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.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

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.     

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.     

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.     

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.     

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≲0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses  ∼10¹⁵ M_⊙  , the effect of the gravitomagnetic term is ≲0.04 per cent on strong lensing estimates and ≲0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≲1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.     

Constraining the Mass Distribution of Cluster Galaxies by Weak Lensing

Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the average mass distribution of cluster galaxies and potentially to test the extent of their dark matter haloes as a function of the density of their environment. The observable image distortions are a consequence of the interplay between the effects of a global cluster mass distribution and the perturbations resulting from individual cluster galaxies. Starting from a reconstruction of the cluster mass distribution with conventional techniques, we apply a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies. From simulations this approach is found to be reliable as long as the galaxies including their dark matter haloes only contribute a small fraction to the total mass of the system. If their haloes are extended, the galaxies contain a substantial mass fraction. In this case our method is still applicable in the outer regions of clusters, where the surface mass density is low, but yields biased estimates of the parameters describing the mass profiles of the cluster galaxies in the central part of the cluster. In that case it will be necessary to resort to more sophisticated strategies by modelling cluster galaxies and an underlying global mass distribution simultaneously. We conclude that galaxy–galaxy lensing in clusters provides a unique means to probe the presence and extent of dark haloes of cluster galaxies.