Weak Lensing Observations Research Articles

Breaking the mass-sheet degeneracy in strong lensing mass modelling with weak lensing observations

ABSTRACT The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring $H_0$ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modelling. We propose and quantitatively assess the use of galaxy–galaxy shear measurements to break the MSD in the strong lensing mass modelling. We use stacked galaxy–galaxy lensing profiles and corresponding covariance matrices from Huang et al. to constrain the MSD in lens mass modelling with a highly flexible mass profile. Our analyses show that if ideally all galaxy–galaxy lensing measurements from the Hyper Suprime-Cam survey can be used to constrain the MSD, we can achieve $\sim 10~{{\ \rm per\ cent}}$ precision on the MSD constraint. We forecast that galaxy–galaxy lensing measurements from Legacy Survey of Space and Time (LSST)-like surveys can in general constrain the MSD with $\sim 1\,\mathrm{ per\,cent}-3~{{\ \rm per\ cent}}$ precision. Furthermore, if we push weak lensing measurements to a lower angular scale of $\sim 0.04\,\rm Mpc$, a survey like LSST can provide $\sim 1~{{\ \rm per\ cent}}$ precision on the MSD constraint, enabling a measurement of $H_0$ at the 1 per cent level. We demonstrate that galaxy–galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone.

Weak lensing mass bias and the alignment of centre proxies

ABSTRACT Galaxy cluster masses derived from observations of weak lensing suffer from a number of biases affecting the accuracy of mass-observable relations calibrated from such observations. In particular, the choice of the cluster centre plays a prominent role in biasing inferred masses. In the past, empirical miscentring distributions have been used to address this issue. Using hydrodynamic simulations, we aim to test the accuracy of weak lensing mass bias predictions based on such miscentring distributions by comparing the results to mass biases computed directly using intracluster medium (ICM)-based centres from the same simulation. We construct models for fitting masses to both centred and miscentred Navarro–Frenk–White profiles of reduced shear, and model the resulting distributions of mass bias with normal and lognormal distributions. We find that the standard approach of using miscentring distributions leads to an overestimation of cluster masses at levels of between 2 per cent and 6 per cent when compared to the analysis in which actual simulated ICM centres are used, even when the underlying miscentring distributions match in terms of the miscentring amplitude. While we find that neither lognormal nor normal distributions are generally reliable for accurately modelling the shapes of the mass bias distributions, both models can serve as reasonable approximations in practice.

Neural style transfer of weak lensing mass maps

We propose a new generative model of projected cosmic mass density maps inferred from weak gravitational lensing observations of distant galaxies (weak lensing mass maps). We construct the model based on a neural style transfer so that it can transform Gaussian weak lensing mass maps into deeply non-Gaussian counterparts as predicted in ray-tracing lensing simulations. We develop an unpaired image-to-image translation method with Cycle-Consistent Generative Adversarial Networks (Cycle GAN), which learn efficient mapping from an input domain to a target domain. Our model is designed to enjoy important advantages; it is trainable with no need for paired simulation data, flexible to make the input domain visually meaningful, and expandable to rapidly-produce a map with a larger sky coverage than training data without additional learning. Using 10,000 lensing simulations, we find that appropriate labeling of training data based on field variance allows the model to reproduce a correct scatter in summary statistics for weak lensing mass maps. Compared with a popular log-normal model, our model improves in predicting the statistical natures of three-point correlations and local properties of rare high-density regions. We also demonstrate that our model enables us to produce a continuous map with a sky coverage of ∼166deg2 but similar non-Gaussian features to training data covering ∼12deg2 in a GPU minute. Hence, our model can be beneficial to massive productions of synthetic weak lensing mass maps, which is of great importance in future precise real-world analyses.

Fast emulation of two-point angular statistics for photometric galaxy surveys

ABSTRACT We develop a set of machine-learning-based cosmological emulators, to obtain fast model predictions for the C(ℓ) angular power spectrum coefficients, characterizing tomographic observations of galaxy clustering and weak gravitational lensing from multiband photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving, with respect to standard Boltzmann solvers, a speed-up of $\mathcal {O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with an accuracy better than 0.175 per cent (<0.1 per cent for the weak lensing case). This corresponds to $\lesssim 2~{{\ \rm per\ cent}}$ of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i) a specific pre-processing optimization, ahead of the training phase, and (ii) an effective neural network architecture. Compared to previous implementations in the literature, we achieve an improvement of a factor of 5 in terms of accuracy, while training a considerably lower amount of neural networks. This results in a cheaper training procedure and a higher computational performance. Finally, we show that our emulators can recover unbiased posteriors when analysing synthetic Stage-IV galaxy survey data sets.

Assessing mass-loss and stellar-to-halo mass ratio of satellite galaxies: a galaxy–galaxy lensing approach utilizing DECaLS DR8 data

ABSTRACT The galaxy–galaxy lensing technique allows us to measure the subhalo mass of satellite galaxies, studying their mass-loss and evolution within galaxy clusters and providing direct observational validation for theories of galaxy formation. In this study, we use the weak gravitational lensing observations from Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys DR8, in combination with the redMaPPer galaxy cluster catalogue from Sloan Digital Sky Survey (SDSS) DR8 to accurately measure the dark matter halo mass of satellite galaxies. We confirm a significant increase in the stellar-to-halo mass ratio of satellite galaxies with their halo-centric radius, indicating clear evidence of mass-loss due to tidal stripping. Additionally, we find that this mass-loss is strongly dependent on the mass of the satellite galaxies, with satellite galaxies above $10^{11}~{{\rm M}_{\odot }}\, h^{-1}$ experiencing more pronounced mass-loss compared to lower mass satellites, reaching 86 per cent at projected halo-centric radius 0.5R200c. The average mass-loss rate, when not considering halo-centric radius, displays a U-shaped variation with stellar mass, with galaxies of approximately $4\times 10^{10}~{{\rm M}_{\odot }}\, h^{-1}$ exhibiting the least mass-loss, around 60 per cent. We compare our results with state-of-the-art hydrodynamical numerical simulations and find that the satellite galaxy stellar-to-halo mass ratio in the outskirts of galaxy clusters is higher compared to the predictions of the Illustris-TNG project about factor 5. Furthermore, the Illustris-TNG project’s numerical simulations did not predict the observed dependence of satellite galaxy mass-loss rate on satellite galaxy mass.

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

ABSTRACT We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10−3 (2.6σ) using third-order map moments and p = 3 × 10−11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

Model-agnostic cosmological constraints from the baryon acoustic oscillation feature in redshift space

ABSTRACT We develop a framework for self-consistently extracting cosmological information from the clustering of tracers in redshift space, without relying on model-dependent templates to describe the baryon acoustic oscillation (BAO) feature. Our approach uses the recently proposed Laguerre reconstruction technique for the BAO feature and its linear point rLP, and substantially extends it to simultaneously model the multipoles ℓ = 0, 2, 4 of the anisotropic galaxy 2-point correlation function (2pcf). The approach is ‘model-agnostic’: it assumes that the nonlinear growth of structure smears the BAO feature by an approximately Gaussian kernel with a smearing scale σv, but does not assume any fiducial cosmology for describing the shape of the feature itself. Using mock observations for two realistic survey configurations assuming Λ cold dark matter (ΛCDM), combined with Bayesian parameter inference, we show that the linear point rLP and smearing scale σv can be accurately recovered by our method in both existing and upcoming surveys. The precision of the recovery of rLP is always better than $1{{\ \rm per\ cent}}$, while σv can be recovered with $\lesssim 10{{\ \rm per\ cent}}$ uncertainty provided the linear galaxy bias b is separately constrained, e.g. using weak lensing observations. Our method is also sensitive to the linear growth rate f, albeit with larger uncertainties and systematic errors, especially for upcoming surveys such as DESI. We discuss how our model can be modified to improve the recovery of f, such that the resulting constraints on {f, σv, rLP} can potentially be used as a test of cosmological models including and beyond ΛCDM.

Superfluid dark matter in tension with weak gravitational lensing data

Superfluid dark matter (SFDM) is a model that promises to reproduce the successes of both particle dark matter on cosmological scales and those of Modified Newtonian Dynamics (MOND) on galactic scales. SFDM reproduces MOND only up to a certain distance from the galactic center, and only for kinematic observables: it does not affect trajectories of light. We test whether this is consistent with a recent analysis of weak gravitational lensing that has probed accelerations around galaxies to unprecedentedly large radii. This analysis found the data to be close to the prediction of MOND, suggesting they might be difficult to fit with SFDM. To investigate this matter, we solved the equations of motion of the model and compared the result to observational data. Our results show that the SFDM model is incompatible with the weak-lensing observations, at least in its current form.

The gravitational bending of acoustic Schwarzschild black hole

Acoustic black hole is becoming an attractive topic in recent years, for it open-up new direction for experimental/observational explorations of black holes. In this work, the gravitational bending of acoustic Schwarzschild black hole is investigated. The gravitational deflection angle of particles traveling along null geodesics, weak gravitational lensing and Einstein ring for acoustic Schwarzschild black hole are carefully studied and analyzed. Particularly, in the calculation of gravitational deflection angle, we resort to two approaches—the Gauss–Bonnet theorem and the geodesic method. The results show that the gravitational bending effect in acoustic Schwarzschild black hole is enhanced, compared with conventional Schwarzschild black hole. This result indicates that the acoustic black holes may be more easily detectable in gravitational bending effects and weak gravitational lensing observations.

Constraining dark matter decay with cosmic microwave background and weak-lensing shear observations

From observations at low and high redshifts, it is well known that the bulk of dark matter (DM) has to be stable or at least very long-lived. However, the possibility that a small fraction of DM is unstable or that all DM decays with a half-life time (τ) significantly longer than the age of the Universe is not ruled out. One-body decaying dark matter (DDM) consists of a minimal extension to the ΛCDM model. It causes a modification of the cosmic growth history as well as a suppression of the small-scale clustering signal, providing interesting consequences regarding theS8tension, which is the observed difference in the clustering amplitude between weak-lensing (WL) and cosmic microwave background (CMB) observations. In this paper, we investigate models in which a fraction or all DM decays into radiation, focusing on the long-lived regime, that is,τ ≳ H0−1(H0−1being the Hubble time). We used WL data from the Kilo-Degree Survey (KiDS) and CMB data fromPlanck. First, we confirm that this DDM model cannot alleviate theS8difference. We then show that the most constraining power for DM decay does not come from the nonlinear WL data, but from CMB via the integrated Sachs-Wolfe effect. From the CMB data alone, we obtain constraints ofτ ≥ 288 Gyr if all DM is assumed to be unstable, and we show that a maximum fraction off = 0.07 is allowed to decay assuming the half-life time to be comparable to (or shorter than) one Hubble time. The constraints from the KiDS-1000 WL data are significantly weaker,τ ≥ 60 Gyr andf < 0.34. Combining the CMB and WL data does not yield tighter constraints than the CMB alone, except for short half-life times, for which the maximum allowed fraction becomesf = 0.03. All limits are provided at the 95% confidence level.

Combining Planck and SPT Cluster Catalogs: Cosmological Analysis and Impact on the Planck Scaling Relation Calibration

We provide the first combined cosmological analysis of the South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the νΛ CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find and , respectively. The results for the mass slope show a ∼4 σ departure from the self-similar evolution, α SZ ∼ 1.8. This shift is mainly driven by the matter density value preferred by SPT data, Ω m = 0.30 ± 0.03, lower than the one obtained by Planck data alone, . The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, (1 − b) ∼ 0.8, and with results required by the Planck cosmic microwave background cosmology, (1 − b) ∼ 0.6. From this analysis, we obtain a new catalog of Planck cluster masses M 500. We estimate the ratio between the published Planck M SZ masses and our derived masses M 500, as a “measured mass bias,” . We analyze the mass, redshift, and detection noise dependence of , finding an increasing trend toward high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass, high-mass, low-z, and high-z regimes.

Field-level inference of galaxy intrinsic alignment from the SDSS-III BOSS survey

As a large-scale overdensity collapses, it affects the orientation and shape of galaxies that form, by exerting tidal shear along their axes. Therefore, the shapes of elliptical galaxies align with the tidal field of cosmic structures. This intrinsic alignment provides insights into galaxy formation and the primordial universe, complements late-time cosmological probes and constitutes a significant systematic effect for weak gravitational lensing observations. In the present study, we provide constraints on the linear alignment model using a fully Bayesian field-level approach, using galaxy shape measurements from the SDSS-III BOSS LOWZ sample and three-dimensional tidal fields constrained with the LOWZ and CMASS galaxy samples of the SDSS-III BOSS survey. We find 4σ evidence of intrinsic alignment, with an amplitude of AI = 2.9 ± 0.7 at 20 Mpch.

Galaxy cluster aperture masses are more robust to baryonic effects than 3D halo masses

ABSTRACT Systematic uncertainties in the mass measurement of galaxy clusters limit the cosmological constraining power of future surveys that will detect more than 105 clusters. Previously, we argued that aperture masses can be inferred more accurately and precisely than 3D masses without loss of cosmological constraining power. Here, we use the Baryons and Haloes of Massive Systems (BAHAMAS) cosmological, hydrodynamical simulations to show that aperture masses are also less sensitive to changes in mass caused by galaxy formation processes. For haloes with $m_\mathrm{200m,dmo} \gt 10^{14} \, h^{-1} \, \mathrm{M_\odot }$, binned by their 3D halo mass, baryonic physics affects aperture masses and 3D halo masses similarly when measured within apertures similar to the halo virial radius, reaching a maximum reduction of $\approx 3 \, \mathrm{per\, cent}$. For lower mass haloes, $10^{13.5} \lt m_\mathrm{200m,dmo} / h^{-1} \, \mathrm{M_\odot }\lt 10^{14}$, and aperture sizes $\sim 1 \, h^{-1} \, \mathrm{cMpc}$, representative of weak lensing observations, the aperture mass is consistently reduced less ($\lesssim 5 \, \mathrm{per\, cent}$) than the 3D halo mass ($\lesssim 10 \, \mathrm{per\, cent}$ for m200m). The halo mass reduction evolves only slightly, by up to 2 $\mathrm{per\, centage}$ points, between redshift 0.25 and 1 for both the aperture mass and m200m. Varying the simulated feedback strength so the mean simulated hot gas fraction covers the observed scatter inferred from X-ray observations, we find that the aperture mass is consistently less biased than the 3D halo mass, by up to $2 \,$$\mathrm{per\, centage}$ points at $m_\mathrm{200m,dmo} = 10^{14} \, h^{-1} \, \mathrm{M_\odot }$. Therefore, aperture mass calibrations provide a fruitful path to reduce the sensitivity of future cluster surveys to systematic uncertainties.

Constraining baryonic feedback and cosmology with weak-lensing, X-ray, and kinematic Sunyaev–Zeldovich observations

ABSTRACT Modern weak-lensing observations are becoming increasingly sensitive to baryonic feedback processes which are still poorly understood. So far, this challenge has been faced either by imposing scale-cuts in the data or by modelling baryonic effects with simple, one-parameter models. In this paper, we rely on a more general, seven-parameter prescription of baryonic feedback effects, which is primarily motivated by observations and has been shown to agree with a plethora of hydrodynamical simulations. By combining weak-lensing data from the Kilo-Degree Survey (KiDS-1000) with observations of gas around galaxy clusters, we are able to constrain baryonic parameters and learn more about feedback and cosmology. In particular, we use cluster gas fractions from X-ray data and gas profiles from kinematic Sunyaev–Zeldovich (kSZ) observations to provide evidence for baryonic feedback that is stronger than predicted by most hydrodynamical simulations. In terms of the matter power spectrum, we report a beyond-per cent effect at wave-modes above k ∼ 0.1–0.45 $h\, {\rm Mpc}^{-1}$ and a maximum suppression of 12–33 per cent at k ∼ 7 $h\, {\rm Mpc}^{-1}$ (68 per cent confidence level). Regarding the combined parameter Σ8 = σ8(Ωm/0.3)0.58, we find the known tension with the Planck satellite data to be reduced from 3.8σ to 2.9σ once baryonic effects are fully included in the analysis pipeline. The tension is further decreased to 2.6σ when the weak-lensing data are combined with X-ray and kSZ observations. We conclude that, while baryonic feedback effects become more important in modern weak-lensing surveys, they are unlikely to act as the main culprit for the observed Σ8-tension.

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies (log M*/M⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u − g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, Lr, 10, and the light-weighted surface brightness slope, Γ10. Results. We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with Lr, 10 and anti-correlates with Γ10. At fixed redshift, Lr, 10 and Γ10, the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass.

First measurement of the characteristic depletion radius of dark matter haloes from weak lensing

ABSTRACT We use weak lensing observations to make the first measurement of the characteristic depletion radius, one of the three radii that characterize the region where matter is being depleted by growing haloes. The lenses are taken from the halo catalogue produced by the extended halo-based group/cluster finder applied to DESI Legacy Imaging Surveys DR9, while the sources are extracted from the DECaLS DR8 imaging data with the fourier_quad pipeline. We study halo masses $12 \lt \log (M_{\rm grp} \,[{\rm M_{\odot }}\, h^{-1}]) \le 15.3$ within redshifts 0.2 ≤ z ≤ 0.3. The virial and splashback radii are also measured and used to test the original findings on the depletion region. When binning haloes by mass, we find consistency between most of our measurements and predictions from the cosmicgrowth simulation, with exceptions to the lowest mass bins. The characteristic depletion radius is found to be roughly 2.5 times the virial radius and 1.7–3 times the splashback radius, in line with an approximately universal outer density profile, and the average enclosed density within the characteristic depletion radius is found to be roughly 29 times the mean matter density of the Universe in our sample. When binning haloes by both mass and a proxy for halo concentration, we do not detect a significant variation of the depletion radius with concentration, on which the simulation prediction is also sensitive to the choice of concentration proxy. We also confirm that the measured splashback radius varies with concentration differently from simulation predictions.

RadioLensfit: An HPC tool for accurate galaxy shape measurement with SKA

The new generation radio telescopes, such as the Square Kilometre Array (SKA), are expected to reach sufficient sensitivity and resolution to provide large number densities of resolved faint sources, and therefore to open weak gravitational lensing observations to the radio band. In this paper we present RadioLensfit, an open-source tool for an efficient and fast galaxy shape measurement for radio weak lensing shear. It performs a single source model fitting in the Fourier domain, after isolating the source visibilities with a sky model and a faceting technique. This approach makes real sized radio datasets accessible to an analysis in this domain, where data is not yet affected by the systematics introduced by the non-linear imaging process. We detail the implementation of the code and discuss limitations of the source extraction algorithm. We describe the hybrid parallelization MPI+OpenMP of the code, implemented to exploit multi-node HPC infrastructures for accelerating the computation and dealing with very large datasets that possibly cannot entirely be stored in the memory of a single processor. Finally, we present performance results both in terms of measurement accuracy and code scalability on SKA-MID simulated datasets. In particular, we compare shape measurements of 1000 sources at the expected source density in SKA Phase 1 with the ones obtained from the same dataset in a previous work by a joint fitting of the raw visibility data, and show that results are comparable while the computational time is highly reduced.

Numerical complexity of the joint nulled weak-lensing probability distribution function

In the context of tomographic cosmic shear surveys, there exists a nulling transformation of weak lensing observations (also called BNT transform) that allows us to simplify the correlation structure of tomographic cosmic shear observations, as well as to build observables that depend only on a localized range of redshifts and thus independent from the low-redshift/small-scale modes. This procedure renders possible accurate, and from-first-principles, predictions of the convergence and aperture mass one-point distributions (PDF). We here explore other consequences of this transformation on the (reduced) numerical complexity of the estimation of the joint PDF between nulled bins and demonstrate how to use these results to make theoretical predictions.

Weak-lensing Mass Reconstruction of Galaxy Clusters with a Convolutional Neural Network

Abstract We introduce a novel method for reconstructing the projected matter distributions of galaxy clusters with weak-lensing (WL) data based on a convolutional neural network (CNN). Training data sets are generated with ray-tracing through cosmological simulations. We control the noise level of the galaxy shear catalog such that it mimics the typical properties of the existing ground-based WL observations of galaxy clusters. We find that the mass reconstruction by our multilayered CNN with the architecture of alternating convolution and trans-convolution filters significantly outperforms the traditional reconstruction methods. The CNN method provides better pixel-to-pixel correlations with the truth, restores more accurate positions of the mass peaks, and more efficiently suppresses artifacts near the field edges. In addition, the CNN mass reconstruction lifts the mass-sheet degeneracy when applied to our projected cluster mass estimation from sufficiently large fields. This implies that this CNN algorithm can be used to measure the cluster masses in a model-independent way for future wide-field WL surveys.

Image rotation from lensing

Forthcoming radio surveys will include full polarisation information, which can be potentially useful for weak lensing observations. We propose a new method to measure the (integrated) gravitational field between a source and the observer, by looking at the angle between the morphology of a radio galaxy and the orientation of the polarisation. For this we use the fact that, while the polarisation of a photon is parallel transported along the photon geodesic, the infinitesimal shape of the source, e.g. its principal axis in the case of an ellipse, is Lie transported as described by the lens map. While at second order, the lens map usually contains a rotation, here we show that the presence of shear alone already induces an apparent rotation of the shape of an elliptical galaxy. As an example, we calculate the rotation of the shape vector with respect to the polarisation direction which is generated by a distribution of foreground Schwarzschild lenses. For radio galaxies, the intrinsic morphological orientation of a source and its polarised emission are correlated. It follows that observing both the polarisation and the morphological orientation provides information on both the unlensed source orientation and on the gravitational potential along the line of sight.