Formation of non-thermal particle spectra in galaxy clusters

The origin of hard X-ray (HXR) excess emission from clusters of galaxies is still an enigma, whose nature is debated. One of the possible mechanism to produce this emission is the bremsstrahlung model. However, previous numerical calculations showed that the intracluster plasma should be overheated very fast if the HXR excess is of non-thermal bremsstrahlung origin. We revisited this problem and found that at some parameters of particle acceleration the rate of plasma heating is rather low. For example, for Coma cluster the temperature rise from the initial temperature T₀ = 7 keV to T = 8 keV takes relatively long time, ∼ 10⁹ year, if the momentum diffusion coefficient has a cut-off at low momenta and rises rapidly above the cut-off. At the same time the intensity of non thermal tail is high enough to produce the HXR in e.g. Coma. We conclude that at these conditions the bremsstrahlung model does not contradict the origin of HXR from galaxy clusters and we can explain the HXR satisfactory without heating the plasma too fast.