Dynamical analysis of stacked samples of asymmetric non-static self-gravitating systems

ABSTRACT We use numerical simulations to explore biases that arise in dynamical estimates of the mean mass profile for a collection of galaxy clusters that have been stacked to make a composite. There are three types of bias. The first one arises from anisotropy of the kinematic pressure tensor and has been already well studied; the second arises from departures from equilibrium; and the third arises because of heterogeneity of the clusters used, from their individual non-sphericity, and because velocities used are measured with respect to centres that are, in general, accelerating. Here we focus on the latter two. We stack clusters to measure the pressure tensor and density profiles and then estimate the dynamical mass profile using the Jeans equation, and compare to the actual mean mass profile. The main result of this paper is an estimate of the bias that can be used to correct the dynamical mass estimate, and we show how it depends on the cluster sample selection. We find that Jeans equation typically overestimates the true mass by about 20 per cent at the virial radius.