  We present an entirely analytic model for a preheated, polytropic
intergalactic medium in hydrostatic equilibrium within a NFW dark halo
potential in which the evolution of the halo structure between major merger
events proceeds inside-out by accretion. This model is used to explain, within
a standard $\Lambda$CDM cosmogony, the observed X-ray properties of nearby
relaxed, non-cooling flow groups and clusters of galaxies. We find that our
preferred solution to the equilibrium equations produces scaling relations in
excellent agreement with observations, while simultaneously accounting for the
typical structural characteristics of the distribution of the diffuse baryons.
In the class of preheating models, ours stands out because it offers a unified
description of the intrahalo medium for galaxy systems with total masses above
$\sm 2\times 10^{13}$\msun, does not produce baryonic configurations with large
isentropic cores, and reproduces faithfully the observed behavior of the gas
entropy at large radii. All this is achieved with a moderate level of energy
injection of about half a keV, which can be easily accommodated within the
limits of the total energy released by the most commonly invoked feedback
mechanisms, as well as with a polytropic index of 1.2, consistent with both
many observational determinations and predictions from high-resolution
gas-dynamical simulations of non-cooling flow clusters. More interestingly, our
scheme offers a physical motivation for the adoption of this specific value of
the polytropic index, as it is the one that best ensures the conservation after
halo virialization of the balance between the total specific energies of the
gas and dark matter components for the full range of masses investigated.
