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Rich, X-ray luminous clusters of galaxies represent the high mass tail of the dark matter overdensity spectrum. Understanding their mass profiles is key to understanding the formation of large scale structure in the universe. For example, on cluster-sized scales, the distribution of dark matter and the relationship between luminosity and mass is not well understood.
Gravitational lens distortion tomography (arclet inversion) is a direct measure of the projected total mass distribution in the lens. The presence of large numbers of faint high-redshift background galaxies allows one to map foreground mass distributions. The appearance of the background galaxies are distorted due to the gravitational bending of light, and at at limiting surface brightness of 29-30 mag arcsec$^{-2}$ there are over 100 background galaxies per arcmin$^2$. High redshift background galaxies can be selected for this purpose by selecting on color and surface brightness.
Using deep 2048$^2$ images we have measured the distortion of over ten thousand background galaxies to trace the mass distribution of the large cluster Abell 1689 to beyond 800 h$^{-1}$ kpc. Multiple realistic simulations allowed us to correct for systematics arising from measurement error and finite image resolution. We were able to calibrate the total mass in the cluster by using the presence of two large arcs located at the Einstein radius.
In our poster we will report on the shape of the mass distribution and compare it to some recent N-body/SPH simulations of X-ray clusters. Outside the core region the mass is not symmetrically distributed around the core. We will compare this with the light distribution in the cluster. We will also show comparisons among the density profiles of the total mass, the hot gas, and the galaxies. Finally we will present comparisons between this gravitational lensing result and both X-ray (ROSAT) and kinematic measurements (optical spectroscopy) in order to quantify systematic differences among these approaches.
