Abstract
Galaxies presumably are sources of cosmic rays due to supernovae or active nuclei. In the centre of clusters of galaxies with high gas densities, where cosmic rays cannot easily escape, the cosmic rays may have an influence on the dynamics of the cluster gas. We have investigated the cosmic ray - gas interaction by means of steady models with spherical symmetry. It was found that the cosmic ray pressure may become comparable to the gas pressure in the halo region around a central galaxy with a cooling flow. Rayleigh Taylor instabilities might develop there and set the scale for inhomogeneities leading to filaments or star formation regions.
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