Physical component analysis of galaxy cluster weak gravitational lensing data

We present a novel approach for reconstructing the projected mass distribution of clusters of galaxies from sparse and noisy weak gravitational lensing shear data. The reconstructions are regularised using knowledge gained from numerical simulations of clusters: trial mass distributions are constructed from N physically-motivated components, each of which has the universal density profile and characteristic geometry observed in simulated clusters. The parameters of these components are assumed to be distributed \emph{a priori} in the same way as they are in the simulated clusters. Sampling mass distributions from the components' parameters' posterior probability density function allows estimates of the mass distribution to be generated, with error bars. The appropriate number of components is inferred from the data itself via the Bayesian evidence, and is typically found to be small, reflecting the quality of the simulated data used in this work. Ensemble average mass maps are found to be robust to the details of the noise realisation, and succeed in recovering the input mass distribution (from a realistic simulated cluster) over a wide range of scales. We comment on the residuals of the reconstruction and their implications, and discuss the extension of the method to include strong lensing information.