scholarly journals Model-independent and model-based local lensing properties of B0128+437 from resolved quasar images

2020 ◽  
Vol 635 ◽  
pp. A86
Author(s):  
Jenny Wagner ◽  
Liliya L. R. Williams
Keyword(s):  
Density Distribution ◽  
Confidence Intervals ◽  
Mass Density ◽  
Property Values ◽  
Free Form ◽  
Small Scale ◽  
Lens Model ◽  
Confidence Bounds ◽  
Multiple Images ◽  
Model Independent

The galaxy-scale gravitational lens B0128+437 generates a quadrupole-image configuration of a background quasar that shows milli-arcsecond-scale subcomponents in the multiple images observed with VLBI. As this multiple-image configuration including the subcomponents has eluded a simple parametric lens-model characterisation so far, we determined local lens properties at the positions of the multiple images with our model-independent approach. Using PixeLens, we also succeeded in setting up a global free-form mass density reconstruction, including all subcomponents as constraints. We compared the model-independent local lens properties with those obtained by PixeLens and those obtained by the parametric modelling algorithm Lensmodel. A comparison of all three approaches and a model-free analysis based on the relative polar angles of the multiple images corroborate the hypothesis that elliptically symmetric models are too simplistic to characterise the asymmetric mass density distribution of this lenticular or late-type galaxy. Determining the local lens properties independently of a model, the sparsity and the strong alignment of the subcomponents yield broad 1-σ confidence intervals ranging from 8% to over 1000% of the local lens property values. The lens model approaches yield comparably broad confidence intervals. Within these intervals, there is a high degree of agreement between the model-independent local lens properties of our approach based on the subcomponent positions and the local lens properties obtained by PixeLens. In addition, the model-independent approach efficiently determines local lens properties on the scale of the quasar subcomponents, which are computationally intensive to obtain by free-form model-based approaches. Relying on the quadrupole moment of each subcomponent, these small-scale local lens properties show tighter 1-σ confidence bounds by at least one order of magnitude on the average with a range of 9% to 535% of the of the local lens property values. As only 40% of the small-scale subcomponent local lens properties overlap within the confidence bounds, mass density gradients on milli-arcsecond scales cannot be excluded. Hence, aiming at a global reconstruction of the deflecting mass density distribution, increasingly detailed observations require flexible free-form models that allow for density fluctuations on milli-arcsecond scale to replace parametric ones, especially for such lenses as B0128, which have an asymmetric mass density distribution that may include localised inhomogeneities.

scholarly journals Model-independent and model-based local lensing properties of CL0024+1654 from multiply imaged galaxies

2018 ◽  
Vol 612 ◽  
pp. A17 ◽  
Author(s):  
Jenny Wagner ◽  
Jori Liesenborgs ◽  
Nicolas Tessore
Keyword(s):  
Gravitational Lensing ◽  
Cosmological Parameters ◽  
Linear Mapping ◽  
Small Scale ◽  
Parametric Modelling ◽  
Lens Model ◽  
Confidence Bounds ◽  
Multiple Images ◽  
Multiple Image ◽  
Model Independent

Context. Local gravitational lensing properties, such as convergence and shear, determined at the positions of multiply imaged background objects, yield valuable information on the smaller-scale lensing matter distribution in the central part of galaxy clusters. Highly distorted multiple images with resolved brightness features like the ones observed in CL0024 allow us to study these local lensing properties and to tighten the constraints on the properties of dark matter on sub-cluster scale. Aim. We investigate to what precision local magnification ratios, $\mathcal{J}$, ratios of convergences, f, and reduced shears, g = (g1, g2), can be determined independently of a lens model for the five resolved multiple images of the source at zs = 1.675 in CL0024. We also determine if a comparison to the respective results obtained by the parametric modelling tool Lenstool and by the non-parametric modelling tool Grale can detect biases in the models. For these lens models, we analyse the influence of the number and location of the constraints from multiple images on the lens properties at the positions of the five multiple images of the source at zs = 1.675. Methods. Our model-independent approach uses a linear mapping between the five resolved multiple images to determine the magnification ratios, ratios of convergences, and reduced shears at their positions. With constraints from up to six multiple image systems, we generate Lenstool and Grale models using the same image positions, cosmological parameters, and number of generated convergence and shear maps to determine the local values of $\mathcal{J}$, f, and g at the same positions across all methods. Results. All approaches show strong agreement on the local values of $\mathcal{J}$, f, and g. We find that Lenstool obtains the tightest confidence bounds even for convergences around one using constraints from six multiple-image systems, while the best Grale model is generated only using constraints from all multiple images with resolved brightness features and adding limited small-scale mass corrections. Yet, confidence bounds as large as the values themselves can occur for convergences close to one in all approaches. Conclusions. Our results agree with previous findings, support the light-traces-mass assumption, and the merger hypothesis for CL0024. Comparing the different approaches can detect model biases. The model-independent approach determines the local lens properties to a comparable precision in less than one second.

scholarly journals Generalised model-independent characterisation of strong gravitational lenses

2018 ◽  
Vol 620 ◽  
pp. A86 ◽  
Author(s):  
Jenny Wagner
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
General Class ◽  
Deflection Angle ◽  
Lens Model ◽  
Gravitational Lenses ◽  
Source Position ◽  
Multiple Images ◽  
Model Independent ◽  
The Deflection Angle

Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigated under which transformations of the source position and of the deflection angle the observable properties of the multiple images remain invariant. These observable properties are time delay differences, the relative image positions, relative shapes, and magnification ratios. As they only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, for example, the mass-sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.

scholarly journals A Model-Independent Characterisation of Strong Gravitational Lensing by Observables

Universe ◽  
2019 ◽  
Vol 5 (7) ◽  
pp. 177 ◽  
Author(s):  
Jenny Wagner
Keyword(s):  
Galaxy Evolution ◽  
Gravitational Lensing ◽  
Mass Density ◽  
Model Fitting ◽  
Mass Scale ◽  
Lens Model ◽  
Multiple Images ◽  
Strong Gravitational Lensing ◽  
Consistent Model ◽  
Local Properties

When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie in its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly distorted images of the source are observed. This strong gravitational lensing effect has so far been treated as a model-fitting problem. Using the observed multiple images as constraints yields a self-consistent model of the deflecting mass density and the source object. As several models meet the constraints equally well, we develop a lens characterisation that separates data-based information from model assumptions. The observed multiple images allow us to determine local properties of the deflecting mass distribution on any mass scale from one simple set of equations. Their solution is unique and free of model-dependent degeneracies. The reconstruction of source objects can be performed completely model-independently, enabling us to study galaxy evolution without a lens-model bias. Our approach reduces the lens and source description to its data-based evidence that all models agree upon, simplifies an automated treatment of large datasets, and allows for an extrapolation to a global description resembling model-based descriptions.

scholarly journals Quantifying the structure of strong gravitational lens potentials with uncertainty-aware deep neural networks

2020 ◽  
Vol 499 (4) ◽  
pp. 5641-5652
Author(s):  
Georgios Vernardos ◽  
Grigorios Tsagkatakis ◽  
Yannis Pantazis
Keyword(s):  
Confidence Intervals ◽  
Galaxy Evolution ◽  
Gravitational Lensing ◽  
Probability Distributions ◽  
Mass Density ◽  
Ground Truth ◽  
Gaussian Random Fields ◽  
Training Data ◽  
Gravitational Lens ◽  
Data Set

ABSTRACT Gravitational lensing is a powerful tool for constraining substructure in the mass distribution of galaxies, be it from the presence of dark matter sub-haloes or due to physical mechanisms affecting the baryons throughout galaxy evolution. Such substructure is hard to model and is either ignored by traditional, smooth modelling, approaches, or treated as well-localized massive perturbers. In this work, we propose a deep learning approach to quantify the statistical properties of such perturbations directly from images, where only the extended lensed source features within a mask are considered, without the need of any lens modelling. Our training data consist of mock lensed images assuming perturbing Gaussian Random Fields permeating the smooth overall lens potential, and, for the first time, using images of real galaxies as the lensed source. We employ a novel deep neural network that can handle arbitrary uncertainty intervals associated with the training data set labels as input, provides probability distributions as output, and adopts a composite loss function. The method succeeds not only in accurately estimating the actual parameter values, but also reduces the predicted confidence intervals by 10 per cent in an unsupervised manner, i.e. without having access to the actual ground truth values. Our results are invariant to the inherent degeneracy between mass perturbations in the lens and complex brightness profiles for the source. Hence, we can quantitatively and robustly quantify the smoothness of the mass density of thousands of lenses, including confidence intervals, and provide a consistent ranking for follow-up science.

scholarly journals Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm

2017 ◽  
Vol 23 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Yue Li ◽  
Di Zhang ◽  
Ilker Capoglu ◽  
Karl A. Hujsak ◽  
Dhwanil Damania ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Density Distribution ◽  
Scanning Transmission Electron Microscopy ◽  
Mass Density ◽  
Three Dimensional ◽  
Force Microscopy ◽  
Statistical Measures ◽  
Atomic Force ◽  
Transmission Electron ◽  
Scanning Transmission

AbstractEssentially all biological processes are highly dependent on the nanoscale architecture of the cellular components where these processes take place. Statistical measures, such as the autocorrelation function (ACF) of the three-dimensional (3D) mass–density distribution, are widely used to characterize cellular nanostructure. However, conventional methods of reconstruction of the deterministic 3D mass–density distribution, from which these statistical measures can be calculated, have been inadequate for thick biological structures, such as whole cells, due to the conflict between the need for nanoscale resolution and its inverse relationship with thickness after conventional tomographic reconstruction. To tackle the problem, we have developed a robust method to calculate the ACF of the 3D mass–density distribution without tomography. Assuming the biological mass distribution is isotropic, our method allows for accurate statistical characterization of the 3D mass–density distribution by ACF with two data sets: a single projection image by scanning transmission electron microscopy and a thickness map by atomic force microscopy. Here we present validation of the ACF reconstruction algorithm, as well as its application to calculate the statistics of the 3D distribution of mass–density in a region containing the nucleus of an entire mammalian cell. This method may provide important insights into architectural changes that accompany cellular processes.

scholarly journals Generalised model-independent characterisation of strong gravitational lenses

2018 ◽  
Vol 613 ◽  
pp. A6 ◽  
Author(s):  
J. Wagner ◽  
N. Tessore
Keyword(s):  
Quadrupole Moment ◽  
Galaxy Cluster ◽  
Transformation Matrix ◽  
Critical Curve ◽  
Reference Points ◽  
Quadrupole Moments ◽  
Multiple Images ◽  
Lower Accuracy ◽  
Cusp Points ◽  
Model Independent

We determine the transformation matrix that maps multiple images with identifiable resolved features onto one another and that is based on a Taylor-expanded lensing potential in the vicinity of a point on the critical curve within our model-independent lens characterisation approach. From the transformation matrix, the same information about the properties of the critical curve at fold and cusp points can be derived as we previously found when using the quadrupole moment of the individual images as observables. In addition, we read off the relative parities between the images, so that the parity of all images is determined when one is known. We compare all retrievable ratios of potential derivatives to the actual values and to those obtained by using the quadrupole moment as observable for two- and three-image configurations generated by a galaxy-cluster scale singular isothermal ellipse. We conclude that using the quadrupole moments as observables, the properties of the critical curve are retrieved to a higher accuracy at the cusp points and to a lower accuracy at the fold points; the ratios of second-order potential derivatives are retrieved to comparable accuracy. We also show that the approach using ratios of convergences and reduced shear components is equivalent to ours in the vicinity of the critical curve, but yields more accurate results and is more robust because it does not require a special coordinate system as the approach using potential derivatives does. The transformation matrix is determined by mapping manually assigned reference points in the multiple images onto one another. If the assignment of the reference points is subject to measurement uncertainties under the influence of noise, we find that the confidence intervals of the lens parameters can be as large as the values themselves when the uncertainties are larger than one pixel. In addition, observed multiple images with resolved features are more extended than unresolved ones, so that higher-order moments should be taken into account to improve the reconstruction precision and accuracy.

Acoustic Design of a Local Scatterer in a Phase-Space

1995 ◽  
Author(s):  
John J. McCoy ◽  
Ben Zion Steinberg
Keyword(s):  
Mechanical Property ◽  
Phase Space ◽  
Mass Density ◽  
Sound Field ◽  
Design Strategy ◽  
Local Region ◽  
Small Scale ◽  
Far Field ◽  
Acoustic Design ◽  
Surrounding Fluid

Abstract A spatially local region of mechanical property heterogeneity is a source of scattering, by which a structure-borne mechanical wavefield is released as sound, to a surrounding fluid. We consider the case of a scatterer which is of the order of the size of the wavelength of a plate-wave field for a frequency which is below coincidence. A design strategy for reducing the strength of the scattered sound field in the fluid, at far-field distances from the scatterer, by adding a small-scale structure to the heterogenity, is presented. The design is accomplished in a wavelet-based phase-space. Emphasized is a significant distinction required of the added structure, depending on the heterogeneity applying to a measure of the local mass density or the local bending stiffness.

Detect the density profile with LAMOST K giants

2017 ◽  
Vol 13 (S334) ◽  
pp. 387-388
Author(s):  
Yan Xu ◽  
Chao Liu
Keyword(s):  
Density Distribution ◽  
Power Law ◽  
Density Profile ◽  
Milky Way ◽  
Galactic Center ◽  
Fitting Method ◽  
Stellar Halo ◽  
Model Independent ◽  
Power Law Index ◽  
K Giants

AbstractThe density distribution of the Milky Way halo is detected with 5351 LAMOST DR3 metal poor K giants using a nonparametric method. The nonparametric fitting method is a model independent way to estimate the halo density distribution while to a large extent avoiding the influence of the halo substucture. We show that the K giants density profile can be fitted well by single power law. We found no indication of a break in the power law index. The powerlaw index n = 5.0−0.64+0.64. The data show that the stellar halo is flattened at smaller radii, and becomes more spherical farther from the Galactic center. The flattening q(r=15Kpc)is about0.64, q(20Kpc) is about 0.8, q(30Kpc) is about 0.96.

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