In the semi-analytical work presented here the feedback from supermassive
black holes on galaxy clusters is investigated. In particular we aim at providing
simple diagnostics tools to constrain the characteristic velocities
and spatial scales of the hot Intra Cluster Medium (ICM) motions. In
the so-called "cold core'' clusters these motions are believed to be
driven by the activity of a central black hole. The methods
developed here, together with present-day and future observations, are designed to help to solve the puzzle of cooling flow clusters (see section 1.3)
and understand better the AGN/gas interaction in smaller systems (down
to individual galaxies).\\
Clusters of galaxies are the largest gravitationally bound systems in
the Universe: they are composed of hundreds to thousands of galaxies,
moving in a deep potential well set by the dominating dark matter. The
whole volume of clusters is filled with hot (temperature ∼107−108~K) and rarefied (electron density 10−4−10−1cm−3) gas. In such a high-temperature regime even heavy elements
(e.g. silicon, sulfur, iron etc.) are highly ionized up to [H]- or
[He]-like ions and they emit in bright lines with energies from ∼0.7 to ∼8 keV. Using X-ray observations one can reliable
measure all the major gas properties: the temperature, density and abundance
of heavy elements.\\
A significant fraction of clusters (called "cool core'' clusters)
show distinct signatures in the central region: the gas temperature
drops inward, while the gas density increases. The central gas
radiative cooling time in such clusters is much shorter than the age
of the cluster and without any external source of energy the gas would cool
well below X-ray temperatures. However observations suggest that the
gas temperature drops only to 1-2 keV. One plausible explanation of
this problem is that the activity of a central supermassive black hole
deposits large amounts of mechanical energy into the cluster gas and that this
balances the gas radiative losses. A direct implication of this
hypothesis is that the hot gas is not at rest, but it is continuously stirred
by the AGN activity.\\
The same class of cool core clusters is characterized by a centrally
peaked distribution of the heavy elements abundance (usually measured
using the He-like iron 6.7 keV line). The peaked abundance profiles are
likely associated with the metals ejection by the stars of very massive
elliptical galaxies, that are always present at the centers of these clusters.
However the observed abundance distributions are significantly broader
than the central galaxy light profiles, suggesting that some gas motions
are spreading the metals ejected from the galaxy. We treat this
process in a diffusion approximation to derive, from the X-ray
observations, constraints on the characteristic velocities and
spatial scales of the gas motions for a sample of cool core clusters and
groups (Chapters 2 and 3). The parameters derived from a simple
semi-analytic model are then compared with the results of numerical
simulations of the AGN/gas interaction in the cluster core (Chapter 4).\\
In Chapter 5 we discuss the impact of the gas motions on the width of
the strongest X-ray emission lines. Since the characteristic thermal
velocities of heavy ions (e.g. iron) are much smaller than the sound speed
of the gas, the width of the lines sensitively depends on the presence
of gas motions. We show that both the absolute value of the linewidth
and its dependence on the projected distance from the cluster center
provide valuable diagnostics of the gas motions. Such measurements
will soon become possible with the launch of X-ray micro-calorimeters
in space.\\
This work has been done in collaboration with E.Churazov, R.Sunyaev,
H.B\"ohringer, M.Br\"uggen, W.Forman and E.Roediger