An analysis of galaxy cluster mis-centring using cosmological hydrodynamic simulations

The choice of which position to assign as the centre of a galaxy cluster can have a significant impact on the inferred physical properties. Centre definitions based on the galactic or gas component of the clusters are easier to measure, but invariably introduce biases due to mis-centring. Using data from the BAHAMAS cosmological hydrodynamic simulations we study this bias in both two and three dimensions for 2000 clusters over the $10^{13} - 10^{15} ~\mathrm{M_{\odot}}$ mass range. We quantify and model the offset distributions between observationally-motivated centres and the `true' centre of the cluster, which is taken to be the most gravitationally bound particle measured in the simulation. We fit the cumulative distribution function of offsets with 6 different analytical models and find that a combination of an exponential distribution and a Gamma distribution fit well with most of the centroid definitions. The galaxy-based centres can be seen to be divided into a mis-centred group and a well-centred group, with the well-centred group making up about $60\%$ of all the clusters. Gas-based centres are not as clearly divided into two groups, but are overall less scattered than galaxy-based centres. We also find a cluster-mass dependence of the offset distribution of gas-based centres, with generally larger offsets for smaller mass clusters. We then measure cluster density profiles centred at each choice of the centres and fit them with empirical models. Stacked, mis-centred density profiles fit to the Navarro-Frenk-White dark-matter profile and Komatsu-Seljak gas profile show that recovered shape and size parameters can significantly deviate from the true values. For the galaxy-based centres, this can lead to cluster masses being underestimated by up to 10 per cent.