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&

CLASH-VLT: A highly precise strong lensing model of the galaxy cluster RXC J2248.7−4431 (Abell S1063) and prospects for cosmography

Aims. We perform a comprehensive study of the total mass distribution of the galaxy cluster RXC J2248.7−4431 (z = 0.348) with a set of high-precision strong lensing models, which take advantage of extensive spectroscopic information on many multiply lensed systems. In the effort to understand and quantify inherent systematics in parametric strong lensing modelling, we explore a collection of 22 models in which we use different samples of multiple image families, different parametrizations of the mass distribution and cosmological parameters. Methods. As input information for the strong lensing models, we use the Cluster Lensing And Supernova survey with Hubble (CLASH) imaging data and spectroscopic follow-up observations, with the VIsible Multi-Object Spectrograph (VIMOS) and Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT), to identify and characterize bona fide multiple image families and measure their redshifts down to m_(F814W) ≃ 26. A total of 16 background sources, over the redshift range 1.0−6.1, are multiply lensed into 47 images, 24 of which are spectroscopically confirmed and belong to ten individual sources. These also include a multiply lensed Lyman-α blob at z = 3.118. The cluster total mass distribution and underlying cosmology in the models are optimized by matching the observed positions of the multiple images on the lens plane. Bayesian Markov chain Monte Carlo techniques are used to quantify errors and covariances of the best-fit parameters. Results. We show that with a careful selection of a large sample of spectroscopically confirmed multiple images, the best-fit model can reproduce their observed positions with a rms scatter of 0.̋3 in a fixed flat ΛCDM cosmology, whereas the lack of spectroscopic information or the use of inaccurate photometric redshifts can lead to biases in the values of the model parameters. We find that the best-fit parametrization for the cluster total mass distribution is composed of an elliptical pseudo-isothermal mass distribution with a significant core for the overall cluster halo and truncated pseudo-isothermal mass profiles for the cluster galaxies. We show that by adding bona fide photometric-selected multiple images to the sample of spectroscopic families, one can slightly improve constraints on the model parameters. In particular, we find that the degeneracy between the lens total mass distribution and the underlying geometry of the Universe, which is probed via angular diameter distance ratios between the lens and sources and the observer and sources, can be partially removed. Allowing cosmological parameters to vary together with the cluster parameters, we find (at 68% confidence level) Ω_m = 0.25^(+0.13)_(-0.16) and w = −1.07^(+0.16)_(-0.42) for a flat ΛCDM model, and Ω_m = 0.31^(+0.12)_(-0.13) and Ω_Λ = 0.38^(+0.38)_(-0.27) for a Universe with w = −1 and free curvature. Finally, using toy models mimicking the overall configuration of multiple images and cluster total mass distribution, we estimate the impact of the line-of-sight mass structure on the positional rms to be 0.̋3 ± 0. We argue that the apparent sensitivity of our lensing model to cosmography is due to the combination of the regular potential shape of RXC J2248, a large number of bona fide multiple images out to z = 6.1, and a relatively modest presence of intervening large-scale structure, as revealed by our spectroscopic survey

Discovery of a faint, star-forming, multiply lensed, Lyman-alpha blob

We report the discovery of a multiply lensed Lyman-$\alpha$ blob (LAB) behind the galaxy cluster AS1063 using the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope (VLT). The background source is at $z=$ 3.117 and is intrinsically faint compared to almost all previously reported LABs. We used our highly precise strong lensing model to reconstruct the source properties, and we find an intrinsic luminosity of $L_{\rm Ly\alpha}$=$1.9\times10^{42}$ erg s$^{-1}$, extending to 33 kpc. We find that the LAB is associated with a group of galaxies, and possibly a protocluster, in agreement with previous studies that find LABs in overdensities. In addition to Lyman-$\alpha$ (Ly$\alpha$) emission, we find \ion{C}{IV}, \ion{He}{II}, and \ion{O}{III}] ultraviolet (UV) emission lines arising from the centre of the nebula. We used the compactness of these lines in combination with the line ratios to conclude that the \Lya nebula is likely powered by embedded star formation. Resonant scattering of the \Lya photons then produces the extended shape of the emission. Thanks to the combined power of MUSE and strong gravitational lensing, we are now able to probe the circumgalatic medium of sub-$L_{*}$ galaxies at $z\approx 3$.Comment: 7 pages, 7 figures; moderate changes to match the accepted A&A versoi

Massive Star cluster formation under the microscope at z=6

We report on a superdense star-forming region with an effective radius (R_e) smaller than 13 pc identified at z=6.143 and showing a star-formation rate density \Sigma_SFR~1000 Msun/yr/kpc2 (or conservatively >300 Msun/yr/kpc2). Such a dense region is detected with S/N>40 hosted by a dwarf extending over 440 pc, dubbed D1 (Vanzella et al. 2017b). D1 is magnified by a factor 17.4+/-5.0 behind the Hubble Frontier Field galaxy cluster MACS~J0416 and elongated tangentially by a factor 13.2+/-4.0 (including the systematic errors). The lens model accurately reproduces the positions of the confirmed multiple images with a r.m.s. of 0.35", and the tangential stretch is well depicted by a giant multiply-imaged Lya arc. D1 is part of an interacting star-forming complex extending over 800 pc. The SED-fitting, the very blue ultraviolet slope (\beta ~ -2.5, F(\lambda) ~ \lambda^\beta) and the prominent Lya emission of the stellar complex imply that very young (< 10-100 Myr), moderately dust-attenuated (E(B-V)<0.15) stellar populations are present and organised in dense subcomponents. We argue that D1 (with a stellar mass of 2 x 10^7 Msun) might contain a young massive star cluster of M < 10^6 Msun and Muv~-15.6 (or m_uv=31.1), confined within a region of 13 pc, and not dissimilar from some local super star clusters (SSCs). The ultraviolet appearance of D1 is also consistent with a simulated local dwarf hosting a SSC placed at z=6 and lensed back to the observer. This compact system fits into some popular globular cluster formation scenarios. We show that future high spatial resolution imaging (e.g., E-ELT/MAORY-MICADO and VLT/MAVIS) will allow us to spatially resolve light profiles of 2-8 pc.Comment: 21 pages, 14 figures, 1 table, MNRAS accepte

CLASH-VLT: Testing the Nature of Gravity with Galaxy Cluster Mass Profiles

We use high-precision kinematic and lensing measurements of the total mass profile of the dynamically relaxed galaxy cluster MACS J1206.2-0847 at $z=0.44$ to estimate the value of the ratio $\eta=\Psi/\Phi$ between the two scalar potentials in the linear perturbed Friedmann-Lemaitre-Robertson-Walker metric.[...] Complementary kinematic and lensing mass profiles were derived from exhaustive analyses using the data from the Cluster Lensing And Supernova survey with Hubble (CLASH) and the spectroscopic follow-up with the Very Large Telescope (CLASH-VLT). Whereas the kinematic mass profile tracks only the time-time part of the perturbed metric (i.e. only $\Phi$), the lensing mass profile reflects the contribution of both time-time and space-space components (i.e. the sum $\Phi+\Psi$). We thus express $\eta$ as a function of the mass profiles and perform our analysis over the radial range $0.5\,Mpc\le r\le r_{200}=1.96\,Mpc$. Using a spherical Navarro-Frenk-White mass profile, which well fits the data, we obtain \eta(r_{200})=1.01\,_{-0.28}^{+0.31} at the 68\% C.L. We discuss the effect of assuming different functional forms for mass profiles and of the orbit anisotropy in the kinematic reconstruction. Interpreting this result within the well-studied $f(R)$ modified gravity model, the constraint on $\eta$ translates into an upper bound to the interaction length (inverse of the scalaron mass) smaller than 2 Mpc. This tight constraint on the $f(R)$ interaction range is however substantially relaxed when systematic uncertainties in the analysis are considered. Our analysis highlights the potential of this method to detect deviations from general relativity, while calling for the need of further high-quality data on the total mass distribution of clusters and improved control on systematic effects.Comment: 18 pages, 3 figures, submitted to JCA

On the accuracy of time-delay cosmography in the Frontier Fields Cluster MACS J1149.5+2223 with supernova Refsdal

We study possible systematic effects on the values of the cosmological parameters measured through strong lensing analyses of the HFF galaxy cluster MACS J1149.5+2223. We use the observed positions of a large set of spectroscopically selected multiple images, including those of supernova "Refsdal" with their estimated time delays. Starting from our reference model in a flat $\Lambda$CDM cosmology, published in Grillo et al. (2018), we confirm the relevance of the longest measurable time delay, between SX and S1, and an approximately linear relation between its value and that of $H_{0}$. We perform true blind tests by considering a range of time delays around its original estimate of $345 \pm 10$ days, as an accurate measurement of this time delay was not known at the time of analysis and writing. We investigate separately the impact of a constant sheet of mass at the cluster redshift, of a power-law profile for the mass density of the cluster main halo and of some scatter in the cluster member scaling relations. Remarkably, we find that these systematic effects do not introduce a significant bias on the inferred values of $H_{0}$ and $\Omega_{\rm m}$ and that the statistical uncertainties dominate the total error budget: a 3% uncertainty on the time delay of image SX translates into approximately 6% and 40% (including both statistical and systematic $1\sigma$) uncertainties for $H_{0}$ and $\Omega_{\rm m}$, respectively. Furthermore, our model accurately reproduces the extended surface brightness distribution of the supernova host, covering more than $3 \times 10^{4}$ $HST$ pixels. We also present the interesting possibility of measuring the value of the equation-of-state parameter $w$ of the dark energy density, currently with a 30% uncertainty. We conclude that time-delay cluster lenses have the potential to become soon an alternative and competitive cosmological probe.Comment: 10 pages, 8 figures, 1 table; ApJ in press (all main results and figures unchanged, only minor changes during revision

Ionising the Intergalactic Medium by Star Clusters: The first empirical evidence

We present a VLT/X-Shooter spectroscopy of the Lyman continuum (LyC) emitting galaxy 'Ion2' at z=3.2121 and compare it to that of the recently discovered strongly lensed LyC-emitter at z=2.37, known as the 'Sunburst' arc. Three main results emerge from the X-Shooter spectrum: (a) the Lya has three distinct peaks with the central one at the systemic redshift, indicating a ionised tunnel through which both Lya and LyC radiation escape; (b) the large O32 oxygen index ([OIII]4959-5007 / [OII]3727-3729) of 9.18(-1.32/+1.82) is compatible to those measured in local (z~0.4) LyC leakers; (c) there are narrow nebular high-ionisation metal lines with \sigma_v < 20 km/s, which confirms the presence of young hot, massive stars. The HeII1640 appears broad, consistent with a young stellar component including Wolf-Rayet stars. Similarly, the Sunburst LyC-emitter shows a triple-peaked Lya profile and from VLT/MUSE spectroscopy the presence of spectral features arising from young hot and massive stars. The strong lensing magnification, (\mu > 20), suggests that this exceptional object is a gravitationally-bound star cluster observed at a cosmological distance, with a stellar mass M <~ 10^7 Msun and an effective radius smaller than 20 pc. Intriguingly, sources like Sunburst but without lensing magnification might appear as Ion2-like galaxies, in which unresolved massive star clusters dominate the ultraviolet emission. This work supports the idea that dense young star clusters can contribute to the ionisation of the IGM through holes created by stellar feedback.Comment: 13 pages, 9 figures and 1 table, MNRAS accepted. Some typos fixe

CLASH-VLT: Environment-driven evolution of galaxies in the z=0.209 cluster Abell 209

The analysis of galaxy properties and the relations among them and the environment, can be used to investigate the physical processes driving galaxy evolution. We study the cluster A209 by using the CLASH-VLT spectroscopic data combined with Subaru photometry, yielding to 1916 cluster members down to a stellar mass of 10^{8.6} Msun. We determine: i) the stellar mass function of star-forming and passive galaxies; ii) the intra-cluster light and its properties; iii) the orbits of low- and high-mass passive galaxies; and iv) the mass-size relation of ETGs. The stellar mass function of the star-forming galaxies does not depend on the environment, while the slope found for passive galaxies becomes flatter in the densest region. The color distribution of the intra-cluster light is consistent with the color of passive members. The analysis of the dynamical orbits shows that low-mass passive galaxies have tangential orbits, avoiding small pericenters around the BCG. The mass-size relation of low-mass passive ETGs is flatter than that of high mass galaxies, and its slope is consistent with that of field star-forming galaxies. Low-mass galaxies are also more compact within the scale radius of 0.65 Mpc. The ratio between stellar and number density profiles shows a mass segregation in the center. The comparative analysis of the stellar and total density profiles indicates that this effect is due to dynamical friction. Our results are consistent with a scenario in which the "environmental quenching" of low-mass galaxies is due to mechanisms such as harassment out to R200, starvation and ram-pressure stripping at smaller radii, as supported by the analysis of the mass function, of the dynamical orbits and of the mass-size relation of passive early-types in different regions. Our analyses support the idea that the intra-cluster light is formed through the tidal disruption of subgiant galaxies.Comment: 17 pages, 20 figures, A&A in pres

The story of supernova 'Refsdal' told by MUSE

We present MUSE observations in the core of the HFF galaxy cluster MACS J1149.5+2223, where the first magnified and spatially-resolved multiple images of SN 'Refsdal' at redshift 1.489 were detected. Thanks to a DDT program with the VLT and the extraordinary efficiency of MUSE, we measure 117 secure redshifts with just 4.8 hours of total integration time on a single target pointing. We spectroscopically confirm 68 galaxy cluster members, with redshift values ranging from 0.5272 to 0.5660, and 18 multiple images belonging to 7 background, lensed sources distributed in redshifts between 1.240 and 3.703. Starting from the combination of our catalog with those obtained from extensive spectroscopic and photometric campaigns using the HST, we select a sample of 300 (164 spectroscopic and 136 photometric) cluster members, within approximately 500 kpc from the BCG, and a set of 88 reliable multiple images associated to 10 different background source galaxies and 18 distinct knots in the spiral galaxy hosting SN 'Refsdal'. We exploit this valuable information to build 6 detailed strong lensing models, the best of which reproduces the observed positions of the multiple images with a rms offset of only 0.26". We use these models to quantify the statistical and systematic errors on the predicted values of magnification and time delay of the next emerging image of SN 'Refsdal'. We find that its peak luminosity should should occur between March and June 2016, and should be approximately 20% fainter than the dimmest (S4) of the previously detected images but above the detection limit of the planned HST/WFC3 follow-up. We present our two-dimensional reconstruction of the cluster mass density distribution and of the SN 'Refsdal' host galaxy surface brightness distribution. We outline the roadmap towards even better strong lensing models with a synergetic MUSE and HST effort.Comment: 21 pages, 9 figures, 6 tables; accepted for publication in the Astrophysical Journal - extra information on data analysis added, all model predictions and results unchange