arXiv subjects

M. P. Hobson

Publications and source records attributed to M. P. Hobson.

130 records · Page 8Linked to original sources

arXiv1998

A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

The 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 regularised 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 on 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 realisations and found to be in good agreement.

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arXiv1997

Effect of a Collapsing Cluster on the CMB temperature and Power Spectrum

We present a new model for the formation of spherically symmetric clusters in an expanding Universe. Both the Universe and the collapsing cluster are governed by the same pressure less fluid equations for which a uniform initial density profile is assumed. A simple perturbation imposed on the initial velocity field gives rise to an over-density which closely models real clusters. The computation of photon paths allows us to evaluate the gravitational effects imprinted on a Cosmic Microwave Background (CMB) photon passing through such an evolving mass. We also consider the lensing properties of collapsing clusters and investigate the effect of a population of such clusters on the primordial microwave background power spectrum.

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arXiv1996

Ideal scales for weighing the Universe

We investigate the performance of a large class of cosmic microwave background experiments with respect to their ability to measure various cosmological parameters. We pay special attention to the measurement of the total cosmological density, $Ω$. We consider interferometer experiments, all-sky single-dish experiments, and also single-dish experiments with a deep-patch technique. Power spectrum estimates for these experiments are studied, and their induced errors in cosmological parameter estimates evaluated. Given this motivation we find various promising corners in the experiment parameter space surveyed. Low noise all-sky satellite experiments are the expensive option, but they are best suited for dealing with large sets of cosmological parameters. At intermediate noises we find a useful corner in high-resolution deep patch single-dish experiments. Interferometers are limited by sample variance, but provide the best estimates based on the very small angular scales. For all these experiments we present conservative, but still promising estimates of the accuracy of the measurement of $Ω$. In these estimates we consider a variety of possible signals not necessarily in the vicinity of standard cold dark matter.

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arXiv1996

Observability of secondary Doppler peaks in the CMBR power spectrum by experiments with small fields

We investigate the effects of finite sky coverage on the spectral resolution $Δ\ell$ in the estimation of the CMBR angular power spectrum $C^{\ell}$. A method is developed for obtaining quasi-independent estimates of the power spectrum, and the cosmic/sample variance of these estimates is calculated. The effect of instrumental noise is also considered for prototype interferometer and single-dish experiments. By proposing a statistic for the detection of secondary (Doppler) peaks in the CMBR power spectrum, we then compute the significance level at which such peaks may be detected for a large range of model CMBR experiments. In particular, we investigate experimental design features required to distinguish between competing cosmological theories, such as cosmic strings and inflation, by establishing whether or not secondary peaks are present in the CMBR power spectrum.

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