On the accuracy of the Perturbative Approach for Strong Lensing: Local Distortion for Pseudo-Elliptical Models

The Perturbative Approach (PA) introduced by \citet{alard07} provides analytic solutions for gravitational arcs by solving the lens equation linearized around the Einstein ring solution. This is a powerful method for lens inversion and simulations in that it can be used, in principle, for generic lens models. In this paper we aim to quantify the domain of validity of this method for three quantities derived from the linearized mapping: caustics, critical curves, and the deformation cross section (i.e. the arc cross section in the infinitesimal circular source approximation). We consider lens models with elliptical potentials, in particular the Singular Isothermal Elliptic Potential and Pseudo-Elliptical Navarro--Frenk--White models. We show that the PA is exact for this first model. For the second, we obtain constraints on the model parameter space (given by the potential ellipticity parameter $\varepsilon$ and characteristic convergence $\kappa_s$) such that the PA is accurate for the aforementioned quantities. In this process we obtain analytic expressions for several lensing functions, which are valid for the PA in general. The determination of this domain of validity could have significant implications for the use of the PA, but it still needs to be probed with extended sources.Comment: Accepted for publication in MNRA

Analytic Solutions for Navarro--Frenk--White Lens Models for Low Characteristic Convergences

The Navarro-Frenk-White (NFW) density profile is often used to model gravitational lenses. For low values of the characteristic convergence ($\kappa_s \ll 1$) of this model - corresponding to galaxy and galaxy group mass scales - a high numerical precision is required in order to accurately compute several quantities in the strong lensing regime. An alternative for fast and accurate computations is to derive analytic approximations in this limit. In this work we obtain analytic solutions for several lensing quantities for elliptical (ENFW) and pseudo-elliptical (PNFW) NFW lens models on the typical scales where gravitational arcs are expected to be formed, in the $\kappa_s \ll 1$ limit, establishing their domain of validity. We derive analytic solutions for the convergence and shear for these models, obtaining explicit expressions for the iso-convergence contours and constant distortion curves (including the tangential critical curve). We also compute the deformation cross section, which is given in closed form for the circular NFW model and in terms of a one-dimensional integral for the elliptical ones. In addition, we provide a simple expression for the ellipticity of the iso-convergence contours of the pseudo-elliptical models and the connection of characteristic convergences among the PNFW and ENFW models. We conclude that the set of solutions derived here is generally accurate for $\kappa_s \lesssim 0.1$. For low ellipticities, values up to $\kappa_s \simeq 0.18$ are allowed. On the other hand, the mapping between PNFW and the ENFW models is valid up to $\kappa_s \simeq 0.4$. The solutions derived in this work can be used to speed up numerical codes and ensure their accuracy in the low $\kappa_s$ regime, including applications to arc statistics and other strong lensing observables. (Abridged)Comment: Accepted for publication in A&

The Mass-Concentration Relation and the Stellar-to-Halo Mass Ratio in the CFHT Stripe 82 Survey

We present a new measurement of the mass-concentration relation and the stellar-to-halo mass ratio over the halo mass range $5\times 10^{12}$ to $2\times 10^{14}M_{\odot}$. To achieve this, we use weak lensing measurements from the CFHT Stripe 82 Survey (CS82), combined with the central galaxies from the redMaPPer cluster catalogue and the LOWZ/CMASS galaxy sample of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Tenth Data Release. The stacked lensing signals around these samples are modelled as a sum of contributions from the central galaxy, its dark matter halo, and the neighboring halos, as well as a term for possible centering errors. We measure the mass-concentration relation: $c_{200c}(M)=A(\frac{M_{200c}}{M_0})^{B}$ with $A=5.24\pm1.24, B=-0.13\pm0.10$ for $0.2<z<0.4$ and $A=6.61\pm0.75, B=-0.15\pm0.05$ for $0.4<z<0.6$. These amplitudes and slopes are completely consistent with predictions from recent simulations. We also measure the stellar-to-halo mass ratio for our samples, and find results consistent with previous measurements from lensing and other techniques.Comment: 10 pages, 3 figures, 3 table

When two worlds collide: A story about collaboration, witnessing and life story research with soldiers returning from war

The story we share here stems from our research with British military personnel who are adapting to life with a physical and/or psychological disability after serving in the Iraq or Afghanistan wars. Throughout our research, we have struggled to answer the kinds of questions that plague qualitative researchers: How might we gain insights into intense, traumatic, even life-changing experiences? Should we be inviting individuals to recount or revisit such potent moments from their lives? What interpretive framework might we draw on to make sense of what are sometimes senseless experiences? How can we share any ensuing understanding with others without diluting, diminishing or disrespecting the lives of soldiers or their families? The story we share here – which responds to Denzin’s (2003) challenge to reanimate life and Erickson’s (2010) provocation to do so with greater modesty, visibility, and reflexivity – offers one answer to these questions

Tuning a Resonance in the Fock Space: Optimization of Phonon Emission in a Resonant Tunneling Device

Phonon-assisted tunneling in a double barrier resonant tunneling device can be seen as a resonance in the electron-phonon Fock space which is tuned by the applied voltage. We show that the geometrical parameters can induce a symmetry condition in this space that can strongly enhance the emission of longitudinal optical phonons. For devices with thin emitter barriers this is achieved by a wider collector's barrier.Comment: 4 pages, 3 figures. Figure 1 changed, typos correcte

Weak-lensing calibration of a stellar mass-based mass proxy for redMaPPer and Voronoi Tessellation clusters in SDSS Stripe 82

We present the first weak lensing calibration of $\mu_{\star}$, a new galaxy cluster mass proxy corresponding to the total stellar mass of red and blue members, in two cluster samples selected from the SDSS Stripe 82 data: 230 redMaPPer clusters at redshift $0.1\leq z<0.33$ and 136 Voronoi Tessellation (VT) clusters at $0.1 \leq z < 0.6$. We use the CS82 shear catalog and stack the clusters in $\mu_{\star}$ bins to measure a mass-observable power law relation. For redMaPPer clusters we obtain $M_0 = (1.77 \pm 0.36) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 1.74 \pm 0.62$. For VT clusters, we find $M_0 = (4.31 \pm 0.89) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.59 \pm 0.54$ and $M_0 = (3.67 \pm 0.56) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.68 \pm 0.49$ for a low and a high redshift bin, respectively. Our results are consistent, internally and with the literature, indicating that our method can be applied to any cluster finding algorithm. In particular, we recommend that $\mu_{\star}$ be used as the mass proxy for VT clusters. Catalogs including $\mu_{\star}$ measurements will enable its use in studies of galaxy evolution in clusters and cluster cosmology.Comment: Updated to be consistent with the published versio

A Systematic Search for High Surface Brightness Giant Arcs in a Sloan Digital Sky Survey Cluster Sample

We present the results of a search for gravitationally-lensed giant arcs conducted on a sample of 825 SDSS galaxy clusters. Both a visual inspection of the images and an automated search were performed and no arcs were found. This result is used to set an upper limit on the arc probability per cluster. We present selection functions for our survey, in the form of arc detection efficiency curves plotted as functions of arc parameters, both for the visual inspection and the automated search. The selection function is such that we are sensitive only to long, high surface brightness arcs with g-band surface brightness mu_g 10. Our upper limits on the arc probability are compatible with previous arc searches. Lastly, we report on a serendipitous discovery of a giant arc in the SDSS data, known inside the SDSS Collaboration as Hall's arc.Comment: 34 pages,8 Fig. Accepted ApJ:Jan-200

Observational Constraints on Silent Quartessence

We derive new constraints set by SNIa experiments (`gold' data sample of Riess et al.), X-ray galaxy cluster data (Allen et al. Chandra measurements of the X-ray gas mass fraction in 26 clusters), large scale structure (Sloan Digital Sky Survey spectrum) and cosmic microwave background (WMAP) on the quartessence Chaplygin model. We consider both adiabatic perturbations and intrinsic non-adiabatic perturbations such that the effective sound speed vanishes (Silent Chaplygin). We show that for the adiabatic case, only models with equation of state parameter $|\alpha |\lesssim 10^{-2}$ are allowed: this means that the allowed models are very close to \LambdaCDM. In the Silent case, however, the results are consistent with observations in a much broader range, -0.3<\alpha<0.7.Comment: 7 pages, 12 figures, to be submitted to JCA