Correlation between centre offsets and gas velocity dispersion of galaxy clusters in cosmological simulations

The gas is the dominant component of baryonic matter in most galaxy groups and clusters. The spatial offsets of the gas centre from the halo centre could be an indicator of the dynamical state of cluster. Knowledge of such offsets is important for estimating the uncertainties when using clusters as cosmological probes. In this paper, we study the centre offsets r(off) of the gas and that of all matter within halo systems in Lambda cold dark matter (Lambda CDM) cosmological hydrodynamic simulations. We focus on two kinds of centre offsets: One is the 3D potential minimum-barycentre (PB) offsets between the gravitational potential minimum of the entire halo and the barycentre of the intra-cluster medium (ICM), and the other is the 2D potential minimum-X-ray centroid (PX) offsets between the potential minimum of the halo and the iterative centroid of the projected synthetic X-ray emission of the halo. Haloes at higher redshifts tend to have larger values of rescaled offsets r(off)/r(200) and larger gas velocity dispersion sigma(gas)(nu)/sigma(200). For both types of offsets, we find that the correlation between the rescaled centre offsets r(off)/r(200) and the rescaled 3D gas velocity dispersion sgas sigma(gas)(nu)/sigma(200) can be approximately described by a quadratic function as r(off)/r(200) proportional to (sigma(gas)(nu)/sigma(200) -k(2))(2). ABayesian analysis with the Markov-chain Monte Carlo method is employed to estimate the model parameters. Dependence of the correlation on redshifts and the gas mass fraction is also investigated.