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

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

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

Dark matter astrometry: accuracy of subhalo positions for the measurement of self-interaction cross-sections

Direct evidence for the existence of dark matter and measurements of its interaction cross-section have been provided by the physical offset between dark matter and intracluster gas in merging systems like the Bullet Cluster. Although a smaller signal, this effect is more abundant in minor mergers where infalling substructure dark matter and gas are segregated. In such low-mass systems the gravitational lensing signal comes primarily from weak lensing. A fundamental step in determining such an offset in substructure is the ability to accurately measure the positions of dark matter subpeaks. Using simulated Hubble Space Telescope observations, we make a first assessment of the precision and accuracy with which we can measure infalling groups using weak gravitational lensing. We demonstrate that using an existing and well-used mass reconstruction algorithm can measure the positions of 1.5 × 1013 M⊙ substructures that have parent haloes 10 times more massive with a bias of less than 0.3 arcsec. In this regime, our analysis suggests the precision is sufficient to detect (at 3σ statistical significance) the expected mean offset between dark matter and baryonic gas in infalling groups from a sample of ∼50 massive clusters

A Bayesian approach to strong lensing modelling of galaxy clusters

In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC) sampler ('Bayesys'), allowing us to avoid local minima in the likelihood functions. To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos. We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations. We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ~1-5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre. The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius. Finally, we describe how to rank models quantitatively using the Bayesian evidence. We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way. Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology. The implementation of the MCMC sampler used in this paper has been done within the framework of the Lenstool software package, which is publicly available.Comment: Accepted to "Gravitational Lensing" Focus Issue of the New Journal of Physics (invited), 35 pages, 11 figures at reduced resolutio

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

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

LoCuSS: First Results from Strong-lensing Analysis of 20 Massive Galaxy Clusters at z~0.2

We present a statistical analysis of a sample of 20 strong lensing clusters drawn from the Local Cluster Substructure Survey (LoCuSS), based on high resolution Hubble Space Telescope imaging of the cluster cores and follow-up spectroscopic observations using the Keck-I telescope. We use detailed parameterized models of the mass distribution in the cluster cores, to measure the total cluster mass and fraction of that mass associated with substructures within R<250kpc.These measurements are compared with the distribution of baryons in the cores, as traced by the old stellar populations and the X-ray emitting intracluster medium. Our main results include: (i) the distribution of Einstein radii is log-normal, with a peak and 1sigma width of =1.16+/-0.28; (ii) we detect an X-ray/lensing mass discrepancy of =1.3 at 3 sigma significance -- clusters with larger substructure fractions displaying greater mass discrepancies, and thus greater departures from hydrostatic equilibrium; (iii) cluster substructure fraction is also correlated with the slope of the gas density profile on small scales, implying a connection between cluster-cluster mergers and gas cooling. Overall our results are consistent with the view that cluster-cluster mergers play a prominent role in shaping the properties of cluster cores, in particular causing departures from hydrostatic equilibrium, and possibly disturbing cool cores. Our results do not support recent claims that large Einstein radius clusters present a challenge to the CDM paradigm.Comment: 28 pages, 14 figures, accepted for publication in MNRAS, replaced with accepted versio

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