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.     

QSO lensing magnification associated with galaxy groups

We simulated both the matter and light (galaxy) distributions in a wedge of the Universe and calculated the gravitational lensing magnification caused by the mass along the line-of-sight of galaxies and galaxy groups identified in sky surveys. A large volume redshift cone containing cold dark matter particles mimics the expected cosmological matter distribution in a flat universe with low matter density and a cosmological constant. We generate a mock galaxy catalogue from the matter distribution and identify thousands of galaxy groups in the luminous sky projection. We calculate the expected magnification around galaxies and galaxy groups and then the induced quasi-stellar object (QSO)–lens angular correlation due to magnification bias. This correlation is observable and can be used both to estimate the average mass of the lens population and to make cosmological inferences. We also use analytical calculations and various analyses to compare the observational results with theoretical expectations for the cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies and groups from the Automated Plate Measurement and Sloan Digital Sky Survey Early Data Release. The observed QSO–lens anticorrelations are stronger than the predictions for the cosmological model used. This suggests that there could be unknown systematic errors in the observations and data reduction, or that the model used is not adequate. If the observed signal is assumed to be solely due to gravitational lensing, then the lensing is stronger than expected, due to more massive galactic structures or more efficient lensing than simulated.     

Weak gravitational flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Source–lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source–lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, S ₃, is examined using a non-linear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on S ₃ to be of the order of  5–40  per cent. It depends significantly on the redshift distribution of sources and on the way in which the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.     

The effect of weak lensing on the angular correlation function of faint galaxies

The angular correlation function ο(θ) of faint galaxies is affected both by non-linear gravitational evolution and by magnification bias resulting from gravitational lensing. We compute the resulting ο(θ) for different cosmological models and show how its shape and redshift evolution depend on Ω and Λ. For galaxies at redshift greater than 1 ( R magnitude fainter than about 24), magnification bias can significantly enhance or suppress ο(θ), depending on the slope of the number–magnitude relation. We show, for example, how it changes the ratio of ο(θ) for two galaxy samples with different number count slopes.     

lemomaf: Lensed Mock Map Facility

We present the Lensed Mock Map Facility ( lemomaf ), a tool designed to perform mock weak-lensing measurements on numerically simulated chunks of the Universe. Coupling N -body simulations to a semi-analytical model of galaxy formation, lemomaf can create realistic lensed images and mock catalogues of galaxies, at wavelengths ranging from the ultraviolet to the submillimetre. To demonstrate the power of such a tool, we compute predictions of the source–lens clustering (SLC) effect on the convergence statistics, and quantify the impact of weak lensing on galaxy counts in two different filters. We find that the SLC effect skews the probability density function of the convergence towards low values, with an intensity which strongly depends on the redshift distribution of galaxies. On the other hand, the degree of enhancement or depletion in galaxy counts due to weak lensing is independent of the SLC effect. We discuss the impact on the two-point shear statistics to be measured by future missions like SNAP and LSST . The SLC effect would bias the estimation of σ₈ from two-point statistics up to 5 per cent for a narrow redshift distribution of mean   z ∼ 0.5  , and up to 2 per cent in small angular scales for a redshift distribution of mean   z ∼ 1.5  . We conclude that accurate photometric redshifts for individual galaxies are necessary in order to quantify and isolate the SLC effect.     

Galaxy density profiles and shapes – II. Selection biases in strong lensing surveys

Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio and image separation distribution, with a flexible treatment of magnification bias to mimic different survey strategies. We present our results for two families of density profiles: cusped and deprojected Sérsic models. While we use fixed lens and source redshifts for most of the analysis, we show that the results are applicable to other redshift combinations, and we also explore the physics of how our results change for very different redshifts. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sérsic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

Topology and geometry of the CfA2 redshift survey

We analyse the redshift space topology and geometry of the nearby Universe by computing the Minkowski functionals of the Updated Zwicky Catalogue (UZC). The UZC contains the redshifts of almost 20 000 galaxies, is 96 per cent complete to the limiting magnitude m _Zw=15.5, and includes the Center for Astrophysics (CfA) Redshift Survey (CfA2). From the UZC we can extract volume-limited samples reaching a depth of 70  h ⁻¹ Mpc before sparse sampling dominates. We quantify the shape of the large-scale galaxy distribution by deriving measures of planarity and filamentarity from the Minkowski functionals. The nearby Universe shows a large degree of planarity and a small degree of filamentarity. This quantifies the sheet-like structure of the Great Wall, which dominates the northern region (CfA2N) of the UZC. We compare these results with redshift space mock catalogues constructed from high-resolution N -body simulations of two cold dark matter (CDM) models with either a decaying massive neutrino ( τ CDM) or a non-zero cosmological constant (ΛCDM). We use semi-analytic modelling to form and evolve galaxies in these dark matter‐only simulations. We are thus able, for the first time, to compile redshift space mock catalogues which contain galaxies, along with their observable properties, rather than dark matter particles alone. In both models the large-scale galaxy distribution is less coherent than the observed distribution, especially with regard to the large degree of planarity of the real survey. However, given the small volume of the region studied, this disagreement can still be a result of cosmic variance, as shown by the agreement between the ΛCDM model and the southern region of CfA2.     

The imprint of cosmic reionization on galaxy clustering

We consider the effect of reionization on the clustering properties of galaxy samples at intermediate redshifts ( z ∼ 0.3–5.5). Current models for the reionization of intergalactic hydrogen predict that overdense regions will be reionized early, thus delaying the build-up of stellar mass in the progenitors of massive lower redshift galaxies. As a result, the stellar populations observed in intermediate-redshift galaxies are somewhat younger and hence brighter in overdense regions of the Universe. Galaxy surveys would therefore be sensitive to galaxies with a somewhat lower dark matter mass in overdense regions. The corresponding increase in the observed number density of galaxies can be parametrized as a galaxy bias due to reionization. We model this process using merger trees combined with a stellar synthesis code. Our model demonstrates that reionization has a significant effect on the clustering properties of galaxy samples that are selected based on their star formation properties. The bias correction in Lyman-break galaxies (including those in proposed baryonic oscillation surveys at z < 1) is at the level of 10–20 per cent for a halo mass of  10¹² M_⊙  , leading to corrections factors of 1.5–2 in the halo mass inferred from measurements of clustering length. The reionization of helium could also lead to a sharp increase in the amplitude of the galaxy correlation function at z ∼ 3. We find that the reionization bias is approximately independent of scale and halo mass. However, since the traditional galaxy bias is mass dependent, the reionization bias becomes relatively more important for lower mass systems. The correction to the bias due to reionization is very small in surveys of luminous red galaxies at z < 1.     

Clustering Property of Wolf-Rayet Galaxies in the SDSS

We have analysed, for the first time, the clustering properties of Wolf-Rayet (W-R) galaxies, using a large sample of 846 W-R galaxies selected from the Data Release 4 (DR4) of the Sloan Digital Sky Survey (SDSS). We compute the cross-correlation function between W- R galaxies and a reference sample of galaxies drawn from the DR4. We compare the function to the results for control samples of non-W-R star-forming galaxies that are matched closely in redshift, luminosity, concentration, 4000-A break strength and specific star formation rate (SSFR). On scales larger than a few Mpc, W-R galaxies have almost the same clustering amplitude as the control samples, indicating that W-R galaxies and non-W-R control galax- ies populate dark matter haloes of similar masses. On scales between 0.1-1 h-1 Mpc, W-R galaxies are less clustered than the control samples, and the size of the difference depends on the SSFR. Based on both observational and theoretical considerations, we speculate that this negative bias can be interpreted by W-R galaxies residing preferentially at the centers of their dark matter haloes. We examine the distribution of W-R galaxies more closely using the SDSS galaxy group catalogue of Yang et al., and find that ～82% of our W-R galaxies are the central galaxies of groups, compared to ～74% for the corresponding control galaxies. We find that W-R galaxies are hosted, on average, by dark matter haloes of masses of 1012,3 M☉, compared to 1012,1 M? For centrally-located W-R galaxies and 1012,7 M☉ For satellite ones. We would like to point out that this finding, which provides a direct observational support to our conjecture, is really very crude due to the small number of W-R galaxies and the incom- pleteness of the group catalogue, and needs more work in future with larger samples.     

Strong gravitational lensing by spiral galaxies

We investigate gravitational lensing using a realistic model of disc galaxies. Most of the mass is contained in a large spherical isothermal dark matter halo, but the potential is modified significantly in the core by a gravitationally dominant exponential disc. The method used is adapted from a very general multilens ray-tracing technique developed by Mo¨ller. We investigate the effects of the disc-to-halo mass ratio, the disc scalelength, the disc inclination to the line of sight and the lens redshift on two strong-lensing cross-sections: the cross-section for multiple imaging and the cross-section for large magnifications, in excess of a factor of 10. We find that the multiple-imaging cross-section can be enhanced significantly by an almost edge-on Milky Way disc compared with a singular isothermal sphere (SIS) in individual cases; however, when averaged over all disc inclinations, the cross-section is only increased by about 50 per cent. These results are consistent with other recent work. The presence of a disc, however, increases the inclination-averaged high-magnification cross-section by an order of magnitude compared with a SIS. This result has important implications for magnification bias in future lens surveys, particularly those in the submillimetre waveband, where dust extinction in the lensing galaxy has no effect on the brightness of the images.     

Tidal alignments as a contaminant of redshift space distortions

We investigate the effect of orientation-dependent selection effects on galaxy clustering in redshift space. It is found that if galaxies are aligned by large-scale tidal fields, then these selection effects give rise to a dependence of the observed galaxy density on the local tidal field, in addition to the well-known dependences on the matter density and radial velocity gradient. This alters the galaxy power spectrum in a way that is different for Fourier modes parallel to and perpendicular to the line of sight. These tidal galaxy alignments can thus mimic redshift space distortions (RSD), and thus result in a bias in the measurement of the velocity power spectrum. If galaxy orientations are affected only by the local tidal field, then the tidal alignment effect has exactly the same scale and angular dependence as the RSDs in the linear regime, so it cannot be projected out or removed by masking small scales in the analysis. We consider several toy models of tidal alignments and orientation-dependent selection, normalize their free parameter (an amplitude) to recent observations, and find that they could bias the velocity amplitude   f ( z ) G ( z )  by 5–10 per cent in some models, although most models give much smaller contamination. We conclude that tidal alignments may be a significant systematic error in RSD measurements that aim to test general relativity via the growth of large-scale structure. We briefly discuss possible mitigation strategies.     

Angular correlations between LBQS and APM: weak lensing by the large-scale structure

We detect a positive angular correlation between bright, high-redshift QSOs and foreground galaxies. The QSOs are taken from the optically selected LBQS Catalogue, while the galaxies are from the APM Survey. The correlation amplitude is about a few per cent on angular scales of over a degree. It is a function of QSO redshift and apparent magnitude, in a way expected from weak lensing, and inconsistent with QSO–galaxy correlations being caused by physical associations, or uneven obscuration by Galactic dust. The correlations are ascribed to the weak lensing effect of the foreground dark matter, which is traced by the APM galaxies. The amplitude of the effect found here is compared to the analytical predictions from the literature, and to the predictions of a phenomenological model, which is based on the observed counts-in-cells distribution of APM galaxies. While the latter agree reasonably well with the analytical predictions (namely those of Dolag &38; Bartelmann and Sanz et al.), both underpredict the observed correlation amplitude on degree angular scales. We consider the possible ways to reconcile these observations with theory, and discuss the implications that these observations have on some aspects of extragalactic astronomy.     

Evolution of the dark matter distribution with three-dimensional weak lensing

We present a direct detection of the growth of large-scale structure, using weak gravitational lensing and photometric redshift data from the COMBO-17 survey. We use deep R -band imaging of two  0.5 × 0.5 deg²  fields, affording shear estimates for over 52 000 galaxies; we combine these with photometric redshift estimates from our 17-band survey, in order to obtain a 3D shear field. We find theoretical models for evolving matter power spectra and correlation functions, and fit the corresponding shear correlation functions to the data as a function of redshift. We detect the evolution of the power at the 4.7σ level given reasonable priors, and measure the rate of evolution for  0 < z < 1  . We also fit correlation functions to our 3D data as a function of cosmological parameters σ₈ and  Ω_Λ  . We find joint constraints on  Ω_Λ  and σ₈, demonstrating an improvement in accuracy by ≃40 per cent over that available from 2D weak lensing for the same area.     

Strong lensing optical depths in a ΛCDM universe

We investigate strong gravitational lensing in the concordance ΛCDM cosmology by carrying out ray tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark haloes in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong lensing cross-sections by about 15 per cent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines of sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few per cent of the total surface density.     

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.     

The galaxy environment of a quasar at z= 1.226: a possible cluster merger

We have conducted ultra-deep optical and deep near-infrared observations of a field around the z =1.226 radio-quiet quasar 104420.8+055739 from the Clowes–Campusano LQG of 18 quasars at z ∼1.3, in search of associated galaxy clustering. Galaxies at these redshifts are distinguished by their extremely red colours, with I − K >3.75, and we find a factor ∼11 overdensity of such galaxies in a 2.25×2.25 arcmin² field centred on the quasar. In particular, we find 15–18 galaxies that have colours consistent with being a population of passively evolving massive ellipticals at the quasar redshift. They form 'fingers' in the V − K K , I − K K colour–magnitude plots at V − K ≃6.9, I − K ≃4.3 comparable to the red sequences observed in other z ≃1.2 clusters. We find suggestive evidence for substructure among the red sequence galaxies in the K image, in the form of two compact groups, 40 arcsec to the north, and 60 arcsec to the south-east of the quasar. An examination of the wider optical images indicates that this substructure is significant, and that the clustering extends to form a large-scale structure 2–3  h ⁻¹ Mpc across. We find evidence for a high (≳50 per cent) fraction of blue galaxies in this system, in the form of 15–20 'red outlier' galaxies with I − K >3.75 and V − I <2.00, which we suggest are dusty, star-forming galaxies at the quasar redshift. Within 30 arcsec of the quasar we find a concentration of blue ( V − I <1) galaxies in a band that bisects the two groups of red sequence galaxies. This band of blue galaxies is presumed to correspond to a region of enhanced star formation. We explain this distribution of galaxies as the early stages of a cluster merger which has triggered both the star formation and the quasar.