Characterizing the Properties of Clusters of Galaxies as a Function of
  Luminosity and Redshift
  We report the application of a new Monte Carlo method, Smoothed Particle
Inference (SPI, described in a pair of companion papers), towards analysis and
interpretation of X-ray observations of clusters of galaxies with the
XMM-Newton satellite. Our sample consists of publicly available, well-exposed
observations of clusters at redshifts z > 0.069, totaling 101 objects. We
determine the luminosity and temperature structure of the X-ray emitting gas,
with the goal to quantify the scatter and the evolution of the L_X - T
relation, as well as to investigate the dependence on cluster substructure with
redshift. We confirm that L_X \propto T^3 and we find a weak redshift
dependence (\propto (1+z)^(\beta_LT), \beta_LT=0.50 +- 0.34), in contrast to
some Chandra results. The level of dynamical activity is established using the
"power ratios" method, and we find signs of evolution in the P_3/P_0 power
ratio. A new method, the "temperature two-point correlation function," is
proposed. This method is used to determine the "power spectrum" of temperature
fluctuations in the X-ray emitting gas as a function of spatial scale. We show
how this method can be fruitfully used to identify cooling core clusters as
well as those with disturbed structures, presumably due to on-going or recent
merger activity.
