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Outside the cores of relaxed clusters, hot gas is in a state of
hydrostatic equilibrium, and since its radiative cooling time is
longer than the Hubble time, it is practically also in thermal
equilibrium. Relatively short cooling time in the inner core, often
dominated by a giant (elliptical) cD galaxy, necessitates a heat
source if the gas is to be in hydrostatic equilibrium. In this work
we consider the possibility that inward conductive heat transfer into
the cD halo prevents rapid cooling of the gas. We have assessed the
viability of this model under typical conditions in a rich and
relaxed cluster. It is found that the resulting gas density and
temperature profiles are consistent with observational results,
demonstrating that this simple model can provide a plausible
alternative to the common practice of assuming two separate (and
unrelated) models for the gas in the cluster and cD galaxy.
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