1,328 research outputs found
Weak lensing goes bananas: What flexion really measures
In weak gravitational lensing, the image distortion caused by shear measures
the projected tidal gravitational field of the deflecting mass distribution. To
lowest order, the shear is proportional to the mean image ellipticity. If the
image sizes are not small compared to the scale over which the shear varies,
higher-order distortions occur, called flexion. For ordinary weak lensing, the
observable quantity is not the shear, but the reduced shear, owing to the
mass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather,
higher-order image distortions measure the reduced flexion, i.e., derivatives
of the reduced shear. We derive the corresponding lens equation in terms of the
reduced flexion and calculate the resulting relation between brightness moments
of source and image. Assuming an isotropic distribution of source orientations,
estimates for the reduced shear and flexion are obtained; these are then tested
with simulations. In particular, the presence of flexion affects the
determination of the reduced shear. The results of these simulations yield the
amount of bias of the estimators, as a function of the shear and flexion. We
point out and quantify a fundamental limitation of the flexion formalism, in
terms of the product of reduced flexion and source size. If this product
increases above the derived threshold, multiple images of the source are formed
locally, and the formalism breaks down. Finally, we show how a general
(reduced) flexion field can be decomposed into its four components: two of them
are due to a shear field, carrying an E- and B-mode in general. The other two
components do not correspond to a shear field; they can also be split up into
corresponding E- and B-modes.Comment: 17 pages, 6 figures, submitted to A&
Weak lensing from space: first cosmological constraints from three-point shear statistics
We use weak lensing data from the Hubble Space Telescope COSMOS survey to
measure the second- and third-moments of the cosmic shear field, estimated from
about 450,000 galaxies with average redshift ~ 1.3. We measure two- and
three-point shear statistics using a tree-code, dividing the signal in E, B and
mixed components. We present a detection of the third-order moment of the
aperture mass statistic and verify that the measurement is robust against
systematic errors caused by point spread function (PSF) residuals and by the
intrinsic alignments between galaxies. The amplitude of the measured
three-point cosmic shear signal is in very good agreement with the predictions
for a WMAP7 best-fit model, whereas the amplitudes of potential systematics are
consistent with zero. We make use of three sets of large Lambda CDM simulations
to test the accuracy of the cosmological predictions and to estimate the
influence of the cosmology-dependent covariance. We perform a likelihood
analysis using the measurement and find that the Omega_m-sigma_8 degeneracy
direction is well fitted by the relation: sigma_8
(Omega_m/0.30)^(0.49)=0.78+0.11/-0.26. We present the first measurement of a
more generalised three-point shear statistic and find a very good agreement
with the WMAP7 best-fit cosmology. The cosmological interpretation of this
measurement gives sigma_8 (Omega_m/0.30)^(0.46)=0.69 +0.08/-0.14. Furthermore,
the combined likelihood analysis of this measurement with the measurement of
the second order moment of the aperture mass improves the accuracy of the
cosmological constraints, showing the high potential of this combination of
measurements to infer cosmological constraints.Comment: 17 pages, 11 figures. MNRAS submitte
Ellipticity and circularity measuring via Kullback-Leibler divergence
Using the Kullback-Leibler divergence we provide a simple statistical measure which uses only the covariance matrix of a given set to verify whether the set is an ellipsoid. Similar measure is provided for verification of circles and balls. The new measure is easily computable, intuitive, and can be applied to higher dimensional data. Experiments have been performed to illustrate that the new measure behaves in natural way
Mass-sheet degeneracy: Fundamental limit on the cluster mass reconstruction from statistical (weak) lensing
Weak gravitational lensing is considered to be one of the most powerful tools
to study the mass and the mass distribution of galaxy clusters. However, weak
lensing mass reconstructions are plagued by the so-called mass-sheet
degeneracy--the surface mass density \kappa of the cluster can be determined
only up to a degeneracy transformation \kappa \to \kappa' = \lambda \kappa + (1
-\lambda), where \lambda is an arbitrary constant. This transformation
fundamentally limits the accuracy of cluster mass determinations if no further
assumptions are made. We describe here a method to break the mass-sheet
degeneracy in weak lensing mass maps using distortion and redshift information
of background galaxies and illustrate this by two simple toy models. Compared
to other techniques proposed in the past, it does not rely on any assumptions
on cluster potential; it can be easily applied to non-parametric
mass-reconstructions and no assumptions on boundary conditions have to be made.
In addition it does not make use of weakly constrained information (such as the
source number counts, used in the magnification effect). Our simulations show
that we are effectively able to break the mass-sheet degeneracy for
supercritical lenses, but that for undercritical lenses the mass-sheet
degeneracy is very difficult to be broken, even under idealised conditions.Comment: Accepted for publication in A&
Intrinsic alignment-lensing interference as a contaminant of cosmic shear
Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ∼10% at zs=1 and ∼30% at zs=0.5. We conclude that, depending on the intrinsic-alignment model, the GI correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift
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