LAUSR

The gas is the dominant component of baryonic matter in most galaxy groups and clusters. The spatial offsets of gas centre from the halo centre could be an indicator of the dynamical state of cluster. Knowledge of such offsets is important for estimate the uncertainties when using clusters as cosmological probes. In this paper, we study the centre offsets $r_{\rm off}$ between the gas and that of all the matter within halo systems in $\Lambda$CDM cosmological hydrodynamic simulations. We focus on two kinds of centre offsets: one is the three-dimensional PB offsets between the gravitational potential minimum of the entire halo and the barycentre of the ICM, and the other is the two-dimensional PX offsets between the potential minimum of the halo and the iterative centroid of the projected synthetic X-ray emission of the halo. Halos at higher redshifts tend to have larger values of rescaled offsets $r_{\rm off}/r_{200}$ and larger gas velocity dispersion $\sigma_{v}^{\rm gas}/\sigma_{200}$. For both types of offsets, we find that the correlation between the rescaled centre offsets $r_{\rm off}/r_{200}$ and the rescaled 3D gas velocity dispersion, $\sigma_v^{\rm gas}/\sigma_{200}$ can be approximately described by a quadratic function as $r_{{\rm off}}/r_{200} \propto (\sigma_{v}^{\rm gas}/\sigma_{200} - k_2)^{2}$. A Bayesian analysis with MCMC method is employed to estimate the model parameters. Dependence of the correlation relation on redshifts and the gas mass fraction are also investigated.