A Power Spectrum Comparison of Synthetic X-ray Maps in the Perseus Cluster

The cooling flow problem in cluster highlights a discrepancy between predicted and observed cooling rates and star formation rates in the cores of large, relaxed clusters, which can be explained by one or more sources heating the cluster astmosphere and stopping the cooling flow. One candidate source are jets from active galactic nuclei, which can inject energy into the thermal cluster gas. If AGN can explain the cooling gap there must be a transfer mechanism between the collimated jet and the atmosphere as a whole. Turbulent heating, in which the rising bubble inflated by the AGN transfers energy to a turbulent cascade in the intracluster medium, has been proposed as a viable solution. X-ray observations can reveal the turbulence spectrum in the ICM relative to distance from the jet, constraining the role of different driving mechanisms. We analyze AGN simulations of the Perseus cluster at various times and compare the results to observations to constrain the heating contribution of the jet to the cluster atmosphere. We find that the magnitude of our velocity power spectra are consistent with the Hitomi measurement of ~150 km/s turbulence. Our work shows that multiple jet episodes can readily explain the overall level of turbulence in the core of the Perseus cluster and discuss new diagnostics to decompose annular power spectra as a way to constrain past episodes of AGN activity.