  We present a numerical investigation of dead, or relic, radio galaxies and
the environmental impact that radio galaxy activity has on the host galaxy or
galaxy cluster. We perform axisymmetric hydrodynamical calculations of light,
supersonic, back-to-back jets propagating in a beta-model galaxy/cluster
atmosphere. We then shut down the jet activity and let the resulting structure
evolve passively. The dead source undergoes an initial phase of pressure driven
expansion until it achieves pressure equilibrium with its surroundings.
Thereafter, buoyancy forces drive the evolution and lead to the formation of
two oppositely directed plumes that float high into the galaxy/cluster
atmosphere. These plumes entrain a significant amount of low entropy material
from the galaxy/cluster core and lift it high into the atmosphere. An important
result is that a large fraction (at least half) of the energy injected by the
jet activity is thermalized in the ISM/ICM core. The whole ISM/ICM atmosphere
inflates in order to regain hydrostatic equilibrium. This inflation is mediated
by an approximately spherical disturbance which propagates into the atmosphere
at the sound speed. The fact that such a large fraction of the injected energy
is thermalized suggests that radio galaxies may have an important role in the
overall energy budget of rich ISM/ICM atmospheres. In particular, they may act
as a strong and highly time-dependent source of negative feedback for
galaxy/cluster cooling flows.
