PICACS: a tool for 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.