Consequences of the lack of azimuthal freedom in the modeling of lensing galaxies

Massive elliptical galaxies can display structures that deviate from a pure elliptical shape, such as a twist of the principal axis or variations in the axis ratio with galactocentric distance. Although satisfactory lens modeling is generally achieved without accounting for these azimuthal structures, the question about their impact on inferred lens parameters remains, in particular, on time delays as they are used in time-delay cosmography. This paper aims at characterizing these effects and quantifying their impact considering realistic amplitudes of the variations. We achieved this goal by creating mock lensing galaxies with morphologies based on two data sets: observational data of local elliptical galaxies, and hydrodynamical simulations of elliptical galaxies at a typical lens redshift. We then simulated images of the lensing systems with space-based data quality and modeled them in a standard way to assess the impact of a lack of azimuthal freedom in the lens model. We find that twists in lensing galaxies are easily absorbed in homoeidal lens models by a change in orientation of the lens up to 10{\deg} with respect to the reference orientation at the Einstein radius, and of the shear by up to 20{\deg} with respect to the input shear orientation. The ellipticity gradients, on the other hand, can introduce a substantial amount of shear that may impact the radial mass model and consequently bias $H_0$, up to 10 km/s/Mpc. However, we find that light is a good tracer of azimuthal structures, meaning that direct imaging should be capable of diagnosing their presence. This in turn implies that such a large bias is unlikely to be unaccounted for in standard modeling practices. Furthermore, the overall impact of twists and ellipticity gradients averages out at a population level. For the galaxy populations we considered, the cosmological inference remains unbiased.Comment: Accepted for publication in A&A, 19 page

The impact of mass map truncation on strong lensing simulations

Strong gravitational lensing is a powerful tool to measure cosmological parameters and to study galaxy evolution mechanisms. However, quantitative strong lensing studies often require mock observations. To capture the full complexity of galaxies, the lensing galaxy is often drawn from high resolution, dark matter only or hydro-dynamical simulations. These have their own limitations, but the way we use them to emulate mock lensed systems may also introduce significant artefacts. In this work we identify and explore the specific impact of mass truncation on simulations of strong lenses by applying different truncation schemes to a fiducial density profile with conformal isodensity contours. Our main finding is that improper mass truncation can introduce undesired artificial shear. The amplitude of the spurious shear depends on the shape and size of the truncation area as well as on the slope and ellipticity of the lens density profile. Due to this effect, the value of H0 or the shear amplitude inferred by modelling those systems may be biased by several percents. However, we show that the effect becomes negligible provided that the lens projected map extends over at least 50 times the Einstein radius

Consequences of the lack of azimuthal freedom in the modeling of lensing galaxies

peer reviewedMassive elliptical galaxies can display structures that deviate from a pure elliptical shape, such as a twist of the principal axis or variations in the axis ratio with galactocentric distance. Although satisfactory lens modeling is generally achieved without accounting for these azimuthal structures, the question about their impact on inferred lens parameters remains, in particular, on time delays as they are used in time-delay cosmography. This paper aims at characterizing these effects and quantifying their impact considering realistic amplitudes of the variations. We achieved this goal by creating mock lensing galaxies with morphologies based on two data sets: observational data of local elliptical galaxies, and hydrodynamical simulations of elliptical galaxies at a typical lens redshift. We then simulated images of the lensing systems with space-based data quality and modeled them in a standard way to assess the impact of a lack of azimuthal freedom in the lens model. We find that twists in lensing galaxies are easily absorbed in homoeidal lens models by a change in orientation of the lens up to 10° with respect to the reference orientation at the Einstein radius, and of the shear by up to 20° with respect to the input shear orientation. The ellipticity gradients, on the other hand, can introduce a substantial amount of shear that may impact the radial mass model and consequently bias H0, up to 10 km s−1 Mpc−1. However, we find that light is a good tracer of azimuthal structures, meaning that direct imaging should be capable of diagnosing their presence. This in turn implies that such a large bias is unlikely to be unaccounted for in standard modeling practices. Furthermore, the overall impact of twists and ellipticity gradients averages out at a population level. For the galaxy populations we considered, the cosmological inference remains unbiased

COOLEST: COde-independent Organized LEnsSTandard

peer reviewedAny mass concentration in the Universe, luminous or dark, from vast galaxy clusters to stars within galaxies, can be studied through its gravitational deflection of light rays from background sources. This phenomenon, in its most impressive regime, is known as Strong Gravitational Lensing (SGL). It has several cutting-edge applications, for example: measuring the Hubble constant and shedding more light into the apparent tension between early and late Universe, detecting the presence of massive subhalos within distant galaxies that can constrain different dark matter models, and studying a galaxy’s mass partition between baryons and dark matter with direct implications on galaxy evolution. Extracting information from SGL data requires the careful analysis of images of gravitational lenses, a process referred to as lens modeling, in order to generate an image of the lens based on models of mass and light distributions of the different physical objects in play (e.g., galaxies, quasars). In this paper we call a lens model the full set of model components, including all mass and light models as well as the point spread function (PSF) model. Over the past twenty years, several lens modeling codes have been developed and used in published works. Unfortunately, there is currently no efficient and systematic way to access these published results and use them directly for new studies, which slows down new research and causes a waste of research time. The reason is simple: these modeling codes being based on different methods and conventions, bridging the gap between them is a challenging task. Here we introduce COOLEST—the COde-independent Organized LEnsing STandard—to the lensing community, which allows researchers to, independently of the original modeling code: • store lens models in a JSON format that is lightweight and easy to read and manipulate; • group together all necessary data, model and inference files (such as images and arrays in standard FITS and pickle formats); • compute a set of key lensing quantities, such as the effective Einstein radius and mass density slope; • compare models by generating standardized figures using a Python API. Any lens modeling code can adhere to this standard via a small interface that converts code- dependent quantities to the COOLEST conventions. The documentation and all Python routines incorporated in the API serve to keep development time to a minimum for code developers. Figure Figure 1 below gives a concrete example of panels generated with the plotting API, alongside quantities computed with the analysis API

TDCOSMO VIII: A key test of systematics in the hierarchical method of time-delay cosmography

peer reviewedThe largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H_0$. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated on a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generate samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data are also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allows us to correct the $H_0$ bias associated with model choice, finding $H_0$ within $1.5\sigma$ of the fiducial value. We then combine this set with a sample of corresponding lens systems which have no time delays and have a source at lower $z$, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework successfully accounts for this effect, recovering a value of $H_0$ which is both more precise ($\sigma\sim2\%$) and more accurate ($0.7\%$ median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of $H_0$ via their kinematic constraints, assuming they come from the same global population as the time-delay set

The ellipticity parameterization for an NFW profile: An overlooked angular structure in strong lens modeling

peer reviewedGalaxy-scale gravitational lenses are often modeled with two-component mass profiles where one component represents the stellar mass and the second is an NFW profile representing the dark matter. Outside of the spherical case, the NFW profile is costly to implement, and so it is approximated via two different methods; ellipticity can be introduced via the lensing potential (NFWp) or via the mass by approximating the NFW profile as a sum of analytical profiles (NFWm). While the NFWp method has been the default for lensing applications, it gives a different prescription of the azimuthal structure, which we show introduces ubiquitous gradients in ellipticity and boxiness in the mass distribution rather than having a constant elliptical shape. Because unmodeled azimuthal structure has been shown to be able to bias lens model results, we explore the degree to which this introduced azimuthal structure can affect the model accuracy. We construct input profiles using composite models using both the NFWp and NFWm methods and fit these mocks with a power-law elliptical mass distribution (PEMD) model with external shear. As a measure of the accuracy of the recovered lensing potential, we calculate the value of the Hubble parameter $H_0$ one would determine from the lensing fit. We find that the fits to the NFWp input return $H_0$ values which are systematically biased by about $3\%$ lower than the NFWm counterparts. We explore whether such an effect is attributable to the mass sheet transformation (MST) by using an MST-independent quantity, $\xi_2$. We show that, as expected, the NFWm mocks are degenerate with PEMD through an MST. For the NFWp, an additional bias is found beyond the MST due to azimuthal structures {\it exterior to the Einstein radius}. We recommend modelers use an NFWm prescription in the future, such that azimuthal structure can be introduced explicitly rather than implicitly

TDCOSMO. VII. Boxyness/discyness in lensing galaxies : Detectability and impact on H0H_0

In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios anomalies. Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterized, nor its impact on the H0 inference. We address this task by creating mock images of a point source embedded in an extended source, lensed by an elliptical galaxy on which multipolar components are added to emulate boxy/discy isodensity contours. Modeling such images with a density profile free of angular structure allow us to explore the detectability of image deformation induced by the multipoles in the residual frame. Multipole deformations are almost always detectable for our highest signal-to-noise mock data. However the detectability depends on the lens ellipticity and Einstein radius, on the S/N of the data, and on the specific lens modeling strategy. Multipoles also introduce small changes to the time delays. We therefore quantify how undetected multipoles would impact H0 inference. When no multipoles are detected in the residuals, the impact on H0 for a given lens is in general less than a few km/s/Mpc, but in the worst case scenario, combining low S/N in the ring and large intrinsic boxyness/discyness, the bias on H0 can reach 10-12 km/s/Mpc. If we now look at the inference on H0 from a population of lensing galaxies, having a distribution of multipoles representative of what is found in the light-profile of elliptical galaxies, we then find a systematic bias on H0 < 1%. The comparison of our mock systems to the state-of-the-art time delay lens sample studied by the H0LiCOW and TDCOSMO collaborations, indicates that multipoles are currently unlikely to be a source of substantial systematic bias on the inferred value of H0 from time-delay lenses

Accelerating galaxy dynamical modeling using a neural network for joint lensing and kinematics analyses

Strong gravitational lensing is a powerful tool to provide constraints on galaxy mass distributions and cosmological parameters, such as the Hubble constant, $H_0$. Nevertheless, inference of such parameters from images of lensing systems is not trivial as parameter degeneracies can limit the precision in the measured lens mass and cosmological results. External information on the mass of the lens, in the form of kinematic measurements, is needed to ensure a precise and unbiased inference. Traditionally, such kinematic information has been included in the inference after the image modeling, using spherical Jeans approximations to match the measured velocity dispersion integrated within an aperture. However, as spatially resolved kinematic measurements become available via IFU data, more sophisticated dynamical modeling is necessary. Such kinematic modeling is expensive, and constitutes a computational bottleneck which we aim to overcome with our Stellar Kinematics Neural Network (SKiNN). SKiNN emulates axisymmetric modeling using a neural network, quickly synthesizing from a given mass model a kinematic map which can be compared to the observations to evaluate a likelihood. With a joint lensing plus kinematic framework, this likelihood constrains the mass model at the same time as the imaging data. We show that SKiNN's emulation of a kinematic map is accurate to considerably better precision than can be measured (better than $1\%$ in almost all cases). Using SKiNN speeds up the likelihood evaluation by a factor of $\sim 200$. This speedup makes dynamical modeling economical, and enables lens modelers to make effective use of modern data quality in the JWST era.Comment: (13 pages, 9 figures, submitted to Astronomy & Astrophysics

lenstronomy II: A gravitational lensing softwareecosystem

peer reviewe

Accurate cosmological inference in a gravitationally distorted Universe : Learning from simulated gravitationally lensed systems

In the field of cosmology, one of the few key parameters is the Hubble constant, H0, i.e. the current expansion rate of the Universe. In the last decades, its measurement revealed a mismatch: measurements using probes based on the early Universe conflict with the ones calculated by using distances in the local Universe. In this context, strong gravitational lensing of variable sources is promising to infer a precise value of H0, local and independent of any distance ladder. As massive objects curve the space time, a source of light behind a massive galaxy can be multiply imaged, and the difference in arrival time between the images is inversely proportional to the Hubble constant. The precision and accuracy one can achieve on H0 using lensed quasars may however depend on the assumptions one makes on the mass distribution. Searching for potential systematics and quantifying them is thus essential. Since lensing galaxies are mostly elliptical galaxies(*1), the commonly employed mass models display elliptical symmetry(*2). However, elliptical galaxies have been abundantly observed and are known to be slightly more complex. In this thesis, the influence of using elliptical mass models on lensing galaxies which display azimuthal structures is examined thanks to simulations. Different major types of azimuthal structures are explored: the octupolar moment, i.e. boxyness and discyness, and the variations of ellipticity and position angle with radius. To create realistic mock observations of lensing systems, either analytical models or numerical mass maps can be used. While most simulations in this thesis used analytical models, the use of mass maps is also explored and one related problem is emphasized. Themain results are the following. (1) The use of mass distributions sampled on a grid to simulate lensing systems may introduce artefacts in the lensed images. Mass maps can not be infinite and they are consequently truncated. Such truncation introduces an asymmetry in the mass at the border of the map which impacts the multiple lensed images with a shear. Shear,which stretches and compresses the lensed images, naturally exists in lensing systems due to the galaxies in the vicinity and along the line-of-sight towards the system. However, the truncation also creates a shear, which is artificial and adds up to the fiducial one, hence biasing the model. A prescription to minimize this effect is given in this thesis. (2) The presence of boxyness and discyness in the mass of lensing galaxiesmay not always be visible: it can be absorbed as structures in the light model of the source, or can be hidden in the noise. Consequently, the H0 inference from a single lensing system displaying such azimuthal structures can be biased by several percent. Nevertheless, the analysis of a population of lenses remains unbiased as the contribution of boxy lensing galaxies compensates the one of discy galaxies. (3) Twists and ellipticity gradients impact the strength and orientation of themodelled shear. While twists do not influence cosmography inference, the variations of ellipticity do. The inference on H0 from a population of lensing systems however remains unbiased. The take homemessage of this thesis is threefold. First, simulations of lensing systems using mass maps must always be done with caution. Second, modelled shears in lensing systems cannot be trusted as originating only from contributions which are external to the modelled lensing galaxies: internal structures of the lens may also contribute. Third, the cosmographic inference from a single lens system is not robust when the modelled lensing galaxy lacks the azimuthal freedom that is effectively present in its true mass. (*1)In opposition to spiral galaxies which display a flat disk with a spherical bulge in the centre, embedded in a darkmater halo, elliptical galaxies are 3D ellipsoids or spheres. (*2) Iso-density contours are concentric ellipses displaying the same axis ratio and position angle.En cosmologie, l’un des paramètres clés à connaître est la constante de Hubble, H0. La constante deHubble est le taux actuel d’expansion de l’Univers et différentes méthodes permettent de la calculer. Ces dernières années, une tension est apparue entre la valeur de H0 basée sur l’Univers lointain et celle reposant sur des mesures de distances dans l’Univers proche. Dans ce contexte, l’utilisation de lentilles gravitationnelles pour obtenir une valeur précise de H0 est prometteuse car elle est basée sur l’Univers proche mais ne se repose pas sur un étalon de distance primaire. Comme les objets massifs déforment l’espace-temps, une source de lumière située derrière une galaxie massive peut être imagée plusieurs fois, on parle alors de lentille gravitationnelle. Si la source est variable, on peut observer un délai entre l’apparition de la variation lumineuse dans les différentes images, et ce délai est inversement proportionnel à la constante de Hubble. Ce facteur de proportionnalité dépend de la masse de la lentille. En modélisant cette dernière et en mesurant le délai, il est possible de calculer H0. Toutefois, la précision et l’exactitude pouvant être atteintes par cette méthode peuvent dépendre des hypothèses de travail. Il est donc essentiel de rechercher les sources d’erreurs potentielles et de les quantifier. Les modèles de masse de lentilles gravitationnelles les plus utilisés possèdent une symétrie elliptique(*1). En effet, les lentilles sont généralement des galaxies dites elliptiques(*2) qui, en première approximation, présentent bel et bien une telle symétrie. Cependant, les observations plus détaillées de ces dernières révèlent qu’elles sont plus complexes qu’il n’y paraît. En tenant compte de ces complexités, j’ai réalisé des simulations et ainsi testé l’influence de l’hypothèse de symétrie elliptique pour le modèle de la masse de la galaxie lentille. Plus précisément, j’ai exploré l’influence de plusieurs structures dites azimutales qui complexifient la masse: le moment octupolaire, c’est-à-dire la modification d’une forme elliptique vers une forme rectangulaire ou de disque, et les variations d’ellipticité et d’orientation avec le rayon. Plus généralement, la simulation d’observations de lentilles gravitationnelles requiert un modèle de masse, qui peut être soit analytique, soit pixélisé. Dans cette thèse, j’ai majoritairement simulé des lentilles à l’aide de modèles analytiques mais j’ai également exploré un des problèmes potentiels qui résultent de l’utilisation de cartes de masses pixélisées dans les simulations. Les principaux résultats de cette thèse sont les suivants. (1) Les simulations de lentilles se basant sur une distribution de masse échantillonnée sur une grille (pixels) peuvent être altérées par des artéfacts. En effet, les cartes de masses ne peuvent s’étendre à l’infini et sont donc tronquées. Une telle troncature crée une asymétrie à la frontière de la carte qui se répercute sur les images multiples de la source de lumière, sous forme d’un cisaillement. Un cisaillement, qui se caractérise par une déformation (élongation/compression) des images lentillées, est naturellement présent dans les lentilles gravitationnelles à cause de la présence de galaxies se situant près de la galaxie lentille et dans sa ligne de vue. La troncature induit un cisaillement supplémentaire, qui est artificiel, et la modélisation du cisaillement des lentilles ainsi simulées s’en trouve biaisée. Une prescription pour réduire cet effet en fonction de la finalité des simulations est donnée dans cette thèse. (2) Lorsqu’une lentille est modélisée avec un modèle à symétrie elliptique alors que sa vraie masse est légèrement déformée vers une forme rectangulaire ou de disque, les effets de la déformation peuvent parfois passer inaperçus. En effet, cette déformation a bien un impact sur les images mais ce dernier peut être noyé dans le bruit, ou être confondu avec des structures de la lumière de la source. L’inférence de H0 basée sur une seule lentille affichant de telles structures azimutales peut ainsi être biaisée de plusieurs pourcents. Néanmoins, l’inférence basée sur l’analyse d’une population de lentilles n’est pas biaisée car la contribution des lentilles en forme de disque est compensée par celle des lentilles plus rectangulaires. (3) Les gradients d’ellipticité et les changements d’orientation avec le rayon présents dans la masse des lentilles ont tous deux un impact sur la force et l’orientation du cisaillement modélisé. Cependant, les variations d’orientation n’influencent pas la détermination de H0, alors que c’est le cas pour les variations d’ellipticité. La valeur de H0 inférée pour une population de lentilles avec une variété de gradient d’ellipticité reste cependant correcte. Pour résumer, le message à retenir de cette thèse est triple. Premièrement, la simulation d’observations de lentilles gravitationnelles à l’aide de cartes de masse doit être réalisée avec précaution. Deuxièmement, les cisaillements modélisés dans les lentilles gravitationnelles ne peuvent pas être considérés comme provenant uniquement de contributions externes à la lentille: des structures internes à la lentille peuvent aussi en créer. Troisièmement, l’inférence de H0 grâce à une unique lentille gravitationnelle n’est pas robuste lorsque que la masse réelle de la lentille présente des structures azimutales qui ne sont pas modélisées. (*1) Les contours d’isodensités sont des ellipses concentriques qui possèdent la même orientation et la même ellipticité. (*2) Les galaxies sont généralement classées dans deux grandes catégories: les galaxies spirales, qui sont formées d’un disque plat avec un bulbe sphérique au centre, le tout entouré d’un halo de matière non visible, et les galaxies elliptiques, qui se présentent comme des grandes sphères ou ellipsoïdes plutôt homogènes