Cosmology and Astrophysics from Relaxed Galaxy Clusters III:
  Thermodynamic Profiles and Scaling Relations
  This is the third in a series of papers studying the astrophysics and
cosmology of massive, dynamically relaxed galaxy clusters. Our sample comprises
40 clusters identified as being dynamically relaxed and hot (i.e., massive) in
Papers I and II of this series. Here we consider the thermodynamics of the
intracluster medium, in particular the profiles of density, temperature and
related quantities, as well as integrated measurements of gas mass, average
temperature, total luminosity and center-excluded luminosity. We fit power-law
scaling relations of each of these quantities as a function of redshift and
cluster mass, which can be measured precisely and with minimal bias for these
relaxed clusters using hydrostatic arguments. For the thermodynamic profiles,
we jointly model the density and temperature and their intrinsic scatter as a
function of radius, thus also capturing the behavior of the gas pressure and
entropy. For the integrated quantities, we also jointly fit a multidimensional
intrinsic covariance. Our results reinforce the view that simple hydrodynamical
models provide a good description of relaxed clusters outside their centers,
but that additional heating and cooling processes are important in the inner
regions (radii $r < 0.5r_{2500} \approx 0.15r_{500}$). The thermodynamic
profiles remain regular, with small intrinsic scatter, down to the smallest
radii where deprojection is straightforward ($\sim 20$ kpc); within this
radius, even the most relaxed systems show clear departures from spherical
symmetry. Our results suggest that heating and cooling are continuously
regulated in a tight feedback loop, allowing the cluster atmosphere to remain
stratified on these scales.
