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We discuss a novel technique of manipulating X-ray images of galaxy clustersto reveal the nature of small-scale density/temperature perturbations in theintra cluster medium (ICM). As we show, this technique can be used todifferentiate between sound waves and isobaric perturbations in Chandra imagesof the Perseus and M87/Virgo clusters. The comparison of the manipulated imageswith the radio data and with the results of detailed spectral analysis showsthat this approach successfully classifies the types of perturbations and helpsto reveal their nature. For the central regions (5-100 kpc) of the M87 andPerseus clusters this analysis suggests that observed images are dominated byisobaric perturbations, followed by perturbations caused by bubbles ofrelativistic plasma and weak shocks. Such a hierarchy is best explained in a"slow" AGN feedback scenario, when much of the mechanical energy output of acentral black hole is captured by the bubble enthalpy that is graduallyreleased during buoyant rise of the bubbles. The "image arithmetic" works bestfor prominent structure and for datasets with excellent statistics, visualizingthe perturbations with a given effective equation of state. The same approachcan be extended to faint perturbations via cross-spectrum analysis of surfacebrightness fluctuations in X-ray images in different energy bands.

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