling rates of enriched, astrophysical plasmas
• Formation of Galaxy Clusters
• Tracing cosmic evolution with clusters of galaxies
• Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts
• Dynamical Friction and Galaxy Merging Timescales
• Chemical enrichment of galaxy clusters from hydrodynamical simulations
• Virial Scaling of Massive Dark Matter Halos: Why Clusters Prefer a High Normalization Cosmology
• Mass estimation in the outer regions of galaxy clusters
• Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties
• CLASH: Weak-Lensing Shear-and-Magnification Analysis of 20 Galaxy Clusters
• The galaxy cluster mass scale and its impact on cosmological constraints from the cluster population
• The relation between velocity dispersion and mass in simulated clusters of galaxies: dependence on the tracer and the baryonic physics
• On the efficiency and reliability of cluster mass estimates based on member galaxies
• Cool Core Clusters from Cosmological Simulations
• Massive Halos in Millennium Gas Simulations: Multivariate Scaling Relations
• Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data
• What determines satellite galaxy disruption?
• Toward Unbiased Galaxy Cluster Masses from Line of Sight Velocity Dispersions
• Optical Spectroscopy and Velocity Dispersions of Galaxy Clusters from the SPT-SZ Survey
• A non-ideal MHD Gadget: Simulating massive galaxy clusters
• The universal distribution of halo interlopers in projected phase space. Bias in galaxy cluster concentration and velocity anisotropy?
• RASS-SDSS Galaxy Cluster Survey. VII. On the Cluster Mass to Light ratio and the Halo Occupation Distribution
• The Atacama Cosmology Telescope (ACT): Beam Profiles and First SZ Cluster Maps
• Velocity Dispersion of 335 Galaxy Clusters Selected from the Sloan Digital Sky Survey: Statistical Evidence for Dynamical Interaction, and Against Ram-Pressure Stripping
• Interloper treatment in dynamical modelling of galaxy clusters
• The Atacama Cosmology Telescope: Dynamical masses for 44 SZ-selected galaxy clusters over 755 square degrees
• Planck Intermediate Results. XXXVI. Optical identification and redshifts of Planck SZ sources with telescopes in the Canary Islands Observatories
• Galaxy Cluster Mass Reconstruction Project - IV. Understanding the effects of imperfect membership on cluster mass estimation
• Optical validation and characterization of Planck PSZ1 sources at the Canary Islands observatories. I. First year of ITP13 observations
• Velocity Segregation and Systematic Biases In Velocity Dispersion Estimates With the SPT-GMOS Spectroscopic Survey
• Velocity segregation effects in galaxy clusters at 0.4<~z<~1.5
• Calibrating the Planck Cluster Mass Scale with Cluster Velocity Dispersions

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