PICACS: self-consistent modelling of galaxy cluster scaling relations
  In this paper, we introduce PICACS, a physically-motivated, internally
consistent model of scaling relations between galaxy cluster masses and their
observable properties. This model can be used to constrain simultaneously the
form, scatter (including its covariance) and evolution of the scaling
relations, as well as the masses of the individual clusters. In this framework,
scaling relations between observables (such as that between X-ray luminosity
and temperature) are modelled explicitly in terms of the fundamental
mass-observable scaling relations, and so are fully constrained without being
fit directly. We apply the PICACS model to two observational datasets, and show
that it performs as well as traditional regression methods for simply measuring
individual scaling relation parameters, but reveals additional information on
the processes that shape the relations while providing self-consistent mass
constraints. Our analysis suggests that the observed combination of slopes of
the scaling relations can be described by a deficit of gas in low-mass clusters
that is compensated for by elevated gas temperatures, such that the total
thermal energy of the gas in a cluster of given mass remains close to
self-similar expectations. This is interpreted as the result of AGN feedback
removing low entropy gas from low mass systems, while heating the remaining
gas. We deconstruct the luminosity-temperature (LT) relation and show that its
steepening compared to self-similar expectations can be explained solely by
this combination of gas depletion and heating in low mass systems, without any
additional contribution from a mass dependence of the gas structure. Finally,
we demonstrate that a self-consistent analysis of the scaling relations leads
to an expectation of self-similar evolution of the LT relation that is
significantly weaker than is commonly assumed.
