Abstract
Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime (Ngal ≤ 75), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the σ–M relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that they can retrieve bias-corrected values for both the mean velocity dispersion and the mean mass.
Highlights
Several authors have used the velocity dispersion mass proxy to study and characterise scaling relations between SZ and dynamical mass [1,2,3]
In this article we present our study of statistical and physical biases introduced in the estimation of velocity dispersion and dynamical mass
We have used 73 simulated galaxy clusters (GCs) from hydrodynamic simulations including AGN feedback and star formation, in order to characterise the statistical and physical biases in three velocity dispersion estimators frequently used in the literature: the biweight, the gapper, and the standard deviation
Summary
Several authors have used the velocity dispersion mass proxy to study and characterise scaling relations between SZ and dynamical mass [1,2,3]. In order to have sample with enough statistical power, it is necessary to estimate the velocity dispersion for hundreds of galaxy clusters (GCs). This goal can be achieved through spectroscopic follow-up [e.g. 4, 5], these studies are extremely expensive in terms of observational time and data reduction. For these reasons, it is extremely difficult to estimate radial velocities for more than few members (typically ∼ 20) for each cluster target. In this article we present our study of statistical and physical biases introduced in the estimation of velocity dispersion and dynamical mass
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