arXiv subjects

Matthias Bartelmann

Publications and source records attributed to Matthias Bartelmann.

At least 145 records · Page 8Linked to original sources

arXiv2003

The impact of cluster mergers on arc statistics

We study the impact of merger events on the strong lensing properties of galaxy clusters. Previous lensing simulations were not able to resolve dynamical time scales of cluster lenses, which arise on time scales which are of order a Gyr. In this case study, we first describe qualitatively with an analytic model how some of the lensing properties of clusters are expected to change during merging events. We then analyse a numerically simulated lens model for the variation in its efficiency for producing both tangential and radial arcs while a massive substructure falls onto the main cluster body. We find that: (1) during the merger, the shape of the critical lines and caustics changes substantially; (2) the lensing cross sections for long and thin arcs can grow by one order of magnitude and reach their maxima when the extent of the critical curves is largest; (3) the cross section for radial arcs also grows, but the cluster can efficiently produce this kind of arcs only while the merging substructure crosses the main cluster centre; (4) while the arc cross sections pass through their maxima as the merger proceeds, the cluster's X-ray emission increases by a factor of $\sim5$. Thus, we conclude that accounting for these dynamical processes is very important for arc statistics studies. In particular, they may provide a possible explanation for the arc statistics problem.

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arXiv2003

Numerical study of halo concentrations in dark-energy cosmologies

We study the concentration parameters, their mass dependence and redshift evolution, of dark-matter halos in different dark-energy cosmologies with constant and time-variable equation of state, and compare them with "standard'' Lambda-CDM and OCDM models. We find that previously proposed algorithms for predicting halo concentrations can be well adapted to dark-energy models. When centred on the analytically expected values, halo concentrations show a log-normal distribution with a uniform standard deviation of ~0.2. The dependence of averaged halo concentrations on mass and redshift permits a simple fit of the form (1+z) c=c0 (M/M0)^a, with a~-0.1 throughout. We find that the cluster concentration depends on the dark energy equation of state at the cluster formation redshift z_{coll} through the linear growth factor D_+(z_{coll}). As a simple correction accounting for dark-energy cosmologies, we propose scaling c0 from Lambda-CDM with the ratio of linear growth factors, c0 -> c0 D_+(z_{coll})/D_{+,Lambda-CDM}(z_{coll}).

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arXiv2003

cD galaxy contribution to the strong lensing cross sections of galaxy clusters

We perform ray-tracing simulations evaluating the effect of a cD galaxy on the strong lensing properties of five galaxy cluster halos obtained from N-body simulations. The cD galaxy is modelled using both axially symmetric and elliptical models and assuming several masses for its dark matter halo. The effect of the cD orientation with respect to the mass distribution of the host galaxy cluster is also investigated. The simulations are carried out in an open and a flat model universe with cosmological constant. We find that the enhancement of the cluster lensing cross sections for long and thin arcs due to the presence of a massive cD at the cluster centre is typically less than 100%, depending on the model used for the cD galaxy and its orientation. The impact of the cD on the cluster efficiency for producing radially magnified images is larger only for those clusters whose lensing cross section for radial arcs is very small in absence of the central galaxy. We conclude that the presence of a cD galaxy at the cluster centre can only moderately influence the cluster efficiency for strong lensing and in particular fails to explain the discrepancy between the observed number of giant arcs in galaxy clusters and their abundance predicted from lensing simulations in the currently most favoured $Λ$CDM model.

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arXiv2003

Arc Statistics in Cosmological Models with Dark Energy

We investigate how the probability of the formation of giant arcs in galaxy clusters is expected to change in cosmological models dominated by dark energy with an equation of state p=w rho c^2 compared to cosmological-constant or open models. To do so, we use a simple analytic model for arc cross sections based on the Navarro-Frenk-White density profile which we demonstrate reproduces essential features of numerically determined arc cross sections. Since analytic lens models are known to be inadequate for accurate absolute quantifications of arc probabilities, we use them only for studying changes relative to cosmological-constant models. Our main results are (1) the order of magnitude difference between the arc probabilities in low density, spatially flat and open CDM models found numerically is reproduced by our analytic model, and (2) dark-energy cosmologies with w>-1 increase the arc optical depth by at most a factor of two and are thus unlikely to reconcile arc statistics with spatially flat cosmological models with low matter density.

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arXiv2003

Arc statistics with realistic cluster models

Arc statistics is known to be a powerful cosmological tool. Numerical lensing simulations show that orders of magnitude differences in the number of {\em giant} arcs on the whole sky are expected in different cosmological models. In this paper, we discuss the analytic and numerical methods in arc statistics and show that analytic models fail to reproduce the efficiency for strong lensing of more realistic numerical cluster models. Then, we discuss two recent extensions of the lensing simulations, i.e. the effects of cD galaxies in the lensing clusters and the impact of cluster mergers on arc statistics. We show that cD galaxies can increase the lensing cross sections for long and thin arcs by perhaps up to $\sim50%$, while major mergers can change the cluster efficiency for producing such arcs by up to one order of magnitude.

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arXiv2003

Numerical Methods in Gravitational Lensing

Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or distortion; (2) propagating light rays through large cosmological simulations; and (3) reconstructing mass distributions from their tidal field. This lecture describes methods for solving such problems. Emphasis is put on using adaptive-grid methods for finding images, issues of spatial resolution and reliability of statistics for weak lensing by large-scale structures, and methodical questions related to shear-inversion techniques.

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arXiv2002

Cluster cross sections for strong lensing: analytic and numerical lens models

The statistics of gravitationally lensed arcs was recognised earlier as a potentially powerful cosmological probe. However, while fully numerical models find orders of magnitude difference between the arc probabilities in different cosmological models, analytic models tend to find markedly different results. We introduce in this paper an analytic cluster lens model which improves upon existing analytic models in four ways. (1) We use the more realistic Navarro-Frenk-White profile instead of singular isothermal spheres, (2) we include the effect of cosmology on the compactness of the lenses, (3) we use elliptical instead of axially symmetric lenses, and (4) we take the intrinsic ellipticity of sources into account. While these improvements to the analytic model lead to a pronounced increase of the arc probability, comparisons with numerical models of the same virial mass demonstrate that the analytic models still fall short by a substantial margin of reproducing the results obtained with numerical models. Using multipole expansions of cluster mass distributions, we show that the remaining discrepancy can be attributed to substructure inside clusters and tidal fields contributed by the cluster surroundings, effects that cannot reasonably and reliably be mimicked in analytic models.

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arXiv2002

Probing Intracluster Magnetic Fields with Cosmic Microwave Background Polarization

Intracluster magnetic fields with $ \sim μG $ strength induce Faraday rotation on the cosmic microwave background (CMB) polarization. Measurements of this effect can potentially probe the detailed structure of intracluster magnetic fields across clusters, since the CMB polarization is a continuously varying field on the sky, in contrast to the conventional method restricted by the limited number of radio sources behind or inside a cluster. We here construct a method for extracting information on magnetic fields from measurements of the effect, combined with possible observations of the Sunyaev-Zel'dovich effect and X-ray emission for the same cluster which are needed to reconstruct the electron density fields. Employing the high-resolution magneto-hydrodynamic simulations performed by Dolag, Bartelmann & Lesch (1999) as a realistic model of magnetized intracluster gas distribution, we demonstrate how our reconstruction technique can well reproduce the magnetic fields, i.e., the spherically average radial profiles of the field strength and the coherence length.

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arXiv2002

Stacking Clusters in the ROSAT All-Sky Survey

Ongoing and planned wide-area surveys at optical and infrared wavelengths should detect a few times 10^5 galaxy clusters, roughly 10% of which are expected to be at redshifts >~ 0.8. We investigate what can be learned about the X-ray emission of these clusters from the ROSAT All-Sky Survey. While individual clusters at redshifts >~ 0.5 contribute at most a few photons to the survey, a significant measurement of the mean flux of cluster subsamples can be obtained by stacking cluster fields. We show that the mean X-ray luminosity of clusters with mass M >~ 2 x 10^{14} M_sun/h selected from the Sloan Digital Sky Survey should be measurable out to redshift unity with signal-to-noise >~ 10, even if clusters are binned with Delta z=0.1 and Delta ln M ~ 0.3. For such bins, suitably chosen hardness ratio allows the mean temperature of clusters to be determined out to z ~ 0.7 with a relative accuracy of Delta T/T <~ 0.15 for M > 10^{14} M_sun/h.

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arXiv2002

Measuring Omega_0 with higher-order Quasar-Galaxy Correlations induced by Weak Lensing

Via the magnification bias, gravitational lensing by large-scale structures causes angular cross-correlations between distant quasars and foreground galaxies on angular scales of arc minutes and above. We investigate the three-point cross-correlation between quasars and galaxy pairs measurable via the second moment of the galaxy counts around quasars and show that it reaches the level of a few per cent on angular scales near one arc minute. Combining two- and three-point correlations, a skewness parameter can be defined which is shown to be virtually independent on the shape and normalisation of the dark-matter power spectrum. If the galaxy bias is linear and deterministic, the skewness depends on the cosmic matter density parameter Omega_0 only; otherwise, it can be used to probe the linearity and stochasticity of the bias. We finally estimate the signal-to-noise ratio of a skewness determination and find that around twenty thousand distant quasars e.g. from the Sloan Digital Sky Survey should suffice for a direct measurement of Omega_0.

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arXiv2002

Strong and weak lensing by galaxy clusters

I present an overview of strong and weak gravitational lensing by galaxy clusters. After briefly introducing the principles of gravitational lensing, I discuss the main lessons learned from lensing on the mass distribution in clusters and their relation to cosmology.

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arXiv2002

Halo Concentrations and Weak-Lensing Number Counts in Dark Energy Cosmologies

We study the effects of a dark energy component with equation of state p=w rho with constant w >= -1 on the formation of Cold Dark Matter (CDM) haloes. We find two main effects: first, haloes form earlier as w increases, and second, the amplitude of the dark-matter power spectrum gets reduced in order to remain compatible with the large scale Cosmic Microwave Background (CMB) anisotropies. These effects counteract. Using recipes derived from numerical simulations, we show that haloes are expected to be up to ~ 50% more concentrated in CDM models with quintessence compared to Lambda-CDM models, the maximum increase being reached for w ~ -0.6. For larger w, the amplitude of the power spectrum decreases rapidly and makes expected halo concentrations drop. Halo detections through weak gravitational lensing are highly sensitive to halo concentrations. We show that weak-lensing halo counts with the aperture-mass technique can increase by a factor of ~ 2 as w is increased from -1 to -0.6, offering a new method for constraining the nature of dark energy.

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arXiv2002

Predicting the clustering properties of galaxy clusters detectable for the Planck satellite

We study the clustering properties of the galaxy clusters detectable for the Planck satellite due to their thermal Sunyaev-Zel'dovich effect. We take the past light-cone effect and the redshift evolution of both the underlying dark matter correlation function and the cluster bias factor into account. A theoretical mass-temperature relation allows us to convert the sensitivity limit of a catalogue into a minimum mass for the dark matter haloes hosting the clusters. We confirm that the correlation length is an increasing function of the sensitivity limits defining the survey. Using the expected characteristics of the Planck cluster catalogue, which will be a quite large and unbiased sample, we predict the two-point correlation function and power spectrum for different cosmological models. We show that the wide redshift distribution of the Planck survey, will allow to constrain the cluster clustering properties up to z=1. The dependence of our results on the main cosmological parameters (the matter density parameter, the cosmological constant and the normalisation of the density power-spectrum) is extensively discussed. We find that the future Planck clustering data place only mild constraints on the cosmological parameters, because the results depend on the physical characteristics of the intracluster medium, like the baryon fraction and the mass-temperature relation. Once the cosmological model and the Hubble constant are determined, the clustering data will allow a determination of the baryon fraction with an accuracy of few per cent.

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arXiv2002

Cosmological Information from Quasar-Galaxy Correlations induced by Weak Lensing

The magnification bias of large-scale structures, combined with galaxy biasing, leads to a cross-correlation of distant quasars with foreground galaxies on angular scales of the order of arc minutes and larger. The amplitude and angular shape of the cross-correlation function w_QG contain information on cosmological parameters and the galaxy bias factor. While the existence of this cross-correlation has firmly been established, existing data did not allow an accurate measurement of w_QG yet, but wide area surveys like the Sloan Digital Sky Survey now provide an ideal database for measuring it. However, w_QG depends on several cosmological parameters and the galaxy bias factor. We study in detail the sensitivity of w_QG to these parameters and develop a strategy for using the data. We show that the parameter space can be reduced to the bias factor b, Omega_0 and sigma_8, and compute the accuracy with which these parameters can be deduced from SDSS data. Under reasonable assumptions, it should be possible to reach relative accuracies of the order of 5%-15% for b, Omega_0, and sigma_8. This method is complementary to other weak-lensing analyses based on cosmic shear.

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arXiv2002

Evolution and structure of magnetic fields in simulated galaxy clusters

We use cosmological magneto-hydrodynamic simulations to study the evolution of magnetic fields in galaxy clusters in two different cosmological models, a standard-CDM and a $Λ$-CDM model. We show that the magnetic field strength profiles closely follow the cluster density profiles outside a core region of radius $\sim200\kpc$. The magnetic field has a correlation length of order $50\kpc$ and reverses on scales of $\sim100\kpc$ along typical lines-of-sight. The power spectrum of the magnetic field can well be approximated by a steep power law with an exponent of $\sim-2.7$. The mean magnetic field in the cluster cores grows roughly exponentially with decreasing redshift, $B\sim10^{-2.5z} \muG$. Merger events have a pronounced effect on magnetic field evolution, which is strongly reflected in measurable quantities like the Faraday rotation. The field evolution in the two different cosmologies proceeds virtually identically. All our cluster models very well reproduce observed Faraday rotation measurements when starting with nG seed fields.

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arXiv2001

Cluster detection from surface-brightness fluctuations in SDSS data

Galaxy clusters can be detected as surface brightness enhancements in smoothed optical surveys. This method does not require individual galaxies to be identifiable, and enables clusters to be detected out to surprisingly high redshifts, as recently demonstrated by the Las Campanas Distant Cluster Survey (LCDCS). Here, we investigate redshift limits for cluster detection in the Sloan Digital Sky Survey (SDSS). Calibrating assumptions about the surface brightness profile, the mass-to-light ratio, and the spectral energy distribution of galaxy clusters using available observational data, we show that it should be possible to detect galaxy groups out to redshifts of ~0.5, and massive galaxy clusters out to redshifts of ~1.2 in summed r'+i'+z' SDSS data. Redshift estimates can be derived from the SDSS magnitudes of brightest cluster members out to redshifts near unity. Over the area of sky it covers, SDSS should find >~98% of the clusters detectable by the Planck satellite through the thermal Sunyaev-Zel'dovich effect. The few Planck clusters not detected in SDSS will almost all be at z>~1.2.

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arXiv2001

The Evolution of Magnetic Fields in Galaxy Clusters

Cosmological simulations of magnetic fields in galaxy clusters show that remarkable agreement between simulations and observations of Faraday rotation and radio haloes can be achieved assuming that seed fields of 10^{-9} G were present at redshifts 15-20. The structure of the seed field is irrelevant for the final intracluster field. On average, the field grows exponentially with decreasing cluster redshift, but merger events cause steep transient increases in the field strength. Typical field-reversal scales are of order 50 kpc/h. In most cases, the intracluster fields are dynamically unimportant. Assuming secondary electron models, the average structure of cluster radio haloes can naturally be reproduced.

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arXiv2001

Constraining cosmological models using arc statistics in future SZ cluster surveys

Upcoming wide-area surveys in the submillimetre regime will allow the construction of complete galaxy cluster samples through their thermal Sunyaev-Zel'dovich effect. We propose an analytic method to predict the number of gravitationally lensed giant arcs produced by the cluster sample expected to be detectable for the Planck satellite. The statistics of lensed arcs can be used to constrain cosmological parameters. This computation implies the choice of an analytic cluster model which has to reproduce the lensing properties of realistic galaxy clusters. Comparing the results of analytic computations and numerical ray-tracing simulations, we show that spherical models with the Navarro-Frenk-White density profile fail by far to produce as many giant arcs as realistic galaxy clusters. This confirms the great importance of asymmetries and substructures in the lensing matter distribution. By elliptically distorting the lensing potential of spherical NFW density profiles, we show that the discrepancy between analytic and numerical computations can almost completely be removed.

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