arXiv subjects

Jenny Wagner

Publications and source records attributed to Jenny Wagner.

35 records · Page 2Linked to original sources

arXiv2020

papaya2: 2D Irreducible Minkowski Tensor computation

A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. Frequently, it is desirable to go beyond scalar shape metrics such as porosity and surface to volume ratios because the samples are anisotropic or because direction-dependent quantities such as conductances or elasticity are of interest. Minkowski Tensors are a systematic family of versatile and robust higher-order shape descriptors that allow for shape characterization of arbitrary order and promise a path to systematic structure-function relationships for direction-dependent properties. Papaya2 is a software to calculate 2D higher-order shape metrics with a library interface, support for Irreducible Minkowski Tensors and interpolated marching squares. Extensions to Matlab, JavaScript and Python are provided as well. While the tensor of inertia is computed by many tools, we are not aware of other open-source software which provides higher-rank shape characterization in 2D.

cs.GR↗

arXiv2020

Self-gravitating dark matter gets in shape

In our current best cosmological model, the vast majority of matter in the Universe is dark, consisting of yet undetected, non-baryonic particles that do not interact electro-magnetically. So far, the only significant evidence for dark matter has been found in its gravitational interaction, as observed in galaxy rotation curves or gravitational lensing effects. The inferred dark matter agglomerations follow almost universal mass density profiles that can be reproduced well in simulations, but have eluded an explanation from a theoretical viewpoint. Forgoing standard (astro-)physical methods, I show that it is possible to derive these profiles from an intriguingly simple mathematical approach that directly determines the most likely spatial configuration of a self-gravitating ensemble of collisionless dark matter particles.

astro-ph.CO↗

arXiv2020

Plasma lensing in comparison to gravitational lensing -- Formalism and degeneracies

Gravitational and plasma lensing share the same mathematical formalism in the limit of geometrical optics. Both phenomena can be effectively described by a projected, two-dimensional deflection potential whose gradient causes an instantaneous light deflection in a single, thin lens plane. We highlight the differences in the time-delay and lensing equations that occur because plasma lensing is caused by a potential directly proportional to the deflecting electron number density and gravitational lensing is caused by a potential related to the deflecting mass density by a Poisson equation. Since we treat plasma and gravitational lensing as thin-screen effective theories, their degeneracies are both caused by the unknown distribution of deflecting objects. Deriving the formalism-intrinsic degeneracies for plasma lensing, we find that they are analogous to those occurring in gravitational lensing. To break the degeneracies, galaxies and galaxy-cluster scale strong gravitational lenses must rely on additional assumptions or complementary observations. Physically realistic assumptions to arrive at self-consistent lens and source reconstructions can be provided by simulations and analytical effective theories. In plasma lensing, a deeper understanding of the deflecting electron density distributions is still under development, so that a model-based comprehensive lens reconstruction is not yet possible. However, we show that transient lenses and multi-wavelength observations help to break the arising degeneracies. We conclude that the development of an observation-based inference of local lens properties seems currently the best way to further probe the morphologies of plasma electron densities. Due to the simpler evidence-based breaking of the lensing degeneracies, we expect to obtain tighter constraints on the local plasma electron densities than on the gravitationally deflecting masses.

astro-ph.CO↗

arXiv2020

Cosmic structures from a mathematical perspective 1. Dark matter halo mass density profiles

The shapes of individual self-gravitating structures of an ensemble of identical, collisionless particles have remained elusive for decades. In particular, a reason why mass density profiles like the Navarro-Frenk-White or the Einasto profile are good fits to simulation- and observation-based dark matter halos has not been found. Given the class of three dimensional, spherically symmetric power-law probability density distributions to locate individual particles in the ensemble mentioned above, we derive the constraining equation for the power-law index for the most and least likely joint ensemble configurations. We find that any dark matter halo can be partitioned into three regions: a core, an intermediate part, and an outskirts part up to boundary radius $r_\mathrm{max}$. The power-law index of the core is determined by the mean radius of the particle distribution within the core. The intermediate region becomes isothermal in the limit of infinitely many particles. The slope of the mass density profile far from the centre is determined by the choice of $r_\mathrm{max}$ with respect to the outmost halo particle, such that two typical limiting cases arise that explain the $r^{-3}$-slope for galaxy-cluster outskirts and the $r^{-4}$-slope for galactic outskirts. Hence, we succeed in deriving the mass density profiles of common fitting functions from a general viewpoint. These results also allow to find a simple explanation for the cusp-core-problem and to separate the halo description from its dynamics.

astro-ph.CO↗

arXiv2020

Extended lens reconstructions with Grale: exploiting time domain, substructural and weak-lensing information

The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in Grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to "over-focusing" the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply-imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole, was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.

astro-ph.CO↗

arXiv2019

Generalised model-independent characterisation of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrisation of a Friedmann cosmological model. The scale, determined by the Hubble constant $H_0$, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio $D$ is determined from the Pantheon sample. Inserting $D$ and its uncertainty into the lensing equations for given $H_0$, esp. the time-delay equation between a pair of multiple images, allows to determine lens properties, esp. differences in the lensing potential ($Δϕ$), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal $χ^2$-parameter estimation, and derive confidence bounds by Monte-Carlo simulations. For typical strong lensing configurations between $z=0.5$ and $z=1.0$, $Δϕ$ can be determined with a relative imprecision of 1.7%, assuming imprecisions of the time delay and the redshift of the lens on the order of 1%. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine $D$ in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for $z\le2.3$ that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.

astro-ph.CO↗

arXiv2019

A model-independent characterisation of strong gravitational lensing by observables

When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on 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.

astro-ph.CO↗

arXiv2019

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

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 parametric lens-model characterisation so far, we determine local lens properties at the positions of the multiple images with our model-independent approach. Using PixeLens, we also succeed in setting up a global free-form mass density reconstruction including all subcomponents as constraints. We compare 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. 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. As only 40% of the small-scale subcomponent local lens properties overlap within the 1-$σ$ 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 asymmetric lenses or lenses with localised inhomogeneities like B0128.

astro-ph.GA↗

arXiv2019

Generalised model-independent characterisation of strong gravitational lenses VI: the origin of the formalism intrinsic degeneracies and their influence on $H_0$

We give a physical interpretation of the formalism intrinsic degeneracies of the gravitational lensing formalism that we derived on a mathematical basis in part IV of this series. We find that all degeneracies occur due to the partition of the mass density along the line of sight. Usually, it is partitioned into a background (cosmic) density and a foreground deflecting object. The latter can be further partitioned into a main deflecting object and perturbers. Weak deflecting objects along the line of sight are also added, either to the deflecting object or as a correction of the angular diameter distances, perturbing the cosmological background density. A priori, this is an arbitrary choice of reference frame and partition. They can be redefined without changing the lensing observables which are sensitive to the integrated deflecting mass density along the entire line of sight. Reformulating the time delay equation such that this interpretation of the degeneracies becomes easily visible, we note that the source can be eliminated from this formulation, which simplifies reconstructions of the deflecting mass distribution or the inference of the Hubble constant, $H_0$. Subsequently, we list necessary conditions to break the formalism intrinsic degeneracies and discuss ways to break them by model choices or including non-lensing observables like velocity dispersions along the line of sight with their advantages and disadvantages. We conclude with a systematic summary of all formalism intrinsic degeneracies and possibilities to break them.

astro-ph.CO↗

arXiv2019

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

We investigate to which precision local magnification ratios, $\mathcal{J}$, ratios of convergences, $f$, and reduced shears, $g = (g_{1}, g_{2})$, can be determined model-independently for the five resolved multiple images of the source at $z_\mathrm{s}=1.675$ in CL0024. We also determine if a comparison to the respective results obtained by the parametric modelling program Lenstool and by the non-parametric modelling program Grale can detect biases in the lens models. For these model-based approaches we additionally analyse the influence of the number and location of the constraints from multiple images on the local lens properties determined at the positions of the five multiple images of the source at $z_\mathrm{s}=1.675$. All approaches show high 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. Our results are in agreement with previous findings, supporting the light-traces-mass assumption and the merger hypothesis for CL0024. Comparing the three different approaches allows to detect modelling biases. Given that the lens properties remain approximately constant over the extension of the image areas covered by the resolvable brightness features, the model-independent approach determines the local lens properties to a comparable precision but within less than a second. (shortened)

astro-ph.CO↗

arXiv2018

Multiply-imaged time-varying sources behind galaxy clusters - Comparing FRBs to QSOs, SNe, and GRBs

With upcoming (continuum) surveys of high-resolution radio telescopes, detection rates of fast radio bursts (FRBs) might approach $10^5$ per sky per day by future extremely large observatories, such as the possible extension of the Square Kilometer Array (SKA) to a phase 2 array. Depending on the redshift distribution of FRBs and using the repeating FRB121102 as a model, we calculate a detection rate of multiply-imaged FRBs with their multiply-imaged hosts caused by the distribution of galaxy-cluster scale gravitational lenses of the order of $10^{-4}$ per square degree per year for a minimum total flux of the host of 10 $μ$Jy at 1.4 GHz for SKA phase 2. Our comparison of estimated detection rates for quasars, supernovae, gamma ray bursts, and FRBs shows that multiple images of FRBs could be more numerous than those of gamma ray bursts and supernovae and as numerous as multiple images of quasars. Time delays between the multiple images of an FRB break degeneracies in model-based and model-independent lens reconstructions as other time-varying sources do, yet without a microlensing bias as FRBs are more point-like and have shorter duration times. We estimate the relative imprecision of FRB time-delay measurements to be $10^{-10}$ for time delays on the order of 100 days for galaxy-cluster scale lenses, yielding more precise (local) lens properties than time delays from the other time-varying sources. Using the lens modelling software Grale, we show the increase in accuracy and precision of the reconstructed scaled surface mass density map of a simulated cluster-scale lens when adding time delays for one set of multiple images to the set of observational constraints.

astro-ph.CO↗

arXiv2018

Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies

Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigate under which transformations of the source position and of the deflection angle the observable properties of the multiple images, i.e. the time delay differences, the relative image positions, relative shapes, and magnification ratios, remain invariant. As these observables 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, e.g. 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.

astro-ph.CO↗

arXiv2018

Generalised model-independent characterisation of strong gravitational lenses III: perturbed axisymmetric lenses

In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetries in the brightness distributions along an arc determine differences in the deflection angle of the perturber if the source has a symmetric brightness profile and is oriented parallel to or orthogonal to the caustic. These equations are the only model-independent information retrievable from observations to leading order in the Taylor expansion. General constraints on the derivatives of the perturbing lens are derived such that the perturbation does not change the number of critical curves. To infer physical properties such as the mass of the perturber or its position, models need to be inserted. The same conclusions about the scale of detectable masses and model-dependent degeneracies as in other approaches are then found and supported by analysing B1938 as an example. Yet, the model-independent equations show that there is a fundamental degeneracy between the main lens and the perturber that can only be broken if their relative position is known. This explains the degeneracies between lens models already found in simulations from a more general viewpoint. Depending on the properties of the pertuber, this degeneracy can be broken by characterising the surrounding of the lens or by measuring the time delay between quasar images embedded in the perturbed Einstein ring of the host galaxy.

astro-ph.CO↗

arXiv2017

Generalised model-independent characterisation of strong gravitational lenses II: Transformation matrix between multiple images

(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our model-independent lens characterisation approach. From T, the same information about the critical curve at fold and cusp points is derived as determined by 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 ones 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 at the cusp points are retrieved to higher accuracy, at the fold points to lower accuracy, and the ratios of second order potential derivatives to comparable accuracy. We show that the approach using ratios of convergences and reduced shear is equivalent to ours close to the critical curve but yields more accurate results and is more robust because it does not require a special coordinate system like the approach using potential derivatives. T is determined by mapping manually assigned reference points in the images onto each other. If the assignment of reference points is subject to measurement uncertainties under noise, we find that the confidence intervals of the lens parameters can be as large as the values, when the uncertainties are larger than one pixel. 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.

astro-ph.CO↗

arXiv2017

Generalised model-independent characterisation of strong gravitational lenses I: Theoretical foundations

We extend the model-independent approach to characterise strong gravitational lenses of Wagner & Bartelmann (2016) to its most general form to leading order by using the orientation angles of a set of multiple images with respect to their connection line(s) in addition to the relative distances between the images, their ellipticities and time-delays. For two symmetric images that straddle the critical curve, the orientation angle additionally allows to determine the slope of the critical curve and a second (reduced) flexion coefficient at the critical point on the connection line between the images. It also allows to drop the symmetry assumption that the axis of largest image extension is orthogonal to the critical curve. For three images almost forming a giant arc, the degree of assumed image symmetry is also reduced to the most general case, allowing to describe image configurations for which the source need not be placed on the symmetry axis of the two folds that unite at the cusp. For a given set of multiple images, we set limits on the applicability of our approach, show which information can be obtained in cases of merging images, and analyse the accuracy achievable due to the Taylor expansion of the lensing potential for the fold case on a galaxy cluster scale NFW-profile, a fold and cusp case on a galaxy cluster scale SIE-profile, and compare the generalised approach with the one of Wagner & Bartelmann (2016). The position of the critical points is reconstructed with less than 5" deviation for multiple images closer to the critical points than 30\% of the (effective) Einstein radius and the slope of the critical curve at a fold and its shape in the vicinity of a cusp deviate less than 20\% from the true values for distances of the images to the critical points less than 15\% of the (effective) Einstein radius.

astro-ph.CO↗

arXiv2015

Degeneracies of parametric lens model families near folds and cusps

We develop an approach to select families of lens models that can describe doubly and triply gravitationally lensed images near folds and cusps using the model-independent ratios of lensing-potential derivatives derived in Wagner & Bartelmann (2015). Models are selected by comparing these model-independent ratios of potential derivatives to (numerically determined) ratios of potential derivatives along critical curves for entire lens model families in a given range of parameter values. This comparison returns parameter ranges which lens model families can reproduce observation within, as well as sections of the critical curve where image sets of the observed type can appear. If the model-independent potential-derivative ratios inferred from the observation fall outside the range of these ratios derived for the lens model family, the entire family can be excluded as a feasible model in the given volume in parameter space. We employ this approach for the family of singular isothermal spheres with external shear to examples of lensing by a galaxy and two galaxy clusters (JVAS B1422+231, SDSS J2222+2745, and MACS J1149.5+2223) and show that the results obtained by our general method are in good agreement with results of previous model fits.

astro-ph.CO↗

arXiv2015

Model-independent characterisation of strong gravitational lenses

We develop a new approach to extracting model-independent information from observations of strong gravitational lenses. The approach is based on the generic properties of images near the fold and cusp catastrophes in caustics and critical curves. Observables used are the relative image positions, the magnification ratios and ellipticities of extended images, and time delays between images with temporally varying intensity. We show how these observables constrain derivatives and ratios of derivatives of the lensing potential near a critical curve. Based on these measured properties of the lensing potential, classes of parametric lens models can then easily be restricted to such parameter values compatible with the measurements, thus allowing fast scans of large varieties of models. Applying our approach to a representative galaxy (JVAS B1422+231) and a galaxy-cluster lens (MACS J1149.5+2223), we show which model-independent information can be extracted in those cases and demonstrate that the parameters obtained by our approach for known parametric lens models agree well with those found by detailed model fitting.

astro-ph.CO↗