857 research outputs found

### 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

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