Combining weak and strong lensing in cluster potential reconstruction

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.Comment: 9 pages, 5 figures, A&A in press, changes to match the accepted versio

Do arcs require flat halo cusps?

It was recently claimed that several galaxy clusters containing radial and tangential gravitational arcs and having a measured velocity-dispersion profile for the brightest cluster galaxy had to have central density profiles considerably flatter than those found in CDM cluster simulations. Using a simple analytic mass model, we confirm this result_for axially symmetric_ mass distributions, but show that steep density profiles are well in agreement with the cluster requiring the flattest axially symmetric profile once even small deviations from axial symmetry are introduced.Comment: submitted to A&

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.Comment: 5 pages, 3 figures, submitted to A&

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.Comment: 11 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Smoothing Algorithms and High-order Singularities in Gravitational Lensing

We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter'' interpretation of the discrete density field in the Smoothed Particle Hydrodynamics. We use Monte Carlo simulations of uniform density fields and one isothermal ellipsoid to empirically derive the noise properties, and best smoothing parameters (such as the number of nearest neighbors used). A cluster from high-resolution simulations is then used to assess the reality of high-order singularities such as swallowtails and butterflies in caustics, which are important for the interpretation of substructures in gravitational lenses. We also compare our method with the Delaunay tesselation field estimator using the galaxy studied by Bradac et al. (2004), and find good agreements. We show that higher order singularities are not only connected with bound subhaloes but also with the satellite streams. However, the presence of high-order singularities are sensitive to not only the fluctuation amplitude of the surface density, but also the detailed form of the underlying smooth lensing potential (such as ellipticity and external shear).Comment: ApJ, Accepted,(Released November 1st). The high resolution figures are availabel at http://202.127.29.4/mppg/english/data

Semi-Analytical Models for Lensing by Dark Halos: I. Splitting Angles

We use the semi-analytical approach to analyze gravitational lensing of quasars by dark halos in various cold dark matter (CDM) cosmologies, in order to determine the sensitivity of the prediction probabilities of images separations to the input assumptions regarding halos and cosmologies. The mass function of dark halos is assumed to be given by the Press-Schechter function. The mass density profile of dark halos is alternatively taken to be the singular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) profile, or the generalized NFW profile. The cosmologies include: the Einstein-de Sitter model (SCDM), the open model (OCDM), and the flat \Lambda-model (LCDM). As expected, we find that the lensing probability is extremely sensitive to the mass density profile of dark halos, and somewhat less so to the mean mass density in the universe, and the amplitude of primordial fluctuations. NFW halos are very much less effective in producing multiple images than SIS halos. However, none of these models can completely explain the current observations: the SIS models predict too many large splitting lenses, while the NFW models predict too few small splitting lenses. This indicates that there must be at least two populations of halos in the universe. A combination of SIS and NFW halos can reasonably reproduce the current observations if we choose the mass for the transition from SIS to NFW to be ~ 10^{13} solar masses. Additionally, there is a tendency for CDM models to have too much power on small scales, i.e. too much mass concentration; and it appears that the cures proposed for other apparent difficulties of CDM would help here as well, an example being the warm dark matter (WDM) variant which is shown to produce large splitting lenses fewer than the corresponding CDM model by one order of magnitude.Comment: 46 pages, including 13 figures. Revised version with significant improvemen

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.Comment: 9 pages, 9 figures, submitted to A&

Biases in, and corrections to, KSB shear measurements

We analyse the KSB method to estimate gravitational shear from surface-brightness moments of small and noisy galaxy images. We identify three potentially problematic assumptions. These are: (1) While gravitational shear must be estimated from averaged galaxy images, KSB derives a shear estimate from each individual image and then takes the average. Since the two operations do not commute, KSB gives biased results. (2) KSB implicitly assumes that galaxy ellipticities are small, while weak gravitational lensing assures only that the change in ellipticity due to the shear is small. (3) KSB does not invert the convolution with the point-spread function, but gives an approximate PSF correction which - even for a circular PSF - holds only in the limit of circular sources. The effects of assumptions (2) and (3) partially counter-act in a way dependent on the width of the weight function and of the PSF. We quantitatively demonstrate the biases due to all assumptions, extend the KSB approach consistently to third order in the shear and ellipticity and show that this extension lowers the biases substantially. The issue of proper PSF deconvolution will be addressed in a forthcoming paper.Comment: 12 pages, 10 figures, MNRAS submitte