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Matthias Bartelmann

Publications and source records attributed to Matthias Bartelmann.

At least 181 records · Page 10Linked to original sources
arXiv1997

Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SN Ia). When corrected with the light-curve shape (LCS), the peak magnitude of SN Ia provides a standard candle with an uncertainty in apparent magnitude of $Δm\simeq 0.1-0.2$. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared to that expected from its LCS and redshift. The average detection rate for SN Ia with a significant mismatch of $\ge2Δm$ behind a cluster at $z\simeq0.05-0.15$ is about $1-2$ supernovae per cluster per year at $J,I,R\lesssim25-26$. Since SNe are point-like sources for a limited period, they can experience significant microlensing by MACHOs in the intracluster medium. Microlensing events caused by MACHOs of $\sim10^{-4} M_\odot$ are expected to have time scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow to separate them. Microlensing events due to MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ($z\lesssim0.05$) per year is $\sim 0.02 (f/0.01)$, where $f$ is the fraction of the cluster mass in MACHOs of masses $10^{-7} < M_{macho}/M_\odot < 10^{-4}$.

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arXiv1997

Lectures on Gravitational Lensing

These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to astrophysical problems are discussed.

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arXiv1997

On Arcs and Omega

The gravitational lens effect of galaxy clusters can produce large arcs from source galaxies in their background. Typical source redshifts of ~ 1 require clusters at z ~ 0.3 for arcs to form efficiently. Given the cluster abundance at the present epoch, the fewer clusters exist at z ~ 0.3 the higher Omega_0 is, because the formation epoch of galaxy clusters strongly depends on Omega_0. In addition, at fixed Omega_0, clusters are less concentrated, and hence less efficient lenses, when the cosmological constant is positive, Omega_Lambda > 0. Numerical cluster simulations show that the expected number of arcs on the sky is indeed a sensitive function of Omega_0 and Omega_Lambda. The numerical results are compatible with the statistics of observed arcs only in a universe with low matter density, Omega_0 ~ 0.3, and zero cosmological constant. Other models fail by one or two orders of magnitude, rendering arc statistics a sensitive probe for cosmological parameters.

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arXiv1997

Arc statistics with realistic cluster potentials. IV. Clusters in different cosmologies

We use numerical simulations of galaxy clusters in different cosmologies to study their ability to form large arcs. The cosmological models are: Standard CDM (SCDM; Omega_0=1, Omega_Lambda=0); tauCDM with reduced small-scale power (parameters as SCDM, but with a smaller shape parameter of the power spectrum); open CDM (OCDM; Omega_0=0.3, Omega_Lambda=0); and spatially flat, low-density CDM (LambdaCDM; Omega_0=0.3, Omega_Lambda=0.7). All models are normalised to the local number density of rich clusters. Simulating gravitational lensing by these clusters, we compute optical depths for the formation of large arcs. For large arcs with length-to-width ratio >= 10, the optical depth is largest for OCDM. Relative to OCDM, the optical depth is lower by about an order of magnitude for LambdaCDM, and by about two orders of magnitude for S/tauCDM. These differences originate from the different epochs of cluster formation across the cosmological models, and from the non-linearity of the strong lensing effect. We conclude that only the OCDM model can reproduce the observed arc abundance well, while the other models fail to do so by orders of magnitude.

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arXiv1997

QSO-galaxy correlations due to weak lensing in arbitrary Friedmann-Lemaitre cosmologies

We calculate the angular cross-correlation function between background QSOs and foreground galaxies induced by the weak lensing effect of large-scale structures. Results are given for arbitrary Friedmann-Lemaitre cosmologies. The non-linear growth of density perturbations is included. Compared to the linear growth, the non-linear growth increases the correlation amplitude by about an order of magnitude in an Einstein-de Sitter universe, and by even more for lower Omega_0. The dependence of the correlation amplitude on the cosmological parameters strongly depends on the normalization of the power spectrum. The QSO-galaxy cross-correlation function is most sensitive to density structures on scales in the range (1-10) Mpc/h, where the normalization of the power spectrum to the observed cluster abundance appears most appropriate. In that case, the correlation strength changes by less than a factor of <~ 2 when Omega_0 varies between 0.3 and 1, quite independent of the value of Omega_Lambda. For Omega_0 <~ 0.3, the correlation strength increases with decreasing Omega_0, and it scales approximately linearly with the Hubble constant h.

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arXiv1997

Resolving the line-of-sight structure of galaxy clusters by combining X-ray and lensing data

The projected gravitational potential of galaxy clusters is reflected in both their X-ray emission and their imprint on the images of background sources due to their gravitational lensing effects. Since these projections of the potential are weighted differently along the line-of-sight, we propose a method to combine them and remove the degeneracy between two cases: (i) a cluster consisting of a single potential well, or (ii) an apparent cluster composed of several potential wells projected onto each other. We demonstrate with simulated data of potential models that this method indeed allows to significantly distinguish multiple from single clusters. The confidence limit for this distinction depends on the mass ratio between the clusters. It ranges from ~ 15 sigma for mass ratio 1:1 to ~ 4 sigma for mass ratio 1:6. Furthermore, the method reconstructs the correct cluster mass, the correct mass ratio of the two clusters, and the correct scale radii with typical fractional accuracies of a few percent at 3 sigma confidence. As an aside, our method allows to accurately determine gas fractions in clusters, also with 3 sigma fractional accuracies of order a few percent. We argue that our method provides an alternative to the commonly used beta-fit technique, and yields more reliable results in a broader range of cases.

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arXiv1997

Effects of Dust on Gravitational Lensing by Spiral Galaxies

Gravitational lensing of an optical QSO by a spiral galaxy is often counteracted by dust obscuration, since the line-of-sight to the QSO passes close to the center of the galactic disk. The dust in the lens is likely to be correlated with neutral hydrogen, which in turn should leave a Lyman-alpha absorption signature on the QSO spectrum. We use the estimated dust-to-gas ratio of the Milky-Way galaxy as a mean and allow a spread in its values to calculate the effects of dust on lensing by low redshift spiral galaxies. Using a no-evolution model for spirals at z<1 we find (in Lambda=0 cosmologies) that the magnification bias due to lensing is stronger than dust obscuration for QSO samples with a magnitude limit B<16. The density parameter of neutral hydrogen, Omega_HI, is overestimated in such samples and is underestimated for fainter QSOs.

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arXiv1996

Aperture Multipole Moments from Weak Gravitational Lensing

The projected mass of a gravitational lens inside (circular) apertures can be derived from the measured shear inside an annulus which is caused by the tidal field of the deflecting mass distribution. Here we show that also the multipoles of the two-dimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the shear, which allow large flexibility in the choice of a radial weight function. In contrast to determining multipole moments from weak-lensing mass reconstructions, this approach allows to quantify the signal-to-noise ratio of the multipole moments directly from the observed galaxy ellipticities, and thus to estimate the significance of the multipole detection. Radial weight functions can therefore be chosen such as to optimize the significance of the detection given an assumed radial mass profile. Application of our formulae to numerically simulated clusters demonstrates that the quadrupole moment of realistic cluster models can be detected with high signal-to-noise ratio S/N; in about 85 per cent of the simulated cluster fields S/N >~ 3. We also show that the shear inside a circular annulus determines multipole moments inside and outside the annulus. This is relevant for clusters whose central region is too bright to allow the observation of the shear of background galaxies, or which extend beyond the CCD. We also generalize the aperture mass equation to the case of `radial' weight functions which are constant on arbitrarily-shaped curves which are not necessarily self-similar.

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arXiv1996

A Comparison of X-ray and Strong Lensing Properties of Simulated X-ray Clusters

We use gas-dynamical simulations of galaxy clusters to compare their X-ray and strong lensing properties. Special emphasis is laid on mass estimates. The cluster masses range between 6 x 10^14 solar masses and 4 x 10^15 solar masses, and they are examined at redshifts between 1 and 0. We compute the X-ray emission of the intracluster gas by thermal bremsstrahlung, add background contamination, and mimic imaging and spectral observations with current X-ray telescopes. Although the beta model routinely provides excellent fits to the X-ray emission profiles, the derived masses are typically biased low because of the restricted range of radii within which the fit can be done. For beta values of ~ 2/3, which is the average in our numerically simulated sample, the mass is typically underestimated by ~ 40 per cent. The masses of clusters which exhibit pronounced substructure are often substantially underestimated. We suggest that the ratio between peak temperature and emission-weighted average cluster temperature may provide a good indicator for ongoing merging and, therefore, for unreliable mass estimates. X-ray mass estimates are substantially improved if we fit a King density profile rather than the beta model to the X-ray emission, thereby dropping the degree of freedom associated with beta. Clusters selected for their strong lensing properties are typically dynamically more active than typical clusters. Bulk flows in the intracluster gas contain a larger than average fraction of the internal energy of the gas in such objects, hence the measured gas temperatures are biased low. The bulk of the optical depth for arc formation is contributed by clusters with intermediate rather than high X-ray luminosity. Arcs occur predominantly in clusters which exhibit substructure and are not in an equilibrium state. Finally we explain why the

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arXiv1996

Arcs from a Universal Dark-Matter Halo Profile

Navarro, Frenk, \& White have recently found numerically that the density profile of dark-matter halos can be described by a universal two-parameter function over a broad range of halo masses. The profile is singular, approaching the halo center with $ρ\propto r^{-1}$. It had been argued previously that radially distorted, gravitationally lensed images of background sources in galaxy clusters, so-called radial arcs, required a flat core in the cluster density profile. Such radial arcs have so far been detected in two galaxy clusters, in apparent contradiction with a singular density profile. I show here that the profile suggested by Navarro et al. can produce radial arcs despite its central singularity, and describe how the two parameters of the profile can be determined in clusters where radial and tangential arcs are observed. I then apply this analysis to the two clusters where radial arcs were detected. In both cases, the redshifts of the radial arcs are yet unknown, hence definitive conclusions on the profile parameters cannot yet be drawn. Numerically determined values for the parameters of cluster-sized halos can, however, be used to predict the range of the unknown arc redshifts, thus providing a direct observational test for the proposed density profile. A potential difficulty with the profile is that the radial magnification of tangential arcs is large, hence tangential arcs should be thick or their sources should be very thin in the radial direction.

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arXiv1996

Reanalysis of the association of high-redshift 1-Jansky quasars with IRAS galaxies

We develop a new statistical method to reanalyse angular correlations between background QSOs and foreground galaxies that are supposed to be a consequence of dark matter inhomogeneities acting as weak gravitational lenses. The method is based on a weighted average over the galaxy positions and is optimized to distinguish between a random distribution of galaxies around QSOs and a distribution which follows an assumed QSO-galaxy two-point correlation function, by choosing an appropriate weight function. With simulations we demonstrate that this weighted average is slightly more significant than Spearman's rank-order test which was used in previous investigations. In particular, the advantages of the weighted average show up if the two-point correlation function is weak. We then reanalyze the correlation between high-redshift 1-Jansky QSOs and IRAS galaxies, taken from the IRAS Faint Source Catalog; these samples were analyzed previously using Spearman's rank-order test. In agreement with the previous work, we find moderate to strong correlations between these two samples; considering the angular two-point correlation function of these samples, we find a typical scale of order $5'$ from which most of the correlation signal derives. However, the statistical significance of the correlation changes with the redshift slices of the QSO sample one considers. Comparing with simple theoretical estimates of the expected correlation, we find that the signal we derive is considerably stronger than expected. On the other hand, recent direct verifications of the overdensity of matter in the line-of-sight to high-redshift radio QSOs obtained from the shear field around these sources, indicates that the observed association can be attributed to a gravitational lens effect.

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arXiv1996

Maximum-Likelihood Cluster Recontruction

We present a novel method to recontruct the mass distribution of galaxy clusters from their gravitational lens effect on background galaxies. The method is based on a least-chisquare fit of the two-dimensional gravitational cluster potential. The method combines information from shear and magnification by the cluster lens and is designed to easily incorporate possible additional information. We describe the technique and demonstrate its feasibility with simulated data. Both the cluster morphology and the total cluster mass are well reproduced.

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arXiv1995

GRAVITATIONAL LENSING OF QUASARS BY THEIR DAMPED LYMAN-ALPHA ABSORBERS

Damped Lyman-alpha absorbers are believed to be associated with galactic disks. We show that gravitational lensing can therefore affect the statistics of these systems. First, the magnification bias due to lensing raises faint QSOs above a given magnitude threshold and thereby enhances the probability for observing damped absorption systems. Second, the bending of light rays from the source effectively limits the minimum impact parameter of the line-of-sight relative to the center of the absorber, thus providing an upper cut-off to the observed neutral hydrogen (HI) column density. The combination of these effects yields a pronounced peak in the observed abundance of absorbers with high column densities (>2*10^{21} cm^{-2}) and low redshifts (z<1). The inferred value of the cosmological density parameter of neutral hydrogen, Omega_{HI}, increases with increasing redshift and luminosity of the sources even if the true HI density remains constant. This trend resembles the observed evolution of Omega_{HI}(z). Damped Lyman-alpha absorbers with column densities >10^{21} cm^{-2} and redshifts 0.5<z<1 are reliable flags for lensed QSOs with a close pair of images separated by 0.3 arcsec. Detection of these gravitational lensing signatures with the Hubble Space Telescope can be used to constrain the depth of the absorber potential-wells and the cosmological constant.

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arXiv1995

The lens parallax method: determining redshifts of faint blue galaxies through gravitational lensing

We propose a new technique, which we call the lens parallax method, to determine simultaneously the redshift distribution of the faint blue galaxies and the mass distributions of foreground clusters of galaxies. The method is based on gravitational lensing and makes use of the following: (1) the amplitude of lensing-induced distortions of background galaxies increases with redshift; (2) the surface brightnesses of galaxies decrease steeply with redshift. The distortions of galaxy images due to lensing are thus expected to be inversely correlated with surface brightness, allowing us to obtain relative distances to galaxies as a function of surface brightness. If the redshifts of the brightest galaxies are measured, then the relative distance scale can be converted to mean galaxy redshifts as a function of surface brightness. Further, by comparing the angular sizes of lensed galaxies with those of similar galaxies in empty control fields, it is possible to break the so-called mass sheet degeneracy inherent to cluster mass reconstruction techniques which are based purely on image ellipticities. This allows an unambiguous determination of the surface density of a lensing cluster. We describe an iterative algorithm based on these ideas and present numerical simulations which show that the proposed techniques are feasible with a sample of ~ 10 rich clusters at moderate redshifts ~ 0.3-0.4 and an equal number of control fields. The numerical tests show that the method can be used to determine the redshifts of galaxies with an accuracy of dz ~ 0.1-0.2 at z ~ 1-1.7, and to measure the masses of lensing clusters to about 5% accuracy.

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arXiv1994

Cluster mass estimates from weak lensing

The reliability of cluster lens reconstruction techniques based on weak lensing is studied in terms of the accuracy of their reproduction of the total cluster mass as a function of distance from the cluster center. To do so, a variety of reconstruction algorithms is applied to synthetic lensing data created using a sample of 60 numerically modeled clusters, and the mass reconstruction is compared to the known deflector mass. The results can be summarized as follows: (1) Reconstruction algorithms which require integrations extending over the entire real plane yield unreliable results, because they give rise to boundary effects which are hard to control; mass overestimates are more likely and more substantial in this case than underestimates. (2) Reconstruction techniques which avoid these boundary effects yield reliable lower bounds to the cluster mass. The tightness of such bounds depends on the size of the field, which can be extended synthetically to improve the results considerably. For the sample of numerical cluster models, the best lower bounds, achieved by combining synthetic field extension with non-linear, finite-field reconstruction, decline from 100% to 80% of the true cluster mass going from the cluster center to an angular distance of 2.5'. The 80% error bars of the lower mass bounds are +/- 10% to 15%.

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arXiv1994

The lens parallax method: determining the redshifts of the faint blue galaxies through gravitational lensing

We propose a new technique, which we call the lens parallax method, to determine simultaneously the redshift distribution of the faint blue galaxies and the mass distribution of foreground clusters of galaxies. The method is based on gravitational lensing and uses the fact that the mean angular size of the faint blue galaxies is a well-determined function of surface brightness. The method requires first a calibration of the angular-size vs. surface brightness relation in unlensed blank fields and a determination of the mean redshift of the brightest of the faint blue galaxies. By combining this information with observations of the distorted images of background galaxies in the fields of foreground clusters, we show that it is possible to obtain the mean redshift of the galaxies as a function of their surface brightness. With a sample of about ten moderate redshift rich clusters and using ten bins in surface brightness, a bin-to-bin signal-to-noise ratio of $\sim3.5$ can be achieved. The method simultaneously allows a determination of the convergence and shear of the lensing cluster as a function of position, and through this the mass distribution of the lens can be obtained. The lens parallax method can be used in conjunction with, and will improve the accuracy of, other previously proposed techniques for mapping clusters.

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arXiv1994

Arc Statistics with Realistic Cluster Potentials. III. a Systematic Effect on Cluster Mass Estimates

It is shown in this paper that deviations of galaxy cluster lenses from spherical symmetry can render mass estimates for galaxy clusters based on the formation of large arcs systematically to high. Numerical models show that the mass needed for producing large arcs in clusters can be notably smaller than expected from simple spherically symmetric lens models. The reason is that the enhanced tidal effect in asymmetric and substructured lenses can compensate for part of the convergence necessary for strong lensing effects. An analytic argument is given to explain why deviations from radial symmetry will in general decrease the required lens mass. Mass estimates assuming radially symmetric lenses are on average too high by a factor of $\simeq1.6$, and with a probability of $\simeq20\%$ by a factor of $\simeq2$.

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