  Recent X-ray observations have been used to demonstrate that the cluster gas
mass-temperature relation is steeper than theoretical self-similar predictions
drawn from numerical simulations that consider the evolution of the cluster gas
through the effects of gravity and shock heating alone. One possible
explanation for this is that the gas mass fraction is not constant across
clusters of different temperature, as is usually assumed. Observationally,
however, there is no compelling evidence for gas mass fraction variation,
especially in the case of hot clusters. Seeking an alternative physical
explanation for the observed trends, we investigate the role in the cluster gas
mass - temperature relation of the preheating of the intracluster medium by
some arbitrary source for clusters with emission-weighted mean temperatures of
greater than about 3 keV. Making use of the physically-motivated, analytic
models developed in 2002 by Babul and coworkers, we find that preheating does,
indeed, lead to a steeper relation. This is in agreement with previous
theoretical studies on the relation. However, in apparent conflict with these
studies, we argue that a ``high'' level of entropy injection is required to
match observations. In particular, an entropy floor of greater than about 300
keV cm^2 is required. We also present a new test, namely, the study of the
relation within different fixed radii. This allows one to indirectly probe the
density profiles of clusters, since it samples different fractions of the
virial radius for clusters of different temperature. This test also confirms
that a high level of preheating is required to match observations.
