We present an ensemble X-ray analysis of systematic perturbations in the central hot gas properties for a sample of 28 nearby strong cool-core systems selected from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS). We analyze their cool-core features observed with the Chandra X-ray Observatory. All individual systems in our sample exhibit at least a pair of positive and negative excess perturbations in the X-ray residual image after subtracting the global brightness profile. We extract and analyze X-ray spectra of the intracluster medium (ICM) in the detected perturbed regions. To investigate possible origins of the gas perturbations, we characterize thermodynamic properties of the ICM in the perturbed regions and characterize their correlations between positive and negative excess regions. The best-fit relations for temperature and entropy show a clear offset from the one-to-one relation, $T_mathrm{neg}/T_mathrm{pos}=1.20^{+0.04}_{-0.03}$ and $K_mathrm{neg}/K_mathrm{pos}=1.43pm 0.07$, whereas the best-fit relation for pressure is found to be remarkably consistent with the one-to-one relation $P_mathrm{neg}=P_mathrm{pos}$, indicating that the ICM in the perturbed regions is in pressure equilibrium. These observed features in the HIFLUGCS sample are in agreement with the hypothesis that the gas perturbations in cool cores are generated by gas sloshing. We also analyze synthetic observations of perturbed cluster cores created from binary merger simulations, finding that the observed temperature ratio agrees with the simulations, $T_mathrm{neg}/T_mathrm{pos}sim 1.3$. We conclude that gas sloshing induced by infalling substructures plays a major role in producing the characteristic gas perturbations in cool cores. The ubiquitous presence of gas perturbations in cool cores may suggest a significant contribution of gas sloshing to suppressing runaway cooling of the ICM.
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