Multiscale cluster lens mass mapping – I. Strong lensing modelling

We propose a novel technique to refine the modelling of galaxy cluster 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 multiscale model that allows sharper contrast in regions of higher density where the number of constraints is generally higher. Our model consists of (i) a multiscale 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 us 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 Monte Carlo Markov Chain sampler. For a selected subset of multiple images, we manage to halve the errors between the positions of predicted and observed images compared to previous studies. This is due to the flexibility of multiscale 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 http://www.oamp.fr/cosmology/lenstool .     

Gravitational lens magnification by Abell 1689: distortion of the background galaxy luminosity function

Gravitational lensing magnifies the observed flux of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Under the assumption that these galaxies are a random sample of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use nine filters observed over 12 h with the Calar Alto 3.5-m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 146 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to 0.25  h ⁻¹ Mpc is M _2D(<0.25  h ⁻¹ Mpc)=(0.48±0.16)×10¹⁵  h ⁻¹ M_⊙, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the offset calibration and finite sampling. This result is in good agreement with that found by number-count and shear-based methods and provides a new and independent method to determine cluster masses.     

The dynamical state of RX J1347.5−1145 from a combined strong lensing and X-ray analysis

We perform a combined X-ray and strong lensing analysis of RX J1347.5−1145, one of the most luminous galaxy clusters at X-ray wavelengths. We show that evidence from strong lensing alone, based on published Very Large Telescope (VLT) and new Hubble Space Telescope ( HST ) data, strongly argues in favour of a complex structure. The analysis takes into account arc positions, shapes and orientations, and is done thoroughly in the image plane. The cluster inner regions are well fitted by a bimodal mass distribution, with a total projected mass of   M _tot= (9.9 ± 0.3) × 10¹⁴ M_⊙  h ⁻¹  within a radius of 360 kpc  h ⁻¹ (1.5 arcmin). Such a complex structure could be a signature of a recent major merger as further supported by X-ray data. A temperature map of the cluster, based on deep Chandra observations, reveals a hot front located between the first main component and an X-ray emitting south-eastern subclump. The map also unveils a filament of cold gas in the innermost regions of the cluster, most probably a cooling wake caused by the motion of the cD inside the cool core region. A merger scenario in the plane of the sky between two dark matter subclumps is consistent with both our lensing and X-ray analyses, and can explain previous discrepancies with mass estimates based on the virial theorem.     

A substructure analysis of the A3558 cluster complex

The 'algorithm driven by the density estimate for the identification of clusters' ( DEDICA ) is applied to the A3558 cluster complex in order to find substructures. This complex, located at the centre of the Shapley Concentration supercluster, is a chain formed by the ACO clusters A3556, A3558 and A3562 and the two poor clusters SC 1327-312 and SC 1329-313. We find a large number of clumps, indicating that strong dynamical processes are active. In particular, it is necessary to use a fully three-dimensional sample (i.e. using the galaxy velocity as third coordinate) in order also to recover the clumps superimposed along the line of sight. Even though a large number of detected substructures was already found in a previous analysis, this method is more efficient and faster when compared with a wide battery of tests, and permits the direct estimate of the detection significance. Almost all subclusters previously detected by the wavelet analyses found in the literature are recognized by DEDICA . On the basis of the substructure analysis, we also briefly discuss the origin of the A3558 complex by comparing two hypotheses: (i) the structure is a cluster–cluster collision seen just after the first core–core encounter; or (ii) this complex is the result of a series of incoherent group–group and cluster–group mergings, focused in that region by the presence of the surrounding supercluster. We studied the fraction of blue galaxies in the detected substructures and found that the bluest groups reside between A3562 and A3558, i.e. in the expected position for the scenario of cluster–cluster collision.     

X-ray and strong lensing mass estimate of MS2137.3–2353

We present new mass estimates of the cluster of galaxies MS2137.3–2353, inferred from X-ray and strong lensing analyses. This cluster exhibits an outstanding strong lensing configuration and indicates a well-relaxed dynamical state, being most suitable for a mass reconstruction which combines both techniques. Despite this, several previous studies have claimed a significant discrepancy between the X-ray and the strong lensing mass estimates. The primary aim of this paper is to address and explain this mismatch. For this purpose, we have analysed Chandra observations to recover the profiles of the intracluster medium properties and, assuming a functional form for the matter density, the total mass distribution. The notable strong-lensing features of MS2137.3 allow us to reconstruct its projected mass in the central regions with good accuracy, by taking advantage of the lensing inversion code lenstool . We compare the results obtained for both methods. Our mass estimates for MS2137.3 are in agreement within errors, leading to a mean, extrapolated value of   M ₂₀₀≃ 4.4 ± 0.3 × 10¹⁴ M_⊙  , under the assumption of the Navarro–Frenk–White (NFW) mass profile. However, the strong lensing mass estimate is affected by the details of the brightest cluster galaxy mass modelling, since the radial arc is a very sensitive probe of the total mass derivative in the central region. In particular, we do not find evidence for a high concentration for the NFW density profile, as reported in some earlier works.     

Cosmological constraints from the X-ray gas mass fraction in relaxed lensing clusters observed with Chandra

We present precise measurements of the X-ray gas mass fraction for a sample of luminous, relatively relaxed clusters of galaxies observed with the Chandra observatory, for which independent confirmation of the mass results is available from gravitational lensing studies. Parametrizing the total (luminous plus dark matter) mass profiles using the model of Navarro, Frenk & White, we show that the X-ray gas mass fractions in the clusters asymptote towards an approximately constant value at a radius r ₂₅₀₀, where the mean interior density is 2500 times the critical density of the Universe at the redshifts of the clusters. Combining the Chandra results on the X-ray gas mass fraction and its apparent redshift dependence with recent measurements of the mean baryonic matter density in the Universe and the Hubble constant determined from the Hubble Key Project, we obtain a tight constraint on the mean total matter density of the Universe,     , and measure a positive cosmological constant,     . Our results are in good agreement with recent, independent findings based on analyses of anisotropies in the cosmic microwave background radiation, the properties of distant supernovae, and the large-scale distribution of galaxies.     

Impact of stochastic gas motions on galaxy cluster abundance profiles

The impact of stochastic gas motions on the metal distribution in cluster cores is evaluated. Peaked abundance profiles are a characteristic feature of clusters with cool cores, and abundance peaks are probably associated with the brightest cluster galaxies (BCGs), which dwell in cluster cores. However, the width of the abundance peaks is significantly broader than the BCG light distribution, suggesting that some gas motions are transporting metals originating from within the BCG. Assuming that this process can be treated as diffusive, and using the brightest X-ray cluster A426 (Perseus) as an example, we estimate that a diffusion coefficient of the order of  2 × 10²⁹ cm² s⁻¹  is needed to explain the width of the observed abundance profiles. Much lower (higher) diffusion coefficients would result in too peaked (too shallow) profiles. Such diffusion could be produced by stochastic gas motions, and our analysis provides constraints on the product of their characteristic velocity and their spatial coherence scale. We speculate that the activity of the supermassive black hole of the BCG is driving the stochastic gas motions in cluster cores. When combined with the assumption that the dissipation of the same motions is a key gas heating mechanism, one can estimate both the velocity and the spatial scale of such diffusive processes.     

Infrared observations of gravitational lensing in Abell 2219 with CIRSI

We present the first detection of a gravitational depletion signal at near-infrared wavelengths, based on deep panoramic images of the cluster Abell 2219 ( z =0.22) taken with the Cambridge Infrared Survey Instrument (CIRSI) at the prime focus of the 4.2-m William Herschel Telescope. Infrared studies of gravitational depletion offer a number of advantages over similar techniques applied at optical wavelengths, and can provide reliable total masses for intermediate-redshift clusters. Using the maximum-likelihood technique developed by Schneider, King & Erben, we detect the gravitational depletion at the 3 confidence level. By modelling the mass distribution as a singular isothermal sphere and ignoring the uncertainty in the unlensed number counts, we find an Einstein radius of (66 per cent confidence limit). This corresponds to a projected velocity dispersion of _v 800 km s¹, in agreement with constraints from strongly lensed features. For a Navarro, Frenk & White mass model, the radial dependence observed indicates a best-fitting halo scalelength of 125 h ¹ kpc. We investigate the uncertainties arising from the observed fluctuations in the unlensed number counts, and show that clustering is the dominant source of error. We extend the maximum-likelihood method to include the effect of incompleteness, and discuss the prospects of further systematic studies of lensing in the near-infrared band.