Non-parametric reconstruction of cluster mass distribution from strong lensing: modelling Abell 370

We describe a new non-parametric technique for reconstructing the mass distribution in galaxy clusters with strong lensing, i.e. from multiple images of background galaxies. The observed positions and redshifts of the images are considered as rigid constraints, and through the lens (ray-trace) equation they provide us with linear constraint equations. These constraints confine the mass distribution to some allowed region, which is then found by linear programming. Within this allowed region we study in detail the mass distribution with minimum mass-to-light variation, and also some other distributions, such as the smoothest mass distribution.
The method is applied to the extensively studied cluster Abell 370, which hosts a giant luminous arc and several other multiply imaged background galaxies. Our mass maps are constrained by the observed positions and redshifts (spectroscopic or model-inferred by previous authors) of the giant arc and multiple-image systems. The reconstructed maps obtained for Abell 370 reveal a detailed mass distribution, with substructure quite different from the light distribution. The method predicts the bimodal nature of the cluster, and that the projected mass distribution is indeed elongated along the axis defined by the two dominant cD galaxies. However, the peaks in the mass distribution appear to be offset from the centres of the cDs.
We also present an estimate for the total mass of the central region of the cluster. This is in good agreement with previous mass determinations. The total mass of the central region is M =(2.0–2.7)×10¹⁴ M⊙ h ⁻¹₅₀, depending on the solution chosen.     

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.     

Constraints on a quintessence model from gravitational lensing statistics

Constraints on an exact quintessence scalar-field model with an exponential potential are derived from gravitational lens statistics. An exponential potential can account for data from both optical quasar surveys and radio-selected sources. Based on the Cosmic Lens All-Sky Survey (CLASS) sample, lensing statistics provides, for the pressureless matter density parameter, an estimate of  Ω_M0= 0.31^+0.12_−0.14  .     

Chandra measurements of the distribution of mass in the luminous lensing cluster Abell 2390

We present spatially resolved X-ray spectroscopy of the luminous lensing cluster Abell 2390, using observations made with the Chandra observatory. The temperature of the X-ray gas rises with increasing radius within the central ∼ 200 kpc of the cluster, and then remains approximately isothermal, with kT =11.5_−1.6^+1.5 keV , out to the limits of the observations at r ∼1.0 Mpc . The total mass profile determined from the Chandra data has a form in good agreement with the predictions from numerical simulations. Using the parametrization of Navarro, Frenk and White, we measure a scale radius r _s∼0.8 Mpc and a concentration parameter c ∼3 . The best-fitting X-ray mass model is in good agreement with independent gravitational lensing results and optical measurements of the galaxy velocity dispersion in the cluster. The X-ray gas to total mass ratio rises with increasing radius with f _gas∼21 per cent at r =0.9 Mpc . The azimuthally averaged 0.3–7.0 keV surface brightness profile exhibits a small core radius and a clear 'break' at r ∼500 kpc , where the slope changes from S _X ∼^∝  r ^−1.5 to S _X ∼^∝  r ^−3.6 . The data for the central region of the cluster indicate the presence of a cooling flow with a mass deposition rate of 200–300 M_⊙ yr⁻¹ and an effective age of 2–3 Gyr .     

Infrared constraints on the dark mass concentration observed in the cluster Abell 1942

We present a deep H -band image of the region in the vicinity of the cluster Abell 1942 containing the puzzling dark matter concentration detected in an optical weak lensing study by Erben et al. We demonstrate that our limiting magnitude, H =22 , would be sufficient to detect clusters of appropriate mass out to redshifts comparable with the mean redshift of the background sources. Despite this, our infrared image reveals no obvious overdensity of sources at the location of the lensing mass peak, nor an excess of sources in the I − H versus H colour–magnitude diagram. We use this to constrain further the luminosity and mass-to-light ratio of the putative dark clump as a function of its redshift. We find that for spatially flat cosmologies, background lensing clusters with reasonable mass-to-light ratios lying in the redshift range 0< z <1 are strongly excluded, leaving open the possibility that the mass concentration is a new type of truly dark object.     

Halo masses for optically selected and for radio-loud AGN from clustering and galaxy–galaxy lensing

We compute two-point correlation functions and measure the shear signal due to galaxy–galaxy lensing for 80 000 optically identified and 5700 radio-loud active galactic nuclei (AGN) from Data Release 4 of the Sloan Digital Sky Survey. Halo occupation models are used to estimate halo masses and satellite fractions for these two types of AGN. The large sample size allows us to separate AGN according to the stellar mass of their host galaxies. We study how the halo masses of optical and radio AGN differ from those of the parent population at fixed   M _*  . Halo masses deduced from clustering and from lensing agree satisfactorily. Radio AGN are found in more massive haloes than optical AGN: in our samples, their mean halo masses are  1.6 × 10¹³  and  8 × 10¹¹  h ⁻¹ M_⊙  , respectively. Optical AGN follow the same relation between stellar mass and halo mass as galaxies selected without regard to nuclear properties, but radio-loud AGN deviate significantly from this relation. The dark matter haloes of radio-loud AGN are about twice as massive as those of control galaxies of the same stellar mass. This boost is independent of radio luminosity, and persists even when our analysis is restricted to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a crucial role in producing observable radio emission. The dark matter halo masses that we derive for the AGN in our two samples are in good agreement with recent models in which feedback from radio AGN becomes dominant in haloes where gas cools quasi-statically.     

X-ray group and cluster mass profiles in MOND: unexplained mass on the group scale

Although very successful in explaining the observed conspiracy between the baryonic distribution and the gravitational field in spiral galaxies without resorting to dark matter (DM), the modified Newtonian dynamics (MOND) paradigm still requires DM in X-ray bright systems. Here, to get a handle on the distribution and importance of this DM, and thus on its possible form, we deconstruct the mass profiles of 26 X-ray emitting systems in MOND, with temperatures ranging from 0.5 to 9 keV. Initially, we compute the MOND dynamical mass as a function of radius, then subtract the known gas mass along with a component of galaxies which include the cD galaxy with   M / L _K = 1  . Next, we test the compatibility of the required DM with ordinary massive neutrinos at the experimental limit of detection  ( m _ν= 2 eV)  , with density given by the Tremaine–Gunn limit. Even by considering that the neutrino density stays constant and maximal within the central 100 or 150 kpc (which is the absolute upper limit of a possible neutrino contribution there), we show that these neutrinos can never account for the required DM within this region. The natural corollary of this finding is that, whereas clusters  ( T ≳ 3 keV)  might have most of their mass accounted for if ordinary neutrinos have a 2 eV mass, groups  ( T ≲ 2 keV)  cannot be explained by a 2 eV neutrino contribution. This means that, for instance, cluster baryonic dark matter (CBDM, Milgrom) or even sterile neutrinos would present a more satisfactory solution to the problem of missing mass in MOND X-ray emitting systems.     

Probing galactic dark matter in dense environments: on the strong lensing efficiency of galaxies in rich clusters

The recent detection by Limousin et al. of five new strong lensing events dominated by galaxy cluster members in Abell 1689, and outside the critical regime of the cluster itself, offers a way to obtain constraints on the cluster mass distribution in a region inaccessible to standard lensing analysis. In addition, modelling such systems will provide another window on the dark matter haloes of galaxies in very dense environments. Here, it is shown that the boost in image separation due to the external shear and convergence from a smooth cluster component means that more numerous, less massive galaxies have the potential to create multiple images with detectable separations, relative to isolated field galaxies. This comes in addition to a potential increase in their lensing (source plane) cross-section. To gain insight into the factors involved and as a precursor to a numerical study using N -body simulations, a simple analytic model of a cluster at   z = 0.3  lensing background galaxies at   z = 2  is considered here. The fiducial model has cluster members with isothermal density profiles and luminosities L , distributed in a Schechter function (faint-end slope  ν=−1.25  ), related to their velocity dispersions σ via the Faber–Jackson scaling L ∝σ⁴. Just outside the critical regime of the cluster, the scale of galaxy-dominated image separations is significantly increased. Folding in the fact that less massive galaxies present a lower lensing cross-section, and that the cross-section can itself be enhanced in an external field leads to a factor of a few times more detected events relative to field galaxies. These values will be higher closer to the critical curve. Given that the events in Abell 1689 were detected over a very small region of the cluster where ACS data were available, this motivates the search for such events in other clusters.     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.