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.     

Quasar–galaxy associations revisited

Gravitational lensing predicts an enhancement of the density of bright, distant quasi-stellar objects (QSOs) around foreground galaxies. We measure this QSO–galaxy correlation w _qg for two complete samples of radio-loud quasars, the southern 1 Jy and half-Jansky samples. The existence of a positive correlation between     quasars and     galaxies is confirmed at a     per cent significance level (>99.9 per cent if previous measurements on the northern hemisphere are included). A comparison with the results obtained for incomplete quasar catalogues (e.g. the Veron-Cetty and Veron compilation) suggests the existence of an 'identification bias', which spuriously increases the estimated amplitude of w _qg for incomplete samples. This effect may explain many of the surprisingly strong quasar–galaxy associations found in the literature. Nevertheless, the value of w _qg that we measure in our complete catalogues is still considerably higher than the predictions from weak lensing. We consider two effects which could help to explain this discrepancy: galactic dust extinction and strong lensing.     

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.     

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.     

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.     

The environments of intermediate-redshift QSOs: 0.3 < z < 0.7

An angular correlation of low significance (2 σ ) is observed between 0.3< z <0.5 QSOs and V 23 galaxies. Overall, the cross-correlation function between 82 intermediate-redshift (0.3< z <0.7) X-ray selected QSOs and V ≲24 galaxies is investigated, but no signal is detected for the z >0.5 QSOs. After converting to an excess of galaxies physically associated with the QSO, this lack of strong correlation is shown to be consistent with the clustering of normal galaxies at the same moderate redshifts. Combined with previous observations, these results imply that the environments of radio-quiet QSOs do not undergo significant evolution with respect to the galaxy population over a wide range of redshifts (0< z <1.5). This is in marked contrast to the rapid increase in the richness of the environments associated with radio-loud QSOs over the same redshift range.     

Cross-correlation of the unresolved X‐ray background with faint galaxies

At the faint end of the deepest X-ray surveys, a population of X-ray luminous galaxies is seen. In this paper, we present the results of a cross-correlation between the residual, unresolved X-ray photons in a very deep X-ray survey and the positions of faint galaxies, in order to examine the importance of these objects at even fainter flux levels. We measure a significant correlation on all angular scales up to ∼1 arcmin. This signal could account for a significant fraction of the unresolved X‐ray background, approximately 35 per cent if the clustering is similar to optically selected galaxies. However, the angular form of the correlation is seen to be qualitatively similar to that expected for clusters of galaxies and the X-ray emission could be associated with hot gas in clusters or with QSOs within galaxy clusters rather than emission from individual faint galaxies. The relative contribution from each of these possibilities cannot be determined with the current data.     

Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring the possible shapes of the redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3 per cent at most.     

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.     

Galaxy–QSO correlation induced by weak gravitational lensing arising from large-scale structure

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.     

Intrinsic and extrinsic galaxy alignment

We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing arising from large-scale mass inhomogeneities ('field lensing') is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or by the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long-range correlations in the tidal field will thus lead to long-range ellipticity–ellipticity correlations that mimic the shear correlations arising from weak gravitational lensing. We calculate the ellipticity–ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity–ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak-lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity–tidal-field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field-lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.     

ARCS, the Arcminute Radio Cluster-lens Search – I. Selection criteria and initial results

We present the results of an unbiased radio search for gravitational lensing events with image separations between 15 and 60 arcsec, which would be associated with clusters of galaxies with masses >10^13–14 M_⊙. A parent population of 1023 extended radio sources stronger than 35 mJy with stellar optical identifications was selected using the FIRST radio catalogue at 1.4 GHz and the APM optical catalogue. The FIRST catalogue was then searched for companions to the parent sources stronger than 7 mJy and with separation in the range 15 to 60 arcsec. Higher-resolution observations of the resulting 38 lens candidates were made with the VLA at 1.4 and 5 GHz, and with MERLIN at 5 GHz in order to test the lens hypothesis in each case. None of our targets was found to be a gravitational lens system. These results provide the best current constraint on the lensing rate for this angular scale, but improved calculations of lensing rates from realistic simulations of the clustering of matter on the relevant scales are required before cosmologically significant constraints can be derived from this null result. We now have an efficient, tested observational strategy with which it will be possible to make an order-of-magnitude larger unbiased search in the near future.     

A pilot survey for KX QSOs in the UKIDSS Ultra Deep Survey Field

We have undertaken a pilot survey for faint quasi-stellar objects (QSOs) in the UKIRT Infrared Deep Survey (UKIDSS) Ultra Deep Survey (UDS) Field using the KX selection technique. These observations exploit the very deep near-infrared and optical imaging of this field from United Kingdom Infrared Telescope (UKIRT) and Subaru to select candidate QSOs based on their VJK colours and morphologies. We determined redshifts for 426 candidates using the AAOmega spectrograph on the Anglo-Australian Telescope in service time. We identify 17 QSOs  ( M _B ≲−23)  in this pilot survey at z = 1.57–3.29. We combine our sample with an X-ray-selected sample of QSOs in the same field (a large fraction of which also comply with our KX selection) to constrain the surface density of QSOs with K ≤ 20, deriving limits on the likely surface density of 85–150 deg⁻². We use the good image quality available from our near-infrared imaging to detect a spatially extended component of the QSO light which probably represents the host galaxies. We also use our sample to investigate routes to improve the selection of KX QSOs at faint limits in the face of the significant contamination by compact, foreground galaxies. The brightest examples from our combined QSO sample will be used in conjunction with a large Very Large Telescope VIMOS spectroscopic survey of high-redshift galaxies in this region to study the structures inhabited by gas, galaxies and growing supermassive black holes at high redshifts in the UKIDSS UDS.     

Sources of contamination to weak lensing three-point statistics: constraints from N-body simulations

We investigate the impact of the observed correlation between a galaxy's shape and its surrounding density field on the measurement of third-order weak lensing shear statistics. Using numerical simulations, we estimate the systematic error contribution to a measurement of the third-order moment of the aperture mass statistic (GGG) from three-point intrinsic ellipticity correlations (III), and the three-point coupling between the weak lensing shear experienced by distant galaxies and the shape of foreground galaxies (GGI and GII). We find that third-order weak lensing statistics are typically more strongly contaminated by these physical systematics compared to second-order shear measurements, contaminating the measured three-point signal for moderately deep surveys with a median redshift   z _m∼ 0.7  by ∼15 per cent. It has been shown that accurate photometric redshifts will be crucial to correct for this effect, once a model and the redshift dependence of the effect can be accurately constrained. To this end we provide redshift-dependent fitting functions to our results and propose a new tool for the observational study of intrinsic galaxy alignments. For a shallow survey with   z _m∼ 0.4  we find III to be an order of magnitude larger than the expected cosmological GGG shear signal. Compared to the two-point intrinsic ellipticity correlation which is similar in amplitude to the two-point shear signal at these survey depths, third-order statistics therefore offer a promising new way to constrain models of intrinsic galaxy alignments. Early shallow data from the next generation of very wide weak lensing surveys will be optimal for this type of study.     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

The local environment of H ii galaxies

We have carried out an investigation of the environments of low redshift H  ii galaxies by cross-correlating their positions on the sky with those of faint field galaxies in the Automatic Plate Measuring Machine (APM) catalogues. We address the question of whether violent star formation in H  ii galaxies is induced by low-mass companions by statistically estimating the mean space density of galaxies around them. We argue that even if low-mass companions were mainly intergalactic H  i clouds, their optical counterparts should be detectable at faint limits of the APM scans.
A significantly positive signal is detected for the H  ii galaxy–APM galaxy angular cross-correlation function, but the amplitude is poorly determined. The projected cross-correlation function has a higher signal-to-noise ratio, and suggests that the amplitude is slightly lower than for normal field galaxies. This implies that these bursting dwarf galaxies inhabit slightly lower density environments than those of normal field galaxies, consistent with other studies of emission-line galaxies. This suggests that in these dwarf starburst galaxies, star formation is not always triggered by tidal interactions, and a significant fraction must have a different origin.     

Hubble Space Telescope Wide Field Planetary Camera 2 observations of hyperluminous infrared galaxies

We present Hubble Space Telescope Wide Field Planetary Camera 2 I -band imaging for a sample of nine hyperluminous infrared galaxies (HLIRGs) spanning a redshift range     . Three of the sample have morphologies showing evidence for interactions and six are quasi-stellar objects (QSOs). Host galaxies in the QSOs are detected reliably out to     . The detected QSO host galaxies have an elliptical morphology with scalelengths spanning     and absolute k -corrected magnitudes spanning     There is no clear correlation between the infrared (IR) power source and the optical morphology. None of the sources in the sample, including F15307+3252, shows any evidence for gravitational lensing. We infer that the IR luminosities are thus real. Based on these results, and previous studies of HLIRGs, we conclude that this class of object is broadly consistent with being a simple extrapolation of the ULIRG population to higher luminosities; ULIRGs being mainly violently interacting systems powered by starbursts and/or active galactic nuclei. Only a small number of sources, the infrared luminosities of which exceed 10¹³ L_⊙, are intrinsically less luminous objects that have been boosted by gravitational lensing.     

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.     

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.     

Constraints on the clustering, biasing and redshift distribution of radio sources

We discuss how different theoretical predictions for the variance σ ² of the counts-in-cells distribution of radio sources can be matched to measurements from the FIRST survey at different flux limits. The predictions are given by the integration of models for the angular correlation function w ( θ ) for three different functional forms of the redshift distribution N ( z ), different spatial correlation functions that match the observed present-day shape and by different evolutions of the bias b ( z ) with redshift. We also consider the two cases of open and flat universes. Although the predicted w ( θ ) show substantial differences because of differences in the values of N ( z ), these differences are not significant compared to the uncertainties in the current observations. It turns out that, independent of the geometry of the universe and the flux limit, the best fit is provided by models with constant biasing at all times, although the difference between models with epoch-independent bias and models with bias that evolves linearly with redshift is not very large. All models with strong evolution of bias with epoch are ruled out, as they grossly overestimate the amplitude of the variance over the whole range of angular scales sampled by the counts-in-cells analysis. As a further step we directly calculated w _obs( θ ) at 3 mJy from the catalogue and matched it with our models for the angular correlation function, in the hypothesis that the clustering signal comes from two different populations, namely AGN-powered sources and starbursting galaxies. The results are consistent with a scenario for hierarchical clustering where the fainter starbursting galaxies trace the mass at all epochs, while the brighter AGNs are strongly biased, with b ( z ) evolving linearly with redshift, as suggested by some theories of galaxy formation and evolution.