A highly desirable technique sought after by cosmology is one which enables the accurate mass measurement of rich galaxy clusters. From observations of their abundance and primarily their mass, clusters give strong constraints on the density parameter of the Universe, models of structure formation and normalisation of the power spectrum of density fluctuations. Gravitational lensing provides such a technique. Prevailing over X-ray temperature and virial velocity methods known to be problematic, lensing permits determination of cluster masses independent of dynamical state.
This thesis concentrates mainly on the exploitation of the magnification properties of lenses rather than those of shear analysis which relies upon the quantification of galaxy image distortions. Magnification allows absolute mass measurements, breaking the slieet-mass degeneracy experienced by shear. To this extent, a theoretical analysis of the geometrical magnification of angular separations between galaxies lying behind a lensing cluster is performed. This sees application to the cluster Abell 1689 using V and I band observations to select background galaxies based on their V-I colour. The distribution of source number counts in the observed field of view results in the determination of a radial mass profile and a mass map for Abell 1689. This predicts a projected mass interior to 0.24/?,_1Mpc of M (< 0.24/i_1Mpc) = (0.50 ± 0.09) x 1O15/i_1M0.
A new method of directly determining accurate, self-consistent lens mass and shear maps in the strong lensing regime from magnification is presented. The method relies upon pixellization of the surface mass density distribution which generates a simple, solvable set of equations. The concept of pixellization is also directed at shear analysis to give rise to a simplified method of application. Through use of cluster models,XI
the method is verified before the magnification data from the colour-selected number counts is input to compute a self-consistent mass map of Abell 1689.
The property of lens magnification to amplify observed background source fluxes is investigated. Using an independent set of observations in nine optimally chosen filters, photometric redshifts of objects lying in the field of Abell 1689 are calculated. In addition to providing an unambiguous distinction between cluster members, foreground objects and background sources this also enables computation of the source luminosity function. Comparison of this with the distribution of luminosities in an observed offset field quantifies the lens-induced flux magnification to arrive at an independent mass profile measurement of Abell 1689. A projected mass interior to 0.25/?,-1 Mpc of M (< 0.25/i-1Mpc) = (0.48 ± 0.16) x 1015/»_1Mo is found.