  Using a set of hydrodynamical simulations of 9 galaxy clusters with masses in
the range 1.5 10^{14} M_sun < M_vir < 3.4 10^{15} M_sun, we have studied the
density, temperature and X-ray surface brightness profiles of the intracluster
medium in the regions around the virial radius. We have analyzed the profiles
in the radial range well above the cluster core, the physics of which are still
unclear and matter of tension between simulated and observed properties, and up
to the virial radius and beyond, where present observations are unable to
provide any constraints. We have modeled the radial profiles between 0.3 R_200
and 3 R_200 with power laws with one index, two indexes and a rolling index.
The simulated temperature and [0.5-2] keV surface brightness profiles well
reproduce the observed behaviours outside the core. The shape of all these
profiles in the radial range considered depends mainly on the activity of the
gravitational collapse, with no significant difference among models including
extraphysics. The profiles steepen in the outskirts, with the slope of the
power-law fit that changes from -2.5 to -3.4 in the gas density, from -0.5 to
-1.8 in the gas temperature, and from -3.5 to -5.0 in the X-ray soft surface
brightness. We predict that the gas density, temperature and [0.5-2] keV
surface brightness values at R_200 are, on average, 0.05, 0.60, 0.008 times the
measured values at 0.3 R_200. At 2 R_200, these values decrease by an order of
magnitude in the gas density and surface brightness, by a factor of 2 in the
temperature, putting stringent limits on the detectable properties of the
intracluster-medium (ICM) in the virial regions.
