Offset between X-ray and optical centers in clusters of galaxies: Connecting eROSITA data with simulations

Context. The characterization of the dynamical state of galaxy clusters is key to studying their evolution, evaluating their selection, and using them as a cosmological probe. In this context, the offsets between different definitions of the center have been used to estimate the cluster disturbance. Aims. Our goal is to study the distribution of the offset between the X-ray and optical centers in clusters of galaxies. We study the offset for clusters detected by the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Spectrum-Roentgen-Gamma (SRG) observatory. We aim to connect observations to predictions by hydrodynamical simulations and N-body models. We assess the astrophysical effects affecting the displacements. Methods. We measured the offset for clusters observed in the eROSITA Final Equatorial-Depth Survey (eFEDS) and the first eROSITA all-sky survey (eRASS1). We focus on a subsample of 87 massive eFEDS clusters at low redshift, with M500c > 1×1014 M⊙ and 0.15 < z < 0.4. We compared the displacements in such sample to those predicted by the TNG and the Magneticum simulations. We additionally link the observations to the offset parameter Xoff measured for dark matter halos in N-body simulations, using the hydrodynamical simulations as a bridge. Results. We find that, on average, the eFEDS clusters show a smaller offset compared to eRASS1 because the latter contains a larger fraction of massive and disturbed structures. We measured an average offset of $ \Delta_\mathrm{X{-}O} = 76.3_{-27.1}^{+30.1} $ kpc, when focusing on the subsample of 87 eFEDS clusters. This is in agreement with the predictions from TNG and Magneticum, and the distribution of Xoff from dark matter only (DMO) simulations. However, the tails of the distributions are different. Using ΔX − O to classify relaxed and disturbed clusters, we measured a relaxed fraction of 31% in the eFEDS subsample. Finally, we found a correlation between the offset measured on hydrodynamical simulations and Xoff measured on their parent dark-matter-only run and we calibrated the relation between them. Conclusions. We conclude that there is good agreement between the offsets measured in eROSITA data and the predictions from simulations. Baryonic effects cause a decrement (increment) in the low (high) offset regime compared to the Xoff distribution from dark matter-only simulations. The offset–Xoff relation provides an accurate prediction of the true Xoff distribution in Magneticum and TNG. It allows for the offsets to be introduced in a cosmological context with a new method in order to marginalize over selection effects related to the cluster dynamical state