Detecting mass substructure in galaxy clusters: an aperture mass statistic for gravitational flexion

Gravitational flexion has been introduced as a technique by which one can map out and study substructure in clusters of galaxies. Previous analyses involving flexion have measured the individual galaxy–galaxy flexion signal, or used either parametric techniques or a Kaiser, Squires and Broadhurst (KSB)-type inversion to reconstruct the mass distribution in Abell 1689. In this paper, we present an aperture mass statistic for flexion, and apply it to the lensed images of background galaxies obtained by ray-tracing simulations through a simple analytic mass distribution and through a galaxy cluster from the Millennium Simulation. We show that this method is effective at detecting and accurately tracing structure within clusters of galaxies on subarcminute scales with high signal to noise even using a moderate background source number density and image resolution. In addition, the method provides much more information about both the overall shape and the small-scale structure of a cluster of galaxies than can be achieved through a weak lensing mass reconstruction using gravitational shear data. Lastly, we discuss how the zero-points of the aperture mass might be used to infer the masses of structures identified using this method.     

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.     

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.     

Quasar–galaxy and galaxy–galaxy cross-correlations: model predictions with realistic galaxies

Several measurements of quasi-stellar object (QSO)–galaxy correlations have reported signals much larger than predictions of magnification by large-scale structure. We find that the expected signal depends strongly on the properties of the foreground galaxy population. On arcmin scales, it can be either larger or smaller by a factor of 2 for different galaxy types in comparison with a linearly biased version of the mass distribution. Thus the resolution of some of the excess measurements may lie in examining the halo occupation properties of the galaxy population sampled by a given survey; this is also the primary information such measurements will provide.
We use the halo model of clustering and simulations to predict the magnification-induced cross-correlations and errors for forthcoming surveys. With the full Sloan Digital Sky Survey, the statistical errors will be below 1 per cent for the galaxy–galaxy correlations and significantly larger for QSO–galaxy correlations. Thus accurate constraints on parameters of the galaxy halo occupation distribution can be obtained from small-scale measurements and on the bias parameter from large scales. Since the lensing-induced cross-correlation measures the first moment of the halo occupation number of galaxies, these measurements can provide the basis for interpreting galaxy clustering measurements that measure the second- and higher-order moments.     

Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass-sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SNe Ia).
When corrected with the light-curve shape (LCS), the peak magnitude of SNe Ia provides a standard candle with an uncertainty in apparent magnitude of Δ m ≃0.1–0.2. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared with that expected from its LCS and redshift. The average detection rate for SNe Ia with a significant mismatch of ≥2Δ m behind a cluster at z ≃0.05–0.15 is about 1–2 supernovae per cluster per year at J , I , R ≲25–26.
Since SNe are point-like sources for a limited period, they can experience significant microlensing by massive compact halo objects (MACHOs) in the intracluster medium. Microlensing events caused by MACHOs of ∼10⁻⁴ M⊙ are expected to have time-scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow us to separate them. Microlensing events caused by MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ( z ≲0.05) per year is ∼0.02 ( f /0.01), where f is the fraction of the cluster mass in MACHOs of masses 10⁻⁷< M _macho/M⊙<10⁻⁴.     

Undistorted lensed images in galaxy clusters

To date, the study of high-magnification gravitational lensing effects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a different type of image, highly magnified yet undistorted, in two widely employed cluster mass density profiles, namely an isothermal sphere with a core, and a universal dark matter halo profile derived from the numerical simulations of Navarro et al. We examine the properties of images of extended sources produced by these two cluster profiles, paying particular attention to the undistorted images. Using simple assumptions about the source and lens population, we estimate the relative frequency of the occurrence of highly magnified, undistorted images and the more commonly known giant arcs.     

The observed concentration–mass relation for galaxy clusters

The properties of clusters of galaxies offer key insights into the assembly process of structure in the universe. Numerical simulations of cosmic structure formation in a hierarchical, dark matter dominated universe suggest that galaxy cluster concentrations, which are a measure of a halo's central density, decrease gradually with virial mass. However, cluster observations have yet to confirm this correlation. The slopes of the run of measured concentrations with virial mass are often either steeper or flatter than that predicted by simulations. In this work, we present the most complete sample of observed cluster concentrations and masses yet assembled, including new measurements for 10 strong-lensing clusters, thereby more than doubling the existing number of strong-lensing concentration estimates. We fit a power law to the observed concentrations as a function of virial mass, and find that the slope is consistent with the slopes found in simulations, though our normalization factor is higher. Observed lensing concentrations appear to be systematically larger than X-ray concentrations, a more pronounced effect than that found in simulations. We also find that at a fixed mass, the bulk of observed cluster concentrations are distributed lognormally, with the exception of a few anomalously high concentration clusters. We examine the physical processes likely responsible for the discrepancy between lensing and X-ray concentrations, and for the anomalously high concentrations in particular. The forthcoming Millennium simulation results will offer the most comprehensive comparison set to our findings of an observed concentration–mass power law relation.     

Clustering of galaxy clusters in cold dark matter universes

We use very large cosmological N -body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ( τ CDM) and a flat low density model with a cosmological constant (ΛCDM). Our simulations each use 10⁹ particles to follow the mass distribution within cubes of side 2  h ⁻¹ Gpc ( τ CDM) and 3  h ⁻¹ Gpc (ΛCDM) with a force resolution better than 10⁻⁴ of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from     for samples with mean separation     to     for samples with     The lower value here corresponds to τ CDM and the upper to ΛCDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10 per cent using the simple model of Sheth, Mo & Tormen. This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the automated plate measurement (APM) cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for ΛCDM. The observed power spectrum (for a cluster sample of mean separation     ) lies significantly above the predictions of both models.