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Energy deposited by black holes in the hot X-ray gas of elliptical galaxies, groups and clusters
Galaxy groups show entropy excesses $ΔS$ with respect to theoretical expectations from models and simulations with purely gravitational heating. We determine the heat $Q_{\rm heat}\simeq TΔS$ deposited by non-gravitational sources into the hot gas of elliptical galaxies, groups and clusters, and to
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