On the r−r-stability of spacelike hypersurfaces

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient spacetime is the de Sitter space

Human Mobility in Large Cities as a Proxy for Crime

We investigate at the subscale of the neighborhoods of a highly populated city the incidence of property crimes in terms of both the resident and the floating population. Our results show that a relevant allometric relation could only be observed between property crimes and floating population. More precisely, the evidence of a superlinear behavior indicates that a disproportional number of property crimes occurs in regions where an increased flow of people takes place in the city. For comparison, we also found that the number of crimes of peace disturbance only correlates well, and in a superlinear fashion too, with the resident population. Our study raises the interesting possibility that the superlinearity observed in previous studies [Bettencourt et al., Proc. Natl. Acad. Sci. USA 104, 7301 (2007) and Melo et al., Sci. Rep. 4, 6239 (2014)] for homicides versus population at the city scale could have its origin in the fact that the floating population, and not the resident one, should be taken as the relevant variable determining the intrinsic microdynamical behavior of the system.Comment: 17 pages, 8 Figure

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

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

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

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

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