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Using a set of 73 numerically simulated galaxy clusters, we havecharacterised the statistical and physical biases for three velocity dispersionand mass estimators, namely biweight, gapper and standard deviation, in thesmall number of galaxies regime ($N_{gal} \leq 75$), both for the determinationof the velocity dispersion and the dynamical mass of the clusters via the$\sigma-M$ relation. These results are used to define a new set of unbiasedestimators, that are able to correct for those statistical biases. By applyingthese new estimators to a subset of simulated observations, we show that theycan retrieve bias-corrected values for both the mean velocity dispersion andthe mean mass.

Biases in the estimation of velocity dispersions and dynamical masses for galaxy clusters