Multi-scale cluster lens mass mapping I. Strong Lensing modelling

We propose a novel technique to refine the modelling of galaxy clusters mass distribution using gravitational lensing. The idea is to combine the strengths of both "parametric" and "non-parametric" methods to improve the quality of the fit. We develop a multi-scale model that allows sharper contrast in regions of higher density where the number of constraints is generally higher. Our model consists of (i) a multi-scale grid of radial basis functions with physically motivated profiles and (ii) a list of galaxy-scale potentials at the location of the cluster member galaxies. This arrangement of potentials of different sizes allows to reach a high resolution for the model with a minimum number of parameters. We apply our model to the well studied cluster Abell 1689. We estimate the quality of our mass reconstruction with a Bayesian MCMC sampler. For a selected subset of multiple images, we manage to halve the errors between the predicted and observed image positions compared to previous studies. This owes to the flexibility of multi-scale models at intermediate scale between cluster and galaxy scale. The software developed for this paper is part of the public lenstool package which can be found at www.oamp.fr/cosmology/lenstool.Comment: 15 pages, 17 figures, accepted for publication in MNRA

Jackknife resampling technique on mocks: an alternative method for covariance matrix estimation

We present a fast and robust alternative method to compute covariance matrix in case of cosmology studies. Our method is based on the jackknife resampling applied on simulation mock catalogues. Using a set of 600 BOSS DR11 mock catalogues as a reference, we find that the jackknife technique gives a similar galaxy clustering covariance matrix estimate by requiring a smaller number of mocks. A comparison of convergence rates show that $\sim$7 times fewer simulations are needed to get a similar accuracy on variance. We expect this technique to be applied in any analysis where the number of available N-body simulations is low.Comment: 11 pages, 11 figures, 2 table

The Bullet cluster at its best: weighing stars, gas and dark matter

We present a new strong lensing mass reconstruction of the Bullet cluster (1E 0657-56) at z=0.296, based on WFC3 and ACS HST imaging and VLT/FORS2 spectroscopy. The strong lensing constraints underwent substantial revision compared to previously published analysis, there are now 14 (six new and eight previously known) multiply-imaged systems, of which three have spectroscopically confirmed redshifts (including one newly measured from this work). The reconstructed mass distribution explicitly included the combination of three mass components: i) the intra-cluster gas mass derived from X-ray observation, ii) the cluster galaxies modeled by their fundamental plane scaling relations and iii) dark matter. The model that includes the intra-cluster gas is the one with the best Bayesian evidence. This model has a total RMS value of 0.158" between the predicted and measured image positions for the 14 multiple images considered. The proximity of the total RMS to resolution of HST/WFC3 and ACS (0.07-0.15" FWHM) demonstrates the excellent precision of our mass model. The derived mass model confirms the spatial offset between the X-ray gas and dark matter peaks. The fraction of the galaxy halos mass to total mass is found to be f_s=11+/-5% for a total mass of 2.5+/-0.1 x 10^14 solar mass within a 250 kpc radial aperture.Comment: Accepted by A&A 15 pages, 12 figure

Gauging the dark matter fraction in a L∗L_* S0 galaxy at z=0.47 through gravitational lensing from deep HST/ACS imaging

We analyze a new gravitational lens, OAC-GL J1223-1239, serendipitously found in a deep I-band image of the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS). The lens is a L_*, edge-on S0 galaxy at z=0.4656. The gravitational arc has a radius of 0.42 arcsec. We have determined the total mass and the dark matter (DM) fraction within the Einstein radius as a function of the lensed source redshift, which is presently unknown. For z ~ 1.3, which is in the middle of the redshift range plausible for the source according to some external constraints, we find the central velocity dispersion to be ~180 km/s. With this value, close to that obtained by means of the Faber-Jackson relation at the lens redshift, we compute a 30% DM fraction within the Einstein radius (given the uncertainty in the source redshift, the allowed range for the DM fraction is 25-35 % in our lensing model). When compared with the galaxies in the local Universe, the lensing galaxy, OAC-GL J1223-1239 seems to fall in the transition regime between massive DM dominated galaxies and lower-mass, DM deficient systems.Comment: 18 pages, 5 figures; accepted for publication in Ap

Probing the Slope of Cluster Mass Profile with Gravitational Einstein Rings: Application to Abell 1689

The strong lensing modelling of gravitational ``rings'' formed around massive galaxies is sensitive to the amplitude of the external shear and convergence produced by nearby mass condensations. In current wide field surveys, it is now possible to find out a large number of rings, typically 10 gravitational rings per square degree. We propose here, to systematically study gravitational rings around galaxy clusters to probe the cluster mass profile beyond the cluster strong lensing regions. For cluster of galaxies with multiple arc systems, we show that rings found at various distances from the cluster centre can improve the modelling by constraining the slope of the cluster mass profile. We outline the principle of the method with simple numerical simulations and we apply it to 3 rings discovered recently in Abell~1689. In particular, the lens modelling of the 3 rings confirms that the cluster is bimodal, and favours a slope of the mass profile steeper than isothermal at a cluster radius \sim 300 \kpc. These results are compared with previous lens modelling of Abell~1689 including weak lensing analysis. Because of the difficulty arising from the complex mass distribution in Abell~1689, we argue that the ring method will be better implemented on simpler and relaxed clusters.Comment: Accepted for publication in MNRAS. Substantial modification after referee's repor

The Frontier Fields Lens Modeling Comparison Project

Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Deriving a lens magnification map for a galaxy cluster is a classic inversion problem and many methods have been developed over the past two decades to solve it. Several research groups have developed techniques independently to map the predominantly dark matter distribution in cluster lenses. While these methods have all provided remarkably high precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have never been directly compared. In this paper, we report the results of comparing various independent lens modeling techniques employed by individual research groups in the community. Here we present for the first time a detailed and robust comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modeling community was provided simulated cluster images -- of two clusters Ares and Hera -- that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that lensing reconstruction methods produce reliable mass distributions that enable the use of clusters as extremely valuable astrophysical laboratories and cosmological probes.Comment: 38 pages, 25 figures, submitted to MNRAS, version with full resolution images can be found at http://pico.bo.astro.it/~massimo/papers/FFsims.pd

Stochastic bias of colour-selected BAO tracers by joint clustering-weak lensing analysis

The baryon acoustic oscillation (BAO) feature in the two-point correlation function of galaxies supplies a standard ruler to probe the expansion history of the Universe. We study here several galaxy selection schemes, aiming at building an emission-line galaxy (ELG) sample in the redshift range $0.6<z<1.7$, that would be suitable for future BAO studies, providing a highly biased galaxy sample. We analyse the angular galaxy clustering of galaxy selections at the redshifts 0.5, 0.7, 0.8, 1 and 1.2 and we combine this analysis with a halo occupation distribution (HOD) model to derive the properties of the haloes these galaxies inhabit, in particular the galaxy bias on large scales. We also perform a weak lensing analysis (aperture statistics) to extract the galaxy bias and the cross-correlation coefficient and compare to the HOD prediction. We apply this analysis on a data set composed of the photometry of the deep co-addition on Sloan Digital Sky Survey (SDSS) Stripe 82 (225 deg$^2$), of Canda-France-Hawai Telescope/Stripe 82 deep \emph{i}-band weak lensing survey and of the {\it Wide-Field Infrared Survey Explorer}infrared photometric band W1. The analysis on the SDSS-III/constant mass galaxies selection at $z=0.5$ is in agreement with previous studies on the tracer, moreover we measure its cross-correlation coefficient $r=1.16\pm0.35$. For the higher redshift bins, we confirm the trends that the brightest galaxy populations selected are strongly biased ($b>1.5$), but we are limited by current data sets depth to derive precise values of the galaxy bias. A survey using such tracers of the mass field will guarantee a high significance detection of the BAO.Comment: 17 pages, 15 figures, submitted to MNRA

On the evolution of environmental and mass properties of strong lens galaxies in COSMOS

Among the 100 strong lens candidates found in the COSMOS field, 20 with redshifts in the range [0.34,1.13], feature multiple images of background sources. Using the multi-wavelength coverage of the field and its spectroscopic follow-up, we characterize the evolution with redshift of the environment and of the dark-matter (DM) fraction of the lens galaxies. We present new redshift of the strong lens candidates. The lens environment is characterized by the projected 10 closest galaxies around each lens and by the number of galaxies with a projected distance less than 1Mpc at the lens galaxy redshift. In both cases, we perform similar measurements on a control sample of twin non-lens early type galaxies (ETGs). In addition, we identify group members and field galaxies in the X-ray and optical catalogs of galaxy groups. From those catalogs, we measure the external shear contribution at the lens galaxy positions. The systems are then modeled using a SIE plus the external shear due to the groups. We observe that the average stellar mass of lens galaxies increases with z and that the environment of lens galaxies is compatible with that of the twins. During the lens modeling, we notice that, when let free, the external shear points in a direction which is the mean direction of the external shear due to groups and of the closest galaxy to the lens. We notice that the DM fraction of the lens galaxies within the Einstein radius decreases as the redshift increases. Given these, we conclude that, while the environment of lens galaxies is compatible with that of non-lens ETGS, their mass properties evolves significantly with redshift: it is still not clear whether this advocates in favor of a stronger lensing bias toward massive objects at high redshift or is simply representative of the high proportion of massive and high stellar density galaxies at high redshift.Comment: Accepted for publication in A&A. Significant modifications in the paper but similar conclusion

Stellar-to-halo mass relation of cluster galaxies

In the hierarchical formation model, galaxy clusters grow by accretion of smaller groups or isolated galaxies. During the infall into the centre of a cluster, the properties of accreted galaxies change. In particular, both observations and numerical simulations suggest that its dark matter halo is stripped by the tidal forces of the host. We use galaxy-galaxy weak lensing to measure the average mass of dark matter haloes of satellite galaxies as a function of projected distance to the centre of the host, for different stellar mass bins. Assuming that the stellar component of the galaxy is less disrupted by tidal stripping, stellar mass can be used as a proxy of the infall mass. We study the stellar to halo mass relation of satellites as a function of the cluster-centric distance to measure tidal stripping. We use the shear catalogues of the DES science verification archive, the CFHTLenS and the CFHT Stripe 82 (CS82) surveys, and we select satellites from the redMaPPer catalogue of clusters. For galaxies located in the outskirts of clusters, we find a stellar to halo mass relation in good agreement with the theoretical expectations from \citet{moster2013} for central galaxies. In the centre of the cluster, we find that this relation is shifted to smaller halo mass for a given stellar mass. We interpret this finding as further evidence for tidal stripping of dark matter haloes in high density environments.Comment: 15 pages, 14 figure

Anomaly distribution in quasar magnitudes: a test of lensing by an hypothetic Supergiant Molecular Cloud in the Galactic halo

An anomaly in the distribution of quasar magnitudes based on the SDSS survey, has been recently reported by Longo (2012). The angular size of this anomaly is of the order of $\rm \pm 15^o$ on the sky. A low surface brightness smooth structure in $\gamma$-rays, coincides with the sky location and extent of the quasar anomaly, and is close to the Northern component of a pair of $\gamma$-ray bubbles discovered in the \sl Fermi Gamma-ray Space Telescope \rm survey. Molecular clouds are thought to be illuminated by cosmic rays. I test the hypothesis that the magnitude anomaly in the quasar distribution, is due to a lensing effect by an hypothetic Supergiant Molecular Cloud (SGMC) in the Galactic halo.A series of grid lens models are built by assuming firstly that a SGMC is a lattice with clumps of $\rm 10^{-3} M_\odot$, 10 AU in size, and assuming various filling factors of the cloud, and secondly a fractal structure. Local amplifications are calculated for these lenses by using the public software LensTool, and the single plane approximation. A complex network of caustics due to the clumpy structure is present. Our best single plane lens model capable of explaining Longo's effect, \sl at least in sparse regions, \rm requires a mass $\rm (1.5-4.1) \times 10^{10} ~M_\odot$ within $\rm 8.7 \times 8.7 \times (5-8.6) kpc^3$ at a lens plane distance of 20 kpc. It is constructed from a molecular cloud building block of $5 \times 10^5 M_\odot$ within a scale of 30 pc expanded by fractal scaling with dimension $D = 1.8-2$ up to 5-8.6 kpc for the SGMC. If such a Supergiant Molecular Cloud were demonstrated, it might be part of a lens explanation for the luminous anomaly discovered in quasars and in red galaxies. The mass budget may be varied by changing the cloud depth and the fractal dimension.Comment: 11 pages, no Figures, 2 table