ALBERT

Description: 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.

Description: With upcoming (continuum) surveys of high-resolution radio telescopes, detection rates of fast radio bursts (FRBs) might approach 105 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 μJy at 1.4 GHz for SKA phase 2. Our comparison of estimated detection rates for quasars (QSOs), supernovae (SNe), gamma ray bursts (GRBs), and FRBs shows that multiple images of FRBs could be more numerous than those of GRBs and SNe and as numerous as multiple images of QSOs. 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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 ‘overfocusing’ 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.

Description: 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 parametrization of a Friedmann cosmological model. The scale, determined by the Hubble constant H0, 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 H0, especially the time-delay equation between a pair of multiple images, allows to determine lens properties, especially 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 χ2-parameter estimation, and derive confidence bounds by Monte Carlo simulations. For typical strong lensing configurations between z = 0.5 and 1.0, Δϕ can be determined with a relative imprecision of 1.7 per cent, assuming imprecisions of the time delay and the redshift of the lens on the order of 1 per cent. 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 ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.