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
intra cluster 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" AGN 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 datasets 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.
