  The X-ray data obtained with XMM-Newton is used to investigate the complex
structure of the gas in the atmosphere of the Virgo cluster around M87. We
construct a simple model for the temperature and density distribution. This
model implies that the cumulative mass of the cluster gas is a power-law of its
entropy index, $kT n^{-2/3}$, similar to the Hydra cluster. This supports the
idea that such power-laws are a direct consequence of gas cooling in a
gravitational potential. In the cluster atmosphere hot bubbles of gas injected
by the AGN are rising buoyantly. We estimate the age of these structures from
the synchrotron radio data and find that this `radiative age' is consistent
with the estimated dynamical timescale. However, this requires a spatial
separation of the relativistic particles from the magnetic field. The age
estimates suggest an activity cycle of the AGN in M87 of roughly $10^8$ years.
We show that the largest radio structures are consistent with being the
remnants of buoyant bubbles injected by the AGN during an even earlier activity
cycle. The wakes behind the currently rising hot bubbles uplift cold gas from
the cluster centre. Using a simple model for the trajectory of the cold gas, we
demonstrate that the observations by XMM-Newton of a mix of hot and cold gas in
the cluster atmosphere in the vicinity of the radio structure can be explained
in this scenario. This may also explain the ridges of enhanced X-ray emission
from cold gas observed with CHANDRA.
