Angular cross-correlation of galaxies: a probe of gravitational lensing by large-scale structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.     

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 lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.     

Statistics of weak lensing at small angular scales: analytical predictions for lower order moments

Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasi-linear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcmin, for which the relevant physical length-scales are in the non-linear regime of gravitational clustering. We use the hierarchical ansatz to compute the multipoint statistics of the weak lensing convergence for these small smoothing angles. We predict the multipoint cumulants and cumulant correlators up to fourth order and compare our results with high-resolution ray-tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Ω and Λ.     

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.     

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w ₀ =  p _x0/ρ_x0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.     

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.     

Gravitational Lensing Effect on the Two-Point Correlation of Hot Spots in the Cosmic Microwave Background

We investigate the weak gravitational lensing effect that is due to the large-scale structure of the universe on two-point correlations of local maxima (hot spots) in the two-dimensional sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics, as most inflationary scenarios predict, the hot spots are discretely distributed, with some characteristic angular separations on the last scattering surface that are due to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hot spots, which are separated with the characteristic scale, to be observed with various separations. We found that the lensing fairly smooths out the oscillatory features of the two-point correlation function of hot spots. This indicates that the hot spot correlations can be a new statistical tool for measuring the shape and normalization of the power spectrum of matter fluctuations from the lensing signatures.     

Intrinsic correlation of galaxy shapes: implications for weak lensing measurements

Weak gravitational lensing is now established as a powerful method to measure mass fluctuations in the universe. It relies on the measurement of small coherent distortions of the images of background galaxies. Even low-level correlations in the intrinsic shapes of galaxies could however produce a significant spurious lensing signal. These correlations are also interesting in their own right, since their detection would constrain models of galaxy formation. Using     haloes found in N -body simulations, we compute the correlation functions of the intrinsic ellipticity of spiral galaxies assuming that the disc is perpendicular to the angular momentum of the dark matter halo. We also consider a simple model for elliptical galaxies, in which the shape of the dark matter halo is assumed to be the same as that of the light. For deep lensing surveys with median redshifts ∼1, we find that intrinsic correlations of ∼10⁻⁴ on angular scales     are generally below the expected lensing signal, and contribute only a small fraction of the excess signals reported on these scales. On larger scales we find limits to the intrinsic correlation function at a level ∼10⁻⁵, which gives a (model-dependent) range of separations for which the intrinsic signal is about an order of magnitude below the ellipticity correlation function expected from weak lensing. Intrinsic correlations are thus negligible on these scales for dedicated weak lensing surveys. For wider but shallower surveys such as SuperCOSMOS, APM and SDSS, we cannot exclude the possibility that intrinsic correlations could dominate the lensing signal. We discuss how such surveys could be used to calibrate the importance of this effect, as well as study spin–spin correlations of spiral galaxies.     

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.     

Gravitational lenses in the dark Universe

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance, i.e., the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter Ω _i : (i) the cold dark matter model, (ii) the ΛCDM model, (iii) the Bose-Einstein condensate dark matter model, (iv) the Chaplygin gas model, (v) the viscous fluid cosmological model and (vi) the holographic dark energy model by using the singular isothermal sphere (SIS) model for the halos of dark matter. We note that the dependence of the energy-matter content of the universe profoundly modifies the frequency of multiple quasar images.     

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.     

Correlation between the Halo Concentration c and the Virial Mass Mvir Determined from X-Ray Clusters

Numerical simulations of structure formation have suggested that there exists a good correlation between the halo concentration c (or the characteristic density deltac) and the virial mass Mvir for any virialized dark halo described by the Navarro, Frenk, & White density profile. In this Letter, we present an observational determination of the c-Mvir (or deltac-Mvir) relation in the mass range of approximately 1014 M middle dot in circle相似文献   

Weak lensing in the second post-Newtonian approximation: gravitomagnetic potentials and the integrated Sachs–Wolfe effect

Dark matter currents in the large-scale structure give rise to gravitomagnetic terms in the metric, which affect the light propagation. Corrections to the weak-lensing power spectrum due to these gravitomagnetic potentials are evaluated by perturbation theory. A connection between gravitomagnetic lensing and the integrated Sachs–Wolfe (iSW) effect is drawn, which can be described by a line-of-sight integration over the divergence of the gravitomagnetic vector potential. This allows the power spectrum of the iSW-effect to be derived within the framework of the same formalism as derived for gravitomagnetic lensing and reduces the iSW-effect to a second-order lensing phenomenon. The three-dimensional power spectra are projected by means of a generalized Limber-equation to yield the angular power spectra. Gravitomagnetic corrections to the weak-lensing spectrum are negligible at currently accessible scales, and cosmic-variance considerations suggest that the detection of the iSW-effect's contribution to the cosmic microwave background angular power spectrum is too small to be detectable at multipoles probed by the Planck satellite.     

Lensed CMB temperature and polarization maps from the Millennium Simulation

We have constructed the first all-sky cosmic microwave background (CMB) temperature and polarization lensed maps based on a high-resolution cosmological N -body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a previously developed map-making procedure which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to   z = 127  , and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N -body simulation. The lensed sky has been obtained by properly modifying the latest version of the LensPix code to account for the MS structures. We have also produced all-sky lensed maps of the so-called  ψ _E   and  ψ _B   potentials, which are directly related to the electric and magnetic types of polarization. The angular power spectra of the simulated lensed temperature and polarization maps agree well with semi-analytic estimates up to   l ≤ 2500  , while on smaller scales we find a slight excess of power which we interpret as being due to non-linear clustering in the MS. We also observe how non-linear lensing power in the polarized CMB is transferred to large angular scales by suitably misaligned modes in the CMB and the lensing potential. This work is relevant in view of the future CMB probes, as a way to analyse the lensed sky and disentangle the contribution from primordial gravitational waves.     

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.     

Theoretical estimates of intrinsic galaxy alignment

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity–ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that, for low-redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces ' E -mode' correlations enhanced by a factor of 3.5 over B -modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.     

Testing deprojection algorithms on mock angular catalogues: evidence for a break in the power spectrum

We produce mock angular catalogues from simulations with different initial power spectra to test methods that recover measures of clustering in three dimensions, such as the power spectrum, variance and higher order cumulants. We find that the statistical properties derived from the angular mock catalogues are in good agreement with the intrinsic clustering in the simulations. In particular, we concentrate on the detailed predictions for the shape of the power spectrum, P ( k ). We find that there is good evidence for a break in the galaxy P ( k ) at scales in the range 0.02< k <0.06 h Mpc⁻¹, using an inversion technique applied to the angular correlation function measured from the APM Galaxy Survey. For variants on the standard cold dark matter (CDM) model, a fit at the location of the break implies Ω h =0.45±0.10, where Ω is the ratio of the total matter density to the critical density, and Hubble's constant is parametrized as H ₀=100 h km s⁻¹ Mpc⁻¹. On slightly smaller, though still quasi-linear scales, there is a feature in the APM power spectrum where the local slope changes appreciably, with the best match to CDM models obtained for Ω h ≃0.2. Hence the location and narrowness of the break in the APM power spectrum combined with the rapid change in its slope on quasi-linear scales cannot be matched by any variant of CDM, including models that have a non-zero cosmological constant or a tilt to the slope of the primordial P ( k ). These results are independent of the overall normalization of the CDM models or any simple bias that exists betwen the galaxy and mass distributions.     

On Einstein clusters as galactic dark matter haloes

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of weakly interacting massive particles (WIMPs) as galactic dark matter haloes. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters as compared to the singular isothermal density sphere model for dark matter. Therefore, lensing observations may discriminate, at least, in principle, between Einstein cluster and the other dark matter models.