Towards an understanding of third-order galaxy-galaxy lensing

Third-order galaxy-galaxy lensing (G3L) is a next generation galaxy-galaxy lensing technique that either measures the excess shear about lens pairs or the excess shear-shear correlations about lenses. It is clear that these statistics assess the three-point correlations between galaxy positions and projected matter density. For future applications of these novel statistics, we aim at a more intuitive understanding of G3L to isolate the main features that possibly can be measured. We construct a toy model ("isolated lens model"; ILM) for the distribution of galaxies and associated matter to determine the measured quantities of the two G3L correlation functions and traditional galaxy-galaxy lensing (GGL) in a simplified context. The ILM presumes single lens galaxies to be embedded inside arbitrary matter haloes that, however, are statistically independent ("isolated") from any other halo or lens position. In the ILM, the average mass-to-galaxy number ratio of clusters of any size cannot change. GGL and galaxy clustering alone cannot distinguish an ILM from any more complex scenario. The lens-lens-shear correlator in combination with second-order statistics enables us to detect deviations from a ILM, though. This can be quantified by a difference signal defined in the paper. We demonstrate with the ILM that this correlator picks up the excess matter distribution about galaxy pairs inside clusters. The lens-shear-shear correlator is sensitive to variations among matter haloes. In principle, it could be devised to constrain the ellipticities of haloes, without the need for luminous tracers, or maybe even random halo substructure. [Abridged]Comment: 14 pages, 3 figures, 1 table, accepted by A&A; some "lens-shear-shear" were falsely "lens-lens-shear

Einstein metrics and the number of smooth structures on a four-manifold

We prove that for every natural number k there are simply connected topological four-manifolds which have at leat k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not supporting Einstein metrics. Moreover, all these smooth structures become diffeomorphic after connected sum with only one copy of the complex projective plane. We prove that manifolds with these properties cover a large geographical area.Comment: 23 page

Integral equations PS-3 and moduli of pants

More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems for two adjacent domains with the spectral parameter in the conditions on the common boundary of the domains arises in a variety of situations: in justification and optimization of domain decomposition method, simple 2D models of oil extraction, (thermo)conductivity of composite materials. Singular 1D integral Poincare-Steklov equation with spectral parameter naturally emerges after reducing this 2D problem to the common boundary of the domains. We present a constructive representation for the eigenvalues and eigenfunctions of this integral equation in terms of moduli of explicitly constructed pants, one of the simplest Riemann surfaces with boundary. Essentially the solution of integral equation is reduced to the solution of three transcendent equations with three unknown numbers, moduli of pants. The discreet spectrum of the equation is related to certain surgery procedure ('grafting') invented by B.Maskit (1969), D.Hejhal (1975) and D.Sullivan- W.Thurston (1983).Comment: 27 pages, 13 figure

Radial Alignment in Simulated Clusters

Observational evidence for the radial alignment of satellites with their dark matter host has been accumulating steadily in the past few years. The effect is seen over a wide range of scales, from massive clusters of galaxies down to galaxy-sized systems, yet the underlying physical mechanism has still not been established. To this end, we have carried out a detailed analysis of the shapes and orientations of dark matter substructures in high-resolution N-body cosmological simulations. We find a strong tendency for radial alignment of the substructure with its host halo: the distribution of halo major axes is very anisotropic, with the majority pointing towards the center of mass of the host. The alignment peaks once the sub-halo has passed the virial radius of the host for the first time, but is not subsequently diluted, even after the halos have gone through as many as four pericentric passages. This evidence points to the existence of a very rapid dynamical mechanism acting on these systems and we argue that tidal torquing throughout their orbits is the most likely candidate.Comment: v2: 13 pages, 10 figures, ApJ in press. Revisions include a new section (4.2) comparing our results with observations, and a few added reference

Constraints on the shapes of galaxy dark matter haloes from weak gravitational lensing

We study the shapes of galaxy dark matter haloes by measuring the anisotropy of the weak gravitational lensing signal around galaxies in the second Red-sequence Cluster Survey (RCS2). We determine the average shear anisotropy within the virial radius for three lens samples: all galaxies with 19<m_r'<21.5, and the `red' and `blue' samples, whose lensing signals are dominated by massive low-redshift early-type and late-type galaxies, respectively. To study the environmental dependence of the lensing signal, we separate each lens sample into an isolated and clustered part and analyse them separately. We also measure the azimuthal dependence of the distribution of physically associated galaxies around the lens samples. We find that these satellites preferentially reside near the major axis of the lenses, and constrain the angle between the major axis of the lens and the average location of the satellites to =43.7 deg +/- 0.3 deg for the `all' lenses, =41.7 deg +/- 0.5 deg for the `red' lenses and =42.0 deg +/- 1.4 deg for the `blue' lenses. For the `all' sample, we find that the anisotropy of the galaxy-mass cross-correlation function =0.23 +/- 0.12, providing weak support for the view that the average galaxy is embedded in, and preferentially aligned with, a triaxial dark matter halo. Assuming an elliptical Navarro-Frenk-White (NFW) profile, we find that the ratio of the dark matter halo ellipticity and the galaxy ellipticity f_h=e_h/e_g=1.50+1.03-1.01, which for a mean lens ellipticity of 0.25 corresponds to a projected halo ellipticity of e_h=0.38+0.26-0.25 if the halo and the lens are perfectly aligned. For isolated galaxies of the `all' sample, the average shear anisotropy increases to =0.51+0.26-0.25 and f_h=4.73+2.17-2.05, whilst for clustered galaxies the signal is consistent with zero. (abridged)Comment: 28 pages, 23 figues, accepted for publication in A&

Combining cluster observables and stacked weak lensing to probe dark energy: Self-calibration of systematic uncertainties

We develop a new method of combining cluster observables (number counts and cluster-cluster correlation functions) and stacked weak lensing signals of background galaxy shapes, both of which are available in a wide-field optical imaging survey. Assuming that the clusters have secure redshift estimates, we show that the joint experiment enables a self-calibration of important systematic errors including the source redshift uncertainty and the cluster mass-observable relation, by adopting a single population of background source galaxies for the lensing analysis. It allows us to use the relative strengths of stacked lensing signals at different cluster redshifts for calibrating the source redshift uncertainty, which in turn leads to accurate measurements of the mean cluster mass in each bin. In addition, our formulation of stacked lensing signals in Fourier space simplifies the Fisher matrix calculations, as well as the marginalization over the cluster off-centering effect, the most significant uncertainty in stacked lensing. We show that upcoming wide-field surveys yield stringent constraints on cosmological parameters including dark energy parameters, without any priors on nuisance parameters that model systematic uncertainties. Specifically, the stacked lensing information improves the dark energy FoM by a factor of 4, compared to that from the cluster observables alone. The primordial non-Gaussianity parameter can also be constrained with a level of f_NL~10. In this method, the mean source redshift is well calibrated to an accuracy of 0.1 in redshift, and the mean cluster mass in each bin to 5-10% accuracies, which demonstrates the success of the self-calibration of systematic uncertainties from the joint experiment. (Abridged)Comment: 29 pages, 17 figures, 6 tables, accepted for publication in Phys. Rev.

Contending cultures of counterterrorism: transatlantic divergence or convergence?

Terrorist attacks on the United States, Spain and the United Kingdom have underlined the differing responses of Europe and the United States to the 'new terrorism'. This article analyses these responses through the prism of historically determined strategic cultures. For the last four years the United States has directed the full resources of a 'national security' approach towards this threat and has emphasized unilateralism. Europe, based on its own past experience of terrorism, has adopted a regulatory approach pursued through multilateralism. These divergences in transatlantic approaches, with potentially major implications for the future of the relationship, have appeared to be mitigated by a revised American strategy of counterterrorism that has emerged during 2005. However, this article contends that while strategic doctrines may change, the more immutable nature of strategic culture will make convergence difficult. This problem will be compounded by the fact that neither Europe nor America have yet addressed the deeper connections between terrorism and the process of globalization

Galaxy alignments: An overview

The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an overview on the state of the art in the study of these alignment processes and their observational signatures, aimed at a non-specialist audience. The development of the field over the past one hundred years is briefly reviewed. We also discuss the impact of galaxy alignments on measurements of weak gravitational lensing, and discuss avenues for making theoretical and observational progress over the coming decade.Comment: 43 pages excl. references, 16 figures; minor changes to match version published in Space Science Reviews; part of a topical volume on galaxy alignments, with companion papers at arXiv:1504.05546 and arXiv:1504.0546