Showing papers by "Matthias Bartelmann published in 2005"

Detection of Cosmic Magnification with the Sloan Digital Sky Survey

Abstract: We present an 8 σ detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large-scale structure. To make this measurement we used 3800 deg2 of photometric observations from the Sloan Digital Sky Survey (SDSS) containing ~200,000 quasars and 13 million galaxies. Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence, and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing. We show that observational uncertainties (stellar contamination, Galactic dust extinction, seeing variations, and errors in the photometric redshifts) are well controlled and do not significantly affect the lensing signal. By weighting the quasars with the number count slope, we combine the cross-correlation of quasars for our full magnitude range and detect the lensing signal at >4 σ in all five SDSS filters. Our measurements of cosmic magnification probe scales ranging from 60 h-1 kpc to 10 h-1 Mpc and are in good agreement with theoretical predictions based on the WMAP concordance cosmology. As with galaxy-galaxy lensing, future measurements of cosmic magnification will provide useful constraints on the galaxy-mass power spectrum.

The impact of gas physics on strong cluster lensing

Abstract: Previous studies of strong gravitational lensing by galaxy clusters have neglected the potential impact of the intracluster gas. Here, we compare simulations of strong cluster lensing including gas physics at increasing levels of complexity, i.e. with adiabatic, cooling, star-forming, feedback-receiving, and thermally conducting gas, along with different implementations of the artificial viscosity in the SPH simulations. Each cluster was simulated starting from the same initial conditions so as to allow direct comparison of the simulated clusters. We compare the clusters’ shapes, dynamics, and density profiles and then study their strong-lensing cross sections computed by means of ray-tracing simulations. With the common viscosity implementation, adiabatic gas has little effect on strong cluster lensing, while lower viscosity allows stronger turbulence, thus higher non-thermal pressure and a generally broader gas distribution, which tends to lower lensing cross sections. Conversely, cooling and star formation steepen the core density profiles and can thus increase the strong-lensing efficiency considerably.

An optimal filter for the detection of galaxy clusters through weak lensing

Abstract: We construct a linear filter optimised for detecting dark-matter halos in weak-lensing data. The filter assumes a mean radial profile of the halo hear pattern and modifies that shape by the noise power spectrum. Aiming at separating dark-matter halos from spurious peaks caused by large-scale structure lensing, we model the noise as being composed of weak lensing by large-scale structures and Poisson noise from random galaxy positions and intrinsic ellipticities. Optimal filtering against the noise requires the optimal filter scale to be smaller than typical halo sies. Although a perfect separation of halos from spurious large-scale structure peaks is strictly impossible, we use numerical simulations to demonstrate that our filter produces substantially more sensitive, reliable and stable results than the conventionally used aperture-mass statistic.

A simulation pipeline for the Planck mission

Abstract: We describe an assembly of numerical tools to model the output data of the Planck satellite. These start with the generation of a CMB sky in a chosen cosmology, add in various foreground sources, convolve the sky signal with arbitrary, even non-symmetric and polarised beam patterns, derive the time ordered data streams measured by the detectors depending on the chosen satellite-scanning strategy, and include noise signals for the individual detectors and electronic systems. The simulation products are needed to develop, verify, optimise, and characterise the accuracy and performance of all data processing and scientific analysis steps of the Planck mission, including data handling, data integrity checking, calibration, map making, physical component separation, and power spectrum estimation. In addition, the simulations allow detailed studies of the impact of many stochastic and systematic effects on the scientific results. The efficient implementation of the simulation allows the build-up of extended statistics of signal variances and co-variances. Although being developed specifically for the Planck mission, it is expected that the employed framework as well as most of the simulation tools will be of use for other experiments and CMB-related science in general.

Mass Distributions of HST Galaxy Clusters from Gravitational Arcs

Abstract: Although N-body simulations of cosmic structure formation suggest that dark matter halos have density profiles shallower than isothermal at small radii and steeper at large radii, whether observed galaxy clusters follow this profile is still ambiguous. We use one such density profile, the asymmetric NFW profile, to model the mass distributions of 11 galaxy clusters with gravitational arcs observed by HST. We characterize the galaxy lenses in each cluster as NFW ellipsoids, each defined by an unknown scale convergence, scale radius, ellipticity, and position angle. For a given set of values of these parameters, we compute the arcs that would be produced by such a lens system. To define the goodness of fit to the observed arc system, we define a chi^2 function encompassing the overlap between the observed and reproduced arcs as well as the agreement between the predicted arc sources and the observational constraints on the source system. We minimize this chi^2 to find the values of the lens parameters that best reproduce the observed arc system in a given cluster. Here we report our best-fit lens parameters and corresponding mass estimates for each of the 11 lensing clusters. We find that cluster mass models based on lensing galaxies defined as NFW ellipsoids can accurately reproduce the observed arcs, and that the best-fit parameters to such a model fall within the reasonable ranges defined by simulations. These results assert NFW profiles as an effective model for the mass distributions of observed clusters.

The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples

Abstract: We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples The observed sample consists of 10 X-ray-selected clusters at redshifts zc ~ 02 imaged with HST by Smith et al The simulated data set is produced by lensing the Hubble Deep Field, which serves as a background source image, with 150 realizations (different projections and shifts) of five simulated zc = 02 clusters from a ΛCDM N-body simulation The real and simulated clusters have similar masses, the real photometric redshift is used for each background source, and all the observational effects influencing arc detection in the real data set, including light from cluster galaxies, are simulated in the artificial data set We develop, and apply to both data sets, an objective automatic arc-finding algorithm We find consistent arc statistics in the real and in the simulated sample, with an average of ~1 detected giant (length-to-width ratio l/w ≥ 10) arc per cluster and ~02 giant luminous (RST < 223 mag) arcs per cluster Thus, taking into account a realistic source population and observational effects, the clusters predicted by ΛCDM have the same arc production efficiency as the observed clusters If, as suggested by other studies, there is a discrepancy between the predicted and the observed total number of arcs on the sky, it must be the result of differences between the redshift-dependent cluster mass functions and not due to differences in the lensing efficiency of the most massive clusters

Strong lensing efficiency of galaxy clusters in dark energy cosmologies

Abstract: We study the efficiency for producing strong gravitational lensing events of galaxy clusters numerically simulated in different dark-energy cosmologies with constant and time-variable equation of state, and we compare the results with those obtained in standard ACDM and OCDM models. Our main results are (1) that the expected abundance of gravitational arcs with large length-to-width ratio depends on the equation of state of dark energy at the epoch of formation of the halo; and (2) that the high sensitivity of strong-lensing cross sections of galaxy clusters to dynamical processes like mergers, which was found in earlier studies, varies substantially between different cosmologies, being stronger for models in which halos are less concentrated. As expected, the largest differences in the lensing optical depth occur at intermediate and high redshift.

Combining weak and strong lensing in cluster potential reconstruction

Abstract: We propose a method for recovering the two-dimensional gravitational potential of galaxy clusters which combines data from weak and strong gravitational lensing. A first estimate of the potential from weak lensing is improved at the approximate locations of critical curves. The method can be fully linearised and does not rely on the existence and identification of multiple images. We use simulations to show that it recovers the surface-mass density profiles and distributions very accurately, even if critical curves are only partially known and if their location is realistically uncertain. We further describe how arcs at different redshifts can be combined, and how deviations from weak lensing can be included.

Constraints on dark energy models from galaxy clusters with multiple arcs

Abstract: We make an exploratory study of how well dark energy models can be constrained using lensed arcs at different redshifts behind cluster lenses. Arcs trace the critical curves of clusters, and the growth of critical curves with source redshift is sensitive to the dark energy equation of state. Using analytical models and numerically simulated clusters, we explore the key factors involved in using cluster arcs as a probe of dark energy. We quantify the sensitivity to lens mass, concentration and ellipticity with analytical models that include the effects of dark energy on halo structure. We show with simple examples how degeneracies between mass models and cosmography may be broken using arcs at multiple redshifts or additional constraints on the lens density profile. However, we conclude that the requirements on the data are so stringent that it is very unlikely that robust constraints can be obtained from individual clusters. We argue that surveys of clusters, analysed in conjunction with numerical simulations, are a more promising prospect for arc cosmography. We use such numerically simulated clusters to estimate how large a sample of clusters/arcs could provide interesting constraints on dark energy models. We focus on the scatter produced by differences in the mass distribution of individual clusters. We find from our sample of simulated clusters that at least 1000 pairs of arcs are needed to obtain constraints if the mass distribution of individual clusters is taken to be undetermined. We discuss several unsolved problems that need study to develop this method fully for precision studies with future surveys.

Gravitational lensing of the CMB by galaxy clusters

Abstract: We adapt a non-linear filter proposed by Hu (2001) for detecting lensing of the CMB by large-scale structures to recover surface-density profiles of galaxy clusters from their localised, weak gravitational lensing effect on CMB fields. Shifting the band-pass of the filter to smaller scales, and normalising it such as to reproduce the convergence rather than the deflection angle, we find that the mean density profile of a sample of 100 clusters can be recovered to better than 10% from well within the scale radius to almost the virial radius. The kinetic Sunyaev-Zel'dovich effect is shown to be a negligible source of error. We test the filter applying it to data simulated using the characteristics of the Atacama Cosmology Telescope (ACT), showing that it will be possible to recover mean cluster profiles outside a radius of 1 � corresponding to ACT's angular resolution.

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

Abstract: 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 generalised Limber-equation to yield the angular power spectra. While gravitomagnetic corrections to the weak lensing spectrum are negligible at observationally accessible scales, the angular power spectrum of the iSW-effect should be detectable as a correction to the CMB spectrum up to multipoles of l \~ 100 with the PLANCK-satellite.

Statistical distribution of gravitational-lensing excursion angles: winding ways to us from the deep Universe

Abstract: We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a key role in estimates of lensing effects on angular clustering of objects (such as galaxies, quasi-stellar objects and also the cosmic microwave background temperature map), is known to consist of two components: a Gaussian core and an exponential tail. We use numerical gravitational-lensing experiments in a ACDM cosmology for quantifying these two components. We especially focus on the physical processes responsible for generating these two components. We develop a simple empirical model for the exponential tail which allows us to explore its origin. We find that the tail is generated by the coherent lensing scatter by massive haloes with M > 10 14 h -1 M ○. at z < 1 and that its exponential shape arises due to the exponential cut-off of the halo mass function at that mass range. On scales larger than 1 arcmin, the tail does not have a practical influence on the lensing effects on the angular clustering. Our model predicts that the coherent scatter may have non-negligible effects on angular clustering at subarcminute scales.

Detection of Cosmic Magnification with the Sloan Digital Sky Survey

Abstract: We present an 8 sigma detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large scale structure. To make this measurement we used 3800 square degrees of photometric observations from the Sloan Digital Sky Survey (SDSS) containing \~200,000 quasars and 13 million galaxies. Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing. We show that observational uncertainties (stellar contamination, Galactic dust extinction, seeing variations and errors in the photometric redshifts) are well controlled and do not significantly affect the lensing signal. By weighting the quasars with the number count slope, we combine the cross-correlation of quasars for our full magnitude range and detect the lensing signal at >4 sigma in all five SDSS filters. Our measurements of cosmic magnification probe scales ranging from 60 kpc/h to 10 Mpc/h and are in good agreement with theoretical predictions based on the WMAP concordance cosmology. As with galaxy-galaxy lensing, future measurements of cosmic magnification will provide useful constraints on the galaxy-mass power spectrum.

Non-linear Structure Formation in Cosmologies with Early Dark Energy

Abstract: We argue that a few per cent of "Early Dark Energy" can be detected by the statistics of nonlinear structures. The presence of Dark Energy during linear structure formation is natural in models where the present tiny Dark-Energy density is related to the age of the Universe rather than a new fundamental small parameter. Generalisation of the spherical collapse model shows that the linear collapse parameter delta_c is lowered. The corresponding relative enhancement of weak gravitational lensing on arc-minute scales lowers the value of sigma_8 inferred from a given lensing amplitude as compared to Lambda-CDM. In presence of Early Dark Energy, structures grow slower, such that for given sigma_8 the number of galaxies and galaxy clusters is substantially increased at moderate and high redshift. For realistic models, the number of clusters detectable through their thermal Sunyaev-Zel'dovich effect at redshift unity and above, e.g. with the Planck satellite, can be an order of magnitude larger than for Lambda-CDM.

The effects of ellipticity and substructure on estimates of cluster density profiles based on lensing and kinematics

Abstract: We address the question of how well the density profile of galaxy clusters can be determined by combining strong lensing and velocity dispersion data. We use cosmological dark matter simulations of clusters to test the reliability of the method, producing mock catalogues of tangential and radial gravitational arcs and simulating the radial velocity dispersion profile of the cluster brightest central galaxy. The density profiles of the simulated clusters closely follow the NFW form, but we find that the recovered values of the inner slope are systematically underestimated, by about 0.4 in the mean, if the lens is assumed to be axially symmetric. However, if the ellipticity and orientation of the iso-contours of the cluster lensing potential are taken into account, then the inner slopes can be recovered quite accurately for a significant subset of the clusters whose central surface density profiles appear the most regular. These have lensing potentials with ellipticities in the range 0.15-0.4. Further simulations projecting one cluster along many random lines-of-sight show that, even for lower ellipticities, the central slopes are underestimated by $\sim 10-35%$. These simulations closely mimic past observations (see e.g. Sand et al., 2004), suggesting that existing estimates of the central slopes may be biased towards low values. For the remaining clusters, where the lensing potential is strongly perturbed by active merging or by substructure, the correct determination of the inner slope requires a more accurate model for the lens. When the halo profile is modelled by a generalised NFW profile, we find that the inferred scale radius and characteristic density, unlike the inner slope, are generally poorly constrained, since there is a strong degeneracy between these two parameters.

The impact of gas physics on strong cluster lensing

Abstract: Previous studies of strong gravitational lensing by galaxy clusters neglected the potential impact of the intracluster gas. Here, we compare simulations of strong cluster lensing including gas physics at increasing levels of complexity, i.e. with adiabatic, cooling, star-forming, feedback-receiving, and thermally conducting gas, and with different implementations of the artificial viscosity in the SPH simulations. Each cluster was simulated starting from the same initial conditions such as to allow directly comparing the simulated clusters. We compare the clusters' shapes, dynamics and density profiles and study their strong-lensing cross sections computed by means of ray-tracing simulations. We find that the impact of adiabatic gas depends on the amount of turbulence that builds up, which means that the artificial viscosity plays an important role. With the common viscosity implementation, adiabatic gas has little effect on strong cluster lensing, while lower viscosity allows stronger turbulence, thus higher non-thermal pressure and a generally broader gas distribution which tends to lower lensing cross sections. Conversely, cooling and star formation steepen the core density profiles and can thus increase the strong-lensing efficiency considerably.

Three-dimensional reconstruction of the intra-cluster medium

Abstract: We propose and test a new method based on Richardson-Lucy deconvolution to reconstruct three-dimensional gas density and temperature distributions in galaxy clusters from combined X-ray and thermal Sunyaev-Zel'dovich observations. Clusters are assumed to be axially symmetric and arbitrarily inclined with respect to the line-of-sight. No equilibrium assumption other than local thermal equilibrium is needed. We test the algorithm with synthetic observations of analytically modeled and numerically simulated galaxy clusters and discuss the quality of the density and temperature reconstructions in idealised situations and in presence of observational noise, deviations from axial symmetry and cluster substructure. We find that analytic and numerical gas density and temperature distributions can be accurately reconstructed in three dimensions, even if observational noise is present. We also discuss methods for determining the inclination angle from data and show that it can be constrained using X-ray temperature maps. For a realistic cluster and including observational noise the three-dimensional reconstructions reach a level of accuracy of about 15%.

A fast method for computing strong-lensing cross sections: Application to merging clusters

Abstract: Strong gravitational lensing by irregular mass distributions, such as galaxy clusters, is generally not well quantified by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for accurate cross-section calculations. We describe a fast, semi-analytic method here which is based on surface integrals over high-magnification regions in the lens plane and demonstrate that it yields reliable cross sections even for complex, asymmetric mass distributions. The method is faster than ray-tracing simulations by factors of $\sim30$ and thus suitable for large cosmological simulations, saving large amounts of computing time. We apply this method to a sample of galaxy cluster-sized dark matter haloes with simulated merger trees and show that cluster mergers approximately double the strong-lensing optical depth for lens redshifts $z_\mathrm{l}\gtrsim0.5$ and sources near $z_\mathrm{s} = 2$. We believe that this result hints at one possibility for understanding the recently detected high arcs abundance in clusters at moderate and high redshifts, and is thus worth further studies.