Multi-color detection of gravitational arcs

Strong gravitational lensing provides fundamental insights into the understanding of the dark matter distribution in massive galaxies, galaxy clusters and the background cosmology. Despite their importance, the number of gravitational arcs discovered so far is small. The urge for more complete, large samples and unbiased methods of selecting candidates is rising. A number of methods for the automatic detection of arcs have been proposed in the literature, but large amounts of spurious detections retrieved by these methods forces observers to visually inspect thousands of candidates per square degree in order to clean the samples. This approach is largely subjective and requires a huge amount of eye-ball checking, especially considering the actual and upcoming wide field surveys, which will cover thousands of square degrees. In this paper we study the statistical properties of colours of gravitational arcs detected in the 37 deg^2 of the CARS survey. We have found that most of them lie in a relatively small region of the (g'-r',r'-i') colour-colour diagram. To explain this property, we provide a model which includes the lensing optical depth expected in a LCDM cosmology that, in combination with the sources' redshift distribution of a given survey, in our case CARS, peaks for sources at redshift z~1. By further modelling the colours derived from the SED of the galaxies dominating the population at that redshift, the model well reproduces the observed colours. By taking advantage of the colour selection suggested by both data and model, we show that this multi-band filtering returns a sample 83% complete and a contamination reduced by a factor of ~6.5 with respect to the single-band arcfinder sample. New arc candidates are also proposed.Comment: 13 pages, 7 figures, 4 tables; title modified, text extended, figures improved, error estimate improve

Counting Homomorphisms to Trees Modulo a Prime

Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of #_pHomsToH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies. Our main result states that for every tree H and every prime p the problem #_pHomsToH is either polynomial time computable or #_pP-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of #_pHomsToH are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo 2 case but also for the modular counting functions of all primes p

Automatic Detection of Gravitational Lenses in Astronomical Image Data

Strong gravitational lensing can magnify distant sources and also provides a direct probe of the mass density between source and observer. For these reasons, it has become an important tool in astronomy. Among other applications, it is used to constrain cosmological parameters, reconstruct the projected mass distribution of galaxy clusters and study their dynamics. Determining the statistical abundance of background galaxies projected into heavily distorted arcs by galaxy cluster lenses could improve our understanding of large scale structure formation, but arc statistics is particularly difficult due to possibly significant biases in the selection of galaxy cluster lenses. In order to provide a larger, unbiased sample of strong lenses, an efficient, automated arc detection software that uses a novel approach to detect elongated structures in images was developed for this PhD thesis. The new detection algorithm is based on locally coherent features and is capable of detecting even faint arcs with high computational efficiency. Postprocessing algorithms were developed to classify the detections and to remove false positives. For calibration and to determine its sensitivity to arcs of different magnitudes the completed software was applied to simulated images. The application to real ACS images resulted in 24 new galaxy-type lens candidates

Research Perspectives: The Anatomy of a Design Principle

This essay derives a schema for specifying design principles for information technology-based artifacts in sociotechnical systems. Design principles are used to specify design knowledge in an accessible form, but there is wide variation and lack of precision across views regarding their formulation. This variation is a sign of important issues that should be addressed, including a lack of attention to human actors and levels of complexity as well as differing views on causality, on the nature of the mechanisms used to achieve goals, and on the need for justificatory knowledge. The new schema includes the well-recognized elements of design principles, including goals in a specific context and the mechanisms to achieve the goal. In addition, the schema allows: (1) consideration of the varying roles of the human actors involved and the utility of design principles, (2) attending to the complexity of IT-based artifacts through decomposition, (3) distinction of the types of causation (i.e., deterministic versus probabilistic), (4) a variety of mechanisms in achieving aims, and (5) the optional definition of justificatory knowledge underlying the design principles. We illustrate the utility of the proposed schema by applying it to examples of published research

Research Perspectives: The Anatomy of a Design Principle

This essay derives a schema for specifying design principles for information technology-based artifacts in sociotechnical systems. Design principles are used to specify design knowledge in an accessible form, but there is wide variation and lack of precision across views regarding their formulation. This variation is a sign of important issues that should be addressed, including a lack of attention to human actors and levels of complexity as well as differing views on causality, on the nature of the mechanisms used to achieve goals, and on the need for justificatory knowledge. The new schema includes the well-recognized elements of design principles, including goals in a specific context and the mechanisms to achieve the goal. In addition, the schema allows: (1) consideration of the varying roles of the human actors involved and the utility of design principles, (2) attending to the complexity of IT-based artifacts through decomposition, (3) distinction of the types of causation (i.e., deterministic versus probabilistic), (4) a variety of mechanisms in achieving aims, and (5) the optional definition of justificatory knowledge underlying the design principles. We illustrate the utility of the proposed schema by applying it to examples of published researc

Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties

We present results from a comprehensive lensing analysis in HST data, of the complete CLASH cluster sample. We identify new multiple-images previously undiscovered allowing improved or first constraints on the cluster inner mass distributions and profiles. We combine these strong-lensing constraints with weak-lensing shape measurements within the HST FOV to jointly constrain the mass distributions. The analysis is performed in two different common parameterizations (one adopts light-traces-mass for both galaxies and dark matter while the other adopts an analytical, elliptical NFW form for the dark matter), to provide a better assessment of the underlying systematics - which is most important for deep, cluster-lensing surveys, especially when studying magnified high-redshift objects. We find that the typical (median), relative systematic differences throughout the central FOV are $\sim40\%$ in the (dimensionless) mass density, $\kappa$, and $\sim20\%$ in the magnification, $\mu$. We show maps of these differences for each cluster, as well as the mass distributions, critical curves, and 2D integrated mass profiles. For the Einstein radii ($z_{s}=2$) we find that all typically agree within $10\%$ between the two models, and Einstein masses agree, typically, within $\sim15\%$. At larger radii, the total projected, 2D integrated mass profiles of the two models, within r\sim2\arcmin, differ by $\sim30\%$. Stacking the surface-density profiles of the sample from the two methods together, we obtain an average slope of $d\log (\Sigma)/d\log(r)\sim-0.64\pm0.1$, in the radial range [5,350] kpc. Lastly, we also characterize the behavior of the average magnification, surface density, and shear differences between the two models, as a function of both the radius from the center, and the best-fit values of these quantities.Comment: 35 pages (20 main text pages, plus 15 pages for additional figures and tables); 2 Tables, 17 Figures. V3: accepted version; some minor corrections and additions made. V4: corrected several entries in Table 2. All mass models and magnification maps are made publicly available for the communit

CLASH: Mass Distribution in and around MACS J1206.2-0847 from a Full Cluster Lensing Analysis

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z=0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRIz' imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale structure with the major axis running approximately north-west south-east (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a \sim 2:1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope dln\Sigma/dlnR\sim -1 at cluster outskirts (R>1Mpc/h), whereas the mass distribution excluding the NW-SE excess regions steepens further out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass M_{vir}=(1.1\pm 0.2\pm 0.1)\times 10^{15} M_{sun}/h and a halo concentration c_{vir} = 6.9\pm 1.0\pm 1.2 (\sim 5.7 when the central 50kpc/h is excluded), which falls in the range 4 <7 of average c(M,z) predictions for relaxed clusters from recent Lambda cold dark matter simulations. Our full lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, yield a cumulative gas mass fraction of 13.7^{+4.5}_{-3.0}% at 0.7Mpc/h (\approx 1.7r_{2500}), a typical value observed for high mass clusters.Comment: Accepted by ApJ (30 pages, 17 figures), one new figure (Figure 10) added, minor text changes; a version with high resolution figures available at http://www.asiaa.sinica.edu.tw/~keiichi/upfiles/MACS1206/ms_highreso.pd