A B S T R A C TThe maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass distribution in a model cluster using simulated shear and magnification data to which Gaussian noise is added. The mass distribution is reconstructed directly and the inversion is regularized using the entropic prior for this positive additive distribution. For realistic noise levels, we find that the method faithfully reproduces the main features of the cluster mass distribution not only within the observed field but also slightly beyond it. We estimate the uncertainties in the reconstruction by calculating an analytic approximation to the covariance matrix of the reconstruction values of each pixel. This result is compared with error estimates derived from Monte Carlo simulations for different noise realizations and found to be in good agreement.

The maximum entropy method has been used to reconstruct images in a wide range of astronomical fields, but in its traditional form it is restricted to the reconstruction of strictly positive distributions. We present an extension of the standard method to include distributions that can take both positive and negative values. The method may therefore be applied to a much wider range of astronomical reconstruction problems. In particular, we derive the form of the entropy for positive/negative distributions and use direct counting arguments to find the form of the entropic prior. We also derive the measure on the space of positive/negative distributions, which allows the definition of probability integrals and hence the proper quantification of errors.Comment: 4 pages, no figure

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A new method for modelling spherically symmetric inhomogeneities is applied to the formation of clusters in an expanding Universe. We impose simple initial velocity and density perturbations of finite extent, and we investigate the subsequent evolution of the density field. Photon paths are also calculated, allowing a detailed consideration of gravitational lensing effects and microwave background anisotropies induced by the cluster. We apply the method to modelling high‐redshift clusters and, in particular, we consider the reported microwave decrement observed towards the quasar pair PC 1643+4631 A&B. We also consider the effect on the primordial microwave background power spectrum due to gravitational lensing by a population of massive high‐redshift clusters.

We investigate the dynamics of a cosmological dark matter fluid in the Schrödinger formulation, seeking to evaluate the approach as a potential tool for theorists. We find simple wave-mechanical solutions of the equations for the cosmological homogeneous background evolution of the dark matter field, and use them to obtain a piecewise analytic solution for the evolution of a compensated spherical overdensity. We analyse this solution from a 'quantum mechanical' viewpoint, and establish the correct boundary conditions satisfied by the wavefunction. Using techniques from multiparticle quantum mechanics, we establish the equations governing the evolution of multiple fluids and then solve them numerically in such a system. Our results establish the viability of the Schrödinger formulation as a genuine alternative to standard methods in certain contexts, and a novel way to model multiple fluids.