Parallel integer relation detection: techniques and applications

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Non-parametric mass reconstruction of A1689 from strong lensing data with SLAP

We present the mass distribution in the central area of the cluster A1689 by fitting over 100 multiply lensed images with the non-parametric Strong Lensing Analysis Package (SLAP, Diego et al. 2004). The surface mass distribution is obtained in a robust way finding a total mass of 0.25E15 M_sun/h within a 70'' circle radius from the central peak. Our reconstructed density profile fits well an NFW profile with small perturbations due to substructure and is compatible with the more model dependent analysis of Broadhurst et al. (2004a) based on the same data. Our estimated mass does not rely on any prior information about the distribution of dark matter in the cluster. The peak of the mass distribution falls very close to the central cD and there is substructure near the center suggesting that the cluster is not fully relaxed. We also examine the effect on the recovered mass when we include the uncertainties in the redshift of the sources and in the original shape of the sources. Using simulations designed to mimic the data, we identify some biases in our reconstructed mass distribution. We find that the recovered mass is biased toward lower masses beyond 1 arcmin (150 kpc) from the central cD and that in the very center we may be affected by degeneracy problems. On the other hand, we confirm that the reconstructed mass between 25'' and 70'' is a robust, unbiased estimate of the true mass distribution and is compatible with an NFW profile.Comment: 11 pages, 12 figures. MNRAS submitted. A full resolution of the paper can be found in http://darwin.physics.upenn.edu/SLAP

Mass and Gas Profiles in A1689: Joint X-ray and Lensing Analysis

We carry out a comprehensive joint analysis of high quality HST/ACS and Chandra measurements of A1689, from which we derive mass, temperature, X-ray emission and abundance profiles. The X-ray emission is smooth and symmetric, and the lensing mass is centrally concentrated indicating a relaxed cluster. Assuming hydrostatic equilibrium we deduce a 3D mass profile that agrees simultaneously with both the lensing and X-ray measurements. However, the projected temperature profile predicted with this 3D mass profile exceeds the observed temperature by ~30% at all radii, a level of discrepancy comparable to the level found for other relaxed clusters. This result may support recent suggestions from hydrodynamical simulations that denser, more X-ray luminous small-scale structure can bias observed temperature measurements downward at about the same (~30%) level. We determine the gas entropy at 0.1r_{vir} (where r_{vir} is the virial radius) to be ~800 keV cm^2, as expected for a high temperature cluster, but its profile at >0.1r_{vir} has a power-law form with index ~0.8, considerably shallower than the ~1.1 index advocated by theoretical studies and simulations. Moreover, if a constant entropy ''floor'' exists at all, then it is within a small region in the inner core, r<0.02r_{vir}, in accord with previous theoretical studies of massive clusters.Comment: 18 pages, 20 figures, 7 tables, accepted for publication in MNRAS, minor changes to match published versio