Abstract
The existence of a hot X-ray emitting gas phase in giant elliptical galaxies has long been recognized, but its structure and dynamics are still controversial. We explore the possibility that the gas is heated from below, causing it to convect. This leads to a two-component model in which a cooling flow feeds into an adiabatic core. The heat source for this core is taken to be the central black hole. The model is applied to the three galaxies with the best data from the Einstein observatory: NGC 4472, 4636 and 4649. In our models of NGC 4636, gas flows inwards at all radii, while in NGC 4472 and 4649 the flow is directed outwards at large radii. Consequently, the adiabatic core of NGC 4636 is signicantly larger and more luminous than those of NGC 4472 and 4649
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