Arithmetic with X-ray images of galaxy clusters: effective equation of state for small-scale perturbations in the ICM

We discuss a novel technique of manipulating X-ray images of galaxy clusters to reveal the nature of small-scale density/temperature perturbations in the intracluster medium (ICM). As we show, this technique can be used to differentiate between sound waves and isobaric perturbations in Chandra images of the Perseus and M87/Virgo clusters. The comparison of the manipulated images with the radio data and with the results of detailed spectral analysis shows that this approach successfully classifies the types of perturbations and helps to reveal their nature. For the central regions (5–100 kpc) of the M87 and Perseus clusters, this analysis suggests that observed images are dominated by isobaric perturbations, followed by perturbations caused by bubbles of relativistic plasma and weak shocks. Such a hierarchy is best explained in a ‘slow’ active galactic nuclei feedback scenario, when much of the mechanical energy output of a central black hole is captured by the bubble enthalpy that is gradually released during buoyant rise of the bubbles. The ‘image arithmetic’ works best for prominent structure and for data sets with excellent statistics, visualizing the perturbations with a given effective equation of state. The same approach can be extended to faint perturbations via cross-spectrum analysis of surface brightness fluctuations in X-ray images in different energy bands.