Marco Lombardi

B1422+231: The influence of mass substructure on strong lensing

In this work we investigate the gravitationally lensed system B1422+231. High-quality VLBI image positions, fluxes and shapes as well as an optical HST lens galaxy position are used. First, two simple and smooth models for the lens galaxy are applied to t observed image positions and fluxes; no even remotely acceptable model was found. Such models also do not accurately reproduce the image shapes. In order to t the data successfully, mass substructure has to be added to the lens, and its level is estimated. To explore expectations about the level of substructure in galaxies and its influence on strong lensing, N-body simulation results of a model galaxy are employed. By using the mass distribution of this model galaxy as a lens, synthetic data sets of dierent four image system congurations are generated and simple lens models are again applied to t them. The diculties in tting these lens systems turn out to be similar to the case of some real gravitationally lensed systems, thus possibly providing evidence for the presence and strong influence of substructure in the primary lens galaxy.

Strong and weak lensing united I: the combined strong and weak lensing cluster mass reconstruction method

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, the mass-sheet degeneracy transformation has limited its success. We present a novel method for a cluster mass reconstruction which combines weak and strong lensing information on common scales and can, as a consequence, break the mass-sheet degeneracy. We extend the weak lensing formalism to the inner parts of the cluster and combine it with the constraints from multiple image systems. We demonstrate the feasibility of the method with simulations, finding an excellent agreement between the input and reconstructed mass also on scales within and beyond the Einstein radius. Using a single multiple image system and photometric redshift information of the background sources used for weak and strong lensing analysis, we find that we are effectively able to break the mass-sheet degeneracy, therefore removing one of the main limitations on cluster mass estimates. We conclude that with high resolution (e.g. HST) imaging data the method can more accurately reconstruct cluster masses and their profiles than currently existing lensing techniques.

The signature of substructure on gravitational lensing in the Lambda CDM cosmological model

We present a study of the lens properties of quadruply imaged systems, lensed by numerically simulated galaxies. We investigate a simulated elliptical and disc galaxy drawn from high resolution simulations of galaxy formation in a concor- dance ΛCDM universe. The simulations include the effects of gas dynamics, star formation and feedback processes. Flux-ratio anomalies observed in strong gravitational lensing potentially provide an indicator for the presence of mass substructure in lens galaxies as predicted from CDM simulations. We particularly concentrate on the prediction that, for an ideal cusp caustic, the sum of the signed magnifications of the three highly magnified images should vanish when the source approaches the cusp. Strong violation of this cusp relation indicates the presence of substructure, regardless of the global, smooth mass model of the lens galaxy. We draw the following conclusions: (1) the level of substructure present in simulations produces violations of the cusp relation comparable to those observed; (2) higher-order catastrophes (e.g. swallowtails) can also cause changes of the order of 0.6 in the cusp relation as predicted by a smooth model; (3) the flux anomaly distribution depends on the image parity and flux and both the brightest minimum and saddle-point images are more affected by substructure than the fainter images. In addition, the brightest saddle point is demagnified w.r.t. the brightest minimum. Our results are fully numerical and properly include all mass scales, without making semi-analytic assumptions. They are ultimately limited by the mass resolution of single particles in the simulation determined by current computational limits, however show that our results are not affected by shot-noise due to the finite number of particles.

Strong and weak lensing united: II. The cluster mass distribution of the most X-ray luminous cluster RX J1347.5-1145

We have shown that the cluster-mass reconstruction method which combines strong and weak gravitational lensing data, developed in the first paper in the series, successfully reconstructs the mass distribution of a simulated cluster. In this paper we apply the method to the ground-based high-quality multi-colour data of RX J1347.5-1145 , the most X-ray luminous cluster to date. A new analysis of the cluster core on very deep, multi-colour data analysis of VLT/FORS data reveals many more arc candidates than previously known for this cluster. The combined strong and weak lensing reconstruction confirms that the cluster is indeed very massive. If the redshift and identification of the multiple-image system as well as the redshift estimates of the source galaxies used for weak lensing are correct, we determine the enclosed cluster mass in a cylinder to M(<360 h -1 kpc)= (1.2± 0.3) x 1015 M⊙. In addition the reconstructed mass distribution follows the distribution found with independent methods (X-ray measurements, SZ). With higher resolution (e.g. HST imaging data) more reliable multiple imaging information can be obtained and the reconstruction can be improved to accuracies greater than what is currently possible with weak and strong lensing techniques.

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 distri- bution of galaxy clusters. However, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy - the surface mass density κ of the cluster can be determined only up to a degeneracy transformation κ → κ � = λκ + (1 − λ), where λ 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 the 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 break, even under idealised conditions.

The three-point correlation function of cosmic shear. II. Relation to the bispectrum of the projected mass density and generalized third-order aperture measures

Cosmic shear, the distortion of images of high-redshift sources by the intervening inhomogeneous matter distribu- tion in the Universe, has become one of the essential tools for observational cosmology since it was first measured in 2000. Since then, several surveys have been conducted and analyzed in terms of second-order shear statistics. Current surveys are on the verge of providing useful measurements of third-order shear statistics, and ongoing and future surveys will provide accu- rate measurements of the shear three-point correlation function which contains essential information about the non-Gaussian properties of the cosmic matter distribution. We study the relation of the three-point cosmic shear statistics to the third-order statistical properties of the underlying con- vergence, expressed in terms of its bispectrum. Explicit relations for the natural components of the shear three-point correlation function (which we defined in an earlier paper) in terms of the bispectrum are derived. The behavior of the correlation function under parity transformation is obtained and found to agree with previous results. We find that in contrast to the two-point shear correlation function, the three-point function at a given angular scale θ is not affected by power in the bispectrum on much larger scales. These relations are then inverted to obtain the bispectrum in terms of the three-point shear correlator; two different ex- pressions, corresponding to different natural components of the shear correlator, are obtained and can be used to separate E and B-mode shear contributions. These relations allow us to explicitly show that correlations containing an odd power of B-mode shear vanish for parity-symmetric fields. Generalizing a recent result by Jarvis et al., we derive expressions for the third-order aperture measures, employing multiple angular scales, in terms of the (natural components of the) three-point shear correlator and show that they contain essentially all the information about the underlying bispectrum. We discuss the many useful features these (generalized) aperture measures have that make them convenient for future analyses of the skewness of the cosmic shear field (and any other polar field, such as the polarization of the Cosmic Microwave Background).

Boyle's law and gravitational instability

We have re-examined the classical problem of the macroscopic equation of state for a hydrostatic isothermal self-gravitating gas cloud bounded by an external medium at constant pressure. We have obtained analytical conditions for its equilibrium and stability without imposing any specific shape and symmetry to the cloud density distribution. The equilibrium condition can be stated in the form of an upper limit to the cloud mass; this is found to be inversely proportional to the power

Interpolation and smoothing

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Smooth maps from clumpy data: Covariance analysis

of a form factor μ characterizing the shape of the cloud. In this respect, the spherical solution, associated with the maximum value of the form factor,

Smooth maps from clumpy data: Generalizations

\mu = 1