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Title: PICACS: a tool for self-consistent modelling of galaxy cluster scaling relations
Authors: B. J. Maughan (HH WIlls Physics Laboratory, University of Bristol)

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 several observational datasets, and show that it performs as well as traditional regression methods for simply measuring scaling relation parameters, but presents several significant advantages. For clusters with available X-ray hydrostatic masses, PICACS gives a modest improvement of the precision of the mass estimates, while consistently constraining the mass-observable scaling relations. For a sample of clusters without prior mass estimates, we derive self-consistent constraints on the cluster masses and scaling relations, and find a minor improvement in precision on cluster mass estimates compared with a single scaling relation. We are also able to deconstruct the slope of the luminosity-temperature (LT) relation and show that the steepening compared to self-similar expectations is due to contributions from heating and depletion of the gas within the reference radius R500, and not due to a mass dependence of the gas structure within that radius. Finally, we use PICACS to illustrate the dependence of the expected self-similar evolution of the LT relation on the slopes of the mass scaling relations, and show that our self-consistent modelling predicts self-similar evolution significantly weaker than is commonly assumed.

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