Impact of AGN on the gas in clusters of galaxies

Clusters of galaxies with masses up to few $10^{15}~M_\odot$ are the largest gravitationally bound objects in the Universe. According to the widely accepted hierarchical model of structure formation the largest structures are formed by mergers of smaller (less massive) objects. Massive clusters are therefore expected to appear in the Universe only ``recently'' (redhshifts $z < 1-2$) and their number is very sensitive to the cosmological parameters, such the amplitude of primordial fluctuations and dynamics of the Universe expansion which is in turn related to dark energy and dark matter content of the Universe. Three major constituents make a galaxy cluster: stars (readily observable in bright optical galaxies), hot X-ray emitting gas (observed with modern X-ray space observatories) and dark matter (indirectly observed through its influence on galaxies and gas). It is believed that in clusters the mass fractions of baryons (stars and gas) and the dark matter are representative for the Universe as a whole. Stars is the least massive component out of three, making only few \% of the cluster mass, while hot gas and dark matter account for 10\%-15\% and $\sim 75$\% respectively. Since the dark matter can not be seen directly we have to use other components to determine main parameters of a cluster (such as e.g. total mass). In particular instrumental are X-ray observations of the hot gas, which are used to accurately map the mass profile of a cluster. This hot gas is a fully ionized plasma with the temperature of tens of millions degrees and the density $10^{-2}-10^{-4}$ particles per cm$^3$, which emits radiation primarily through bremsstrahlung and excitation/recombination lines of heavy elements. While we are confident that the parameters of clusters determined from optical and X-ray data are broadly correct, there are a number observed phenomena in galaxy clusters which are yet to be explained and a number of parameters yet to be measured. For instance we do not fully understand if radiative cooling of the gas in the central regions of clusters is compensated by some sources of energy (e.g. from the activity of supermassive black holes). We also do not know what are the values of such fundamental characteristic of the cluster plasma as thermal conductivity or viscosity. In our research we discuss two simple theoretical models aimed at: evaluating thermal conductivity in the gas using X-ray observations of sharp features in the surface brightness distribution of X-ray emission (so called ``cold fronts'') estimating the energetics of the feedback from the supermassive black holes through its influence on the distribution of heavy elements in the hot gas.