Title: Free-form modelling of galaxy clusters: a Bayesian and data-driven approach,
Abstract: A new method is presented for modelling the physical properties of galaxy
clusters. Our technique moves away from the traditional approach of assuming
specific parameterised functional forms for the variation of physical
quantities within the cluster, and instead allows for a 'free-form'
reconstruction, but one for which the level of complexity is determined
automatically by the observational data and may depend on position within the
cluster. This is achieved by representing each independent cluster property as
some interpolating or approximating function that is specified by a set of
control points, or 'nodes', for which the number of nodes, together with their
positions and amplitudes, are allowed to vary and are inferred in a Bayesian
manner from the data. We illustrate our nodal approach in the case of a
spherical cluster by modelling the electron pressure profile Pe(r) in analyses
both of simulated Sunyaev-Zel'dovich (SZ) data from the Arcminute MicroKelvin
Imager (AMI) and of real AMI observations of the cluster MACS J0744+3927 in the
CLASH sample. We demonstrate that one may indeed determine the complexity
supported by the data in the reconstructed Pe(r), and that one may constrain
two very important quantities in such an analysis: the cluster total volume
integrated Comptonisation parameter (Ytot) and the extent of the gas
distribution in the cluster (rmax). The approach is also well-suited to
detecting clusters in blind SZ surveys.