arXiv subjects

Matthias Bartelmann

Publications and source records attributed to Matthias Bartelmann.

At least 109 records · Page 6Linked to original sources

arXiv2011

Shear-flexion cross-talk in weak-lensing measurements

Gravitational flexion, caused by derivatives of the gravitational tidal field, is potentially important for the analysis of the dark-matter distribution in gravitational lenses, such as galaxy clusters or the dark-matter haloes of galaxies. Flexion estimates rely on measurements of galaxy-shape distortions with spin-1 and spin-3 symmetry. We show in this paper that and how such distortions are generally caused not only by the flexion itself, but also by coupling terms of the form (shear $\times$ flexion), which have hitherto been neglected. Similar coupling terms occur between intrinsic galaxy ellipticities and the flexion. We show, by means of numerical tests, that neglecting these terms can introduce biases of up to 85% on the $F$ flexion and 150% on the $G$ flexion for galaxies with an intrinsic ellipticity dispersion of $σ_ε=0.3$. In general, this bias depends on the strength of the lensing fields, the ellipticity dispersion, and the concentration of the lensed galaxies. We derive a new set of equations relating the measured spin-1 and spin-3 distortions to the lensing fields up to first order in the shear, the flexion, the product of shear and flexion, and the morphological properties of the galaxy sample. We show that this new description is accurate with a bias $\leq 7%$ (spin-1 distortion) and $\leq 3%$ (spin-3 distortion) even close to points where the flexion approach breaks down due to merging of multiple images. We propose an explanation why a spin-3 signal could not be measured yet and comment on the difficulties in using a model-fitting approach to measure the flexion signal.

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arXiv2011

Lensed arc statistics: comparison of Millennium-simulation galaxy clusters to Hubble Space Telescope observations of an X-ray selected sample

It has been debated for a decade whether there is a large overabundance of strongly lensed arcs in galaxy clusters, compared to expectations from LambdaCDM cosmology. We perform ray tracing through the most massive halos of the Millennium simulation at several redshifts in their evolution, using the Hubble Ultra Deep Field as a source image, to produce realistic simulated lensed images. We compare the lensed arc statistics measured from the simulations to those of a sample of 45 X-ray selected clusters, observed with the Hubble Space Telescope, that we have analysed in Horesh et al. (2010). The observations and the simulations are matched in cluster masses, redshifts, observational effects, and the algorithmic arc detection and selection. At z=0.6 there are too few massive-enough clusters in the Millennium volume for a proper statistical comparison with the observations. At redshifts 0.3<z<0.5, however, we have large numbers of simulated and observed clusters, and the latter are an unbiased selection from a complete sample. For these redshifts, we find excellent agreement between the observed and simulated arc statistics, in terms of the mean number of arcs per cluster, the distribution of number of arcs per cluster, and the angular separation distribution. At z ~ 0.2 some conflict remains, with real clusters being ~3 times more efficient arc producers than their simulated counterparts. This may arise due to selection biases in the observed subsample at this redshift, to some mismatch in masses between the observed and simulated clusters, or to physical effects that arise at low redshift and enhance the lensing efficiency, but which are not represented by the simulations.

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arXiv2011

Calibration biases in measurements of weak lensing

As recently shown by Viola et al., the common (KSB) method for measuring weak gravitational shear creates a non-linear relation between the measured and the true shear of objects. We investigate here what effect such a non-linear calibration relation may have on cosmological parameter estimates from weak lensing if a simpler, linear calibration relation is assumed. We show that the non-linear relation introduces a bias in the shear-correlation amplitude and thus a bias in the cosmological parameters Omega_matter and sigma_8. Its direction and magnitude depends on whether the point-spread function is narrow or wide compared to the galaxy images from which the shear is measured. Substantial over- or underestimates of the cosmological parameters are equally possible, depending also on the variant of the KSB method. Our results show that for trustable cosmological-parameter estimates from measurements of weak lensing, one must verify that the method employed is free from ellipticity-dependent biases or monitor that the calibration relation inferred from simulations is applicable to the survey at hand.

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arXiv2010

Gravitational Lensing

Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.

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arXiv2010

Triaxial collapse and virialisation of dark-matter haloes

We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass and virialisation redshift. While the hybrid model for the external shear gives results very similar to those obtained from the non-linear model, ellipsoidal collapse changes the collapse parameters typically by (20...50)%, in a way increasing with decreasing halo mass and decreasing virialisation redshift. We qualitatively confirm the dependence on mass and virialisation redshift of a fitting formula for delta_c, but find noticeable quantitative differences in particular at low mass and high redshift. The derived mass function is in good agreement with mass functions recently proposed in the literature.

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arXiv2010

Halo model description of the non-linear dark matter power spectrum at $k \gg 1$ Mpc$^{-1}$

Accurate knowledge of the non-linear dark-matter power spectrum is important for understanding the large-scale structure of the Universe, the statistics of dark-matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark-matter power spectrum and its cross-power spectrum with dark-matter haloes. Our model extends the halo-model formalism, including realistic substructure population within individual dark-matter haloes and the scatter of the concentration parameter at fixed halo mass. We consider three prescriptions for the mass-concentration relation and two for the substructure distribution in dark-matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales, and is crucial for proper modeling the cosmological weak-lensing signal due to low-mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from n-body simulations.

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arXiv2010

The lensing efficiencies of MACS X-ray selected versus RCS optically selected galaxy clusters

The statistics of strongly lensed arcs in samples of galaxy clusters provide information on cluster structure that is complementary to that from individual clusters. However, samples of clusters that have been analyzed to date have been either small, heterogeneous, or observed with limited angular resolution. We measure the lensed-arc statistics of 97 clusters imaged at high angular resolution with the Hubble Space Telescope, identifying lensed arcs using two automated arc detection algorithms. The sample includes similar numbers of X-ray selected (MACS) and optically selected (RCS) clusters, and spans cluster redshifts in the range 0.2 < z < 1. We compile a catalogue of 42 arcs in the X-ray selected subsample and 7 arcs in the optical subsample. All but five of these arcs are reported here for the first time. At 0.3 < z < 0.7, the X-ray selected clusters have a significantly higher mean frequency of arcs, 1.2+/-0.2 per cluster, versus 0.2+/-0.1 in the optical sample. The strikingly different lensing efficiencies indicate that X-ray clusters trace much larger mass concentrations, despite the similar optical luminosities of the X-ray and optical clusters. The mass difference is supported also by the lower space density of the X-ray clusters, and by the small Einstein radii of the few arcs in the optical sample. Higher-order effects, such as differences in concentration or substructure, may also contribute.

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arXiv2010

Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.

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arXiv2009

The Dark Universe

For a few years now, cosmology has a standard model. By this term, we mean a consistent theoretical background which is at the same time simple and broad enough to offer coherent explanations for the vast majority of cosmological phenomena. This review will briefly summarise the cosmological model, then proceed to discuss what we know from observations about the evolution of the Universe and its contents, and what we conclude about the origin and the future of the Universe and the structures it contains.

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arXiv2009

Lensed CMB temperature and polarization maps from the Millennium Simulation

We have constructed the first all-sky 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 map-making procedure (Carbone et al. 2008) 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 (Lewis 2005) 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 polarised 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.

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arXiv2009

Statistics of gravitational potential perturbations: A novel approach to deriving the X-ray temperature function

Context. While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities. Aims. We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential. Methods. We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation. Results. Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses. Conclusions. TThis first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.

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arXiv2009

Impact of early dark energy on the Planck SZ cluster sample

Context. One science goal of the upcoming Planck mission is to perform a full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than LCDM. One class of these models are early dark energy (EDE) cosmologies, where the dark energy contribution does not vanish at early times. Aims. Since structures grow slower in the presence of EDE, one expects an increase in the number of galaxy clusters compared to LCDM at intermediate and high redshifts, which could explain the reported excess of the angular CMB power spectrum on cluster scales via an enhanced SZ contribution. We study the impact of EDE on Planck's expected cluster sample. Methods. To obtain realistic simulations, we constructed full-sky SZ maps for EDE and LCDM cosmologies, taking angular cluster correlation into account. Using these maps, we simulated Planck observations with and without Galactic foregrounds and fed the results into our filter pipeline based on the spherical multi-frequency matched filters. Results. For the case of EDE cosmologies, we clearly find an increase in the detected number of clusters compared to the fiducial LCDM case. This shows that the spherical multi-frequency matched filter is sensitive enough to find deviations from the LCDM sample, being caused by EDE. In addition we find an interesting effect of EDE on the completeness of the cluster sample, such that EDE helps to obtain cleaner samples.

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arXiv2008

Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.

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arXiv2008

Full-sky maps for gravitational lensing of the CMB

We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the deflection angle, aiming at gravitational lensing of the CMB, with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray-tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to $z\sim 11$, producing continuous all-sky maps with arcminute angular resolution. A randomization scheme avoids repetition of structures along the line of sight and structures larger than the MS box size are added to supply the missing contribution of large-scale (LS) structures to the lensing signal. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree quite well with semi-analytic estimates on scales down to a few arcminutes, while we find a slight excess of power on small scales, which we interpret as being due to non-linear clustering in the MS. Our map-making procedure, combined with the LS adding technique, is ideally suited for studying lensing of CMB anisotropies, for analyzing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees-Sciama effect.

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arXiv2008

Comparisons between isothermal and NFW mass profiles for strong-lensing galaxy clusters

While both isothermal and NFW-based mass models for galaxy clusters are widely adopted in strong-lensing studies, they cannot easily be distinguished based solely on observed positions of arcs and arclets. We compare the magnifications predicted for giant arcs obtained from isothermal and NFW profiles, taking axially-symmetric and asymmetric mass distributions into account. We find that arc magnifications can differ strongly between the two types of density profiles even if the image morphology is well reproduced. Magnifications by lenses with NFW density profiles are usually larger than those for lenses with singular or nearly singular isothermal density profiles, unless the latter have large cores. Asymmetries play an important role. We illustrate our results with the two well-studied clusters MS 2137 and A~370. We confirm earlier results showing that both isothermal and NFW mass models can very well reproduce the observed arcs, radial arcs and other arclets. While the mass model for MS 2137 is not very well constrained, the two types of mass models produce strongly differing critical curves and caustics for A~370. We find that the NFW mass profile is preferred for A~370. We identify new arclet candidates in the field of A~370. Redshift estimates allowed by the lens model are consistent with results in the literature, where available. Three newly found counter-images are suggested to arise from an active, dust-enshrouded star-forming galaxy at $z\approx1.1$.

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arXiv2008

Model-independent determination of the cosmic expansion rate. I. Application to type-Ia supernovae

Aims: In view of the substantial uncertainties regarding the possible dynamics of the dark energy, we aim at constraining the expansion rate of the universe without reference to a specific Friedmann model and its parameters. Methods: We show that cosmological observables integrating over the cosmic expansion rate can be converted into a Volterra integral equation which is known to have a unique solution in terms of a Neumann series. Expanding observables such as the luminosity distances to type-Ia supernovae into a series of orthonormal functions, the integral equation can be solved and the cosmic expansion rate recovered within the limits allowed by the accuracy of the data. Results: We demonstrate the performance of the method applying it to synthetic data sets of increasing complexity, and to the first-year SNLS data. In particular, we show that the method is capable of reproducing a hypothetical expansion function containing a sudden transition.

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arXiv2007

Realistic simulations of gravitational lensing by galaxy clusters: extracting arc parameters from mock DUNE images

We present a newly developed code that allows simulations of optical observations of galaxy fields with a variety of instruments. The code incorporates gravitational lensing effects and is targetted at simulating lensing by galaxy clusters. Our goal is to create the tools required for comparing theoretical expectations with observations to obtain a better understanding of how observational noise affects lensing applications such as mass estimates, studies on the internal properties of galaxy clusters and arc statistics. Starting from a set of input parameters, characterizing both the instruments and the observational conditions, the simulator provides a virtual observation of a patch of the sky. It includes several sources of noise such as photon-noise, sky background, seeing, and instrumental noise. Ray-tracing through simulated mass distributions accounts for gravitational lensing. Source morphologies are realistically simulated based on shapelet decompositions of galaxy images retrieved from the GOODS-ACS archive. According to their morphological class, spectral-energy-distributions are assigned to the source galaxies in order to reproduce observations of each galaxy in arbitrary photometric bands. We illustrate our techniques showing virtual observations of a galaxy-cluster core as it would be observed with the space telescope DUNE, which was recently proposed to ESA within its "Cosmic vision" programme. (Abridged)

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arXiv2007

Testing the reliability of weak lensing cluster detections

We study the reliability of dark-matter halo detections with three different linear filters applied to weak-lensing data. We use ray-tracing in the multiple lens-plane approximation through a large cosmological simulation to construct realizations of cosmic lensing by large-scale structures between redshifts zero and two. We apply the filters mentioned above to detect peaks in the weak-lensing signal and compare them with the true population of dark matter halos present in the simulation. We confirm the stability and performance of a filter optimized for suppressing the contamination by large-scale structure. It allows the reliable detection of dark-matter halos with masses above a few times 1e13 M_sun/h with a fraction of spurious detections below ~10%. For sources at redshift two, 50% of the halos more massive than ~7e13 M_sun/h are detected, and completeness is reached at ~2e14 M_sun/h.

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