Testing the Evolution of the Correlations between Supermassive Black Holes and their Host Galaxies using Eight Strongly Lensed Quasars

One of the main challenges in using high redshift active galactic nuclei to study the correlations between the mass of the supermassive Black Hole (MBH) and the properties of their active host galaxies is instrumental resolution. Strong lensing magnification effectively increases instrumental resolution and thus helps to address this challenge. In this work, we study eight strongly lensed active galactic nuclei (AGN) with deep Hubble Space Telescope imaging, using the lens modelling code Lenstronomy to reconstruct the image of the source. Using the reconstructed brightness of the host galaxy, we infer the host galaxy stellar mass based on stellar population models. MBH are estimated from broad emission lines using standard methods. Our results are in good agreement with recent work based on non-lensed AGN, demonstrating the potential of using strongly lensed AGNs to extend the study of the correlations to higher redshifts. At the moment, the sample size of lensed AGN is small and thus they provide mostly a consistency check on systematic errors related to resolution for the non-lensed AGN. However, the number of known lensed AGN is expected to increase dramatically in the next few years, through dedicated searches in ground and space based wide field surveys, and they may become a key diagnostic of black hole and galaxy co-evolution.Comment: 12 pages, 4 figures, 3 tables. MNRAS in press. Comments welcom

Modeling lens potentials with continuous neural fields in galaxy-scale strong lenses

Strong gravitational lensing is a unique observational tool for studying the dark and luminous mass distribution both within and between galaxies. Given the presence of substructures, current strong lensing observations demand more complex mass models than smooth analytical profiles, such as power-law ellipsoids. In this work, we introduce a continuous neural field to predict the lensing potential at any position throughout the image plane, allowing for a nearly model-independent description of the lensing mass. We apply our method on simulated Hubble Space Telescope imaging data containing different types of perturbations to a smooth mass distribution: a localized dark subhalo, a population of subhalos, and an external shear perturbation. Assuming knowledge of the source surface brightness, we use the continuous neural field to model either the perturbations alone or the full lensing potential. In both cases, the resulting model is able to fit the imaging data, and we are able to accurately recover the properties of both the smooth potential and of the perturbations. Unlike many other deep learning methods, ours explicitly retains lensing physics (i.e., the lens equation) and introduces high flexibility in the model only where required, namely, in the lens potential. Moreover, the neural network does not require pre-training on large sets of labelled data and predicts the potential from the single observed lensing image. Our model is implemented in the fully differentiable lens modeling code Herculens

Strong gravitational lensing by AGNs as a probe of the quasar-host relations in the distant Universe

The tight correlations found between the mass of the supermassive black holes (SMBH) and their host galaxy luminosity, stellar mass, and velocity dispersion are often interpreted as a sign of their co-evolution. Studying these correlations across redshift provides a powerful insight into the evolutionary path followed by the quasar and its host galaxy. While the mass of the black hole is accessible from single-epoch spectra, measuring the mass of its host galaxy is challenging as the quasar largely overshines its host. Here, we present a novel technique to probe quasar-host relations beyond the local universe with strong gravitational lensing, hence overcoming the use of stellar population models or velocity dispersion measurements, both prone to degeneracies. We study in detail one of the three known cases of strong lensing by a quasar to accurately measure the mass of its host and to infer a total lensing mass of $\log_{10}(M_{\rm Tot, h}/M_{\odot}) = 10.27^{+0.06}_{-0.07}~$ within the Einstein radius of 1.2 kpc. The lensing measurement is more precise than any other alternative techniques and compatible with the local $M_{BH}$-$M_{\star, h}$ scaling relation. The sample of such quasar-galaxy or quasar-quasar lensing systems should reach a few hundreds with Euclid and Rubin-LSST, thus enabling the application of such a method with statistically significant sample sizes.Comment: Author's pre-review version, published in Nature Astronomy, 13 pages, 5 figure

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

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

lenstronomy II: A gravitational lensing softwareecosystem

peer reviewe

Next generation modeling techniques for strong gravitational lensing and measuring the Hubble constant

For many years, observations of the Universe suggest a series problems with our theoretical models, particularly its dark energy and dark matter components. Fortunately, the Universe also provides us with a tool to solve these problems, called strong gravitational lensing. This natural phenomenon, observed as multiple images of a distant background source, distorted by the mass of a foreground galaxy, offers a unique opportunity to detect the otherwise invisible total mass of that galaxy. Yet, this detection is only possible if both background and foreground objects are accurately modeled, a task of increasing difficulty because our telescopes reveal more and more of the intrinsic complexity of galaxies. The primary goal of this thesis is to demonstrate how novel and well-motivated techniques can go beyond the current simplifying assumptions to improve the modeling of luminous and dark components of galaxies. Gravitational lens modeling is an under-constrained problem that has several possible solutions. The new techniques I introduce here are based on two key concepts to overcome this difficulty: sparsity and the wavelet transform. Sparsity selects the solution that contains the fewest parameters, namely the least complex one that best fits the observation. The wavelet transform separates the various spatial scales of the solution and enables the reconstruction of the small-scale compact features up to the larger, smoother variations, which are all found in real galaxies. Since the complexity and size of data sets are dramatically increasing, modeling techniques must also be fast and scalable. I address these requirements using differentiable programming to enable unprecedented gains in computation time. The proposed modeling framework allows us to effortlessly combine simple and more complex techniques together, if required by the observations. In this work, I demonstrate that sparsity and wavelets can address the limitations of current methods for modeling the full complexity of gravitational lenses. Compared to the many methods based on smoothness assumptions, I show how multi-scale modeling techniques significantly improve the reconstruction of lensed galaxies at high resolution. Moreover, I demonstrate that those same techniques are well-suited to characterize the invisible mass distributions of galaxies, notably when it deviates from the widely used smooth elliptical profiles. These results offer exciting possibilities to measure better the properties of galaxies via gravitational lensing, including their dark matter content, ultimately improving our understanding of galaxy evolution. Additionally, I take part to the long-standing debate regarding the role of dark energy in the expansion of the Universe using the method of time-delay cosmography. Based on the gravitational lensing of distant quasars, this method plays a central role in this context because it can measure the expansion rate of the Universe (the Hubble constant) independently of all other methods. The results I present are various: searching for systematic errors in past measurements, testing modeling techniques on a blind challenge, and modeling recent Hubble Space Telescope observations of lensed quasars to measure their absolute distance. I also describe the new approach introduced within the TDCOSMO collaboration, based on relaxing most assumptions on the mass distribution of galaxies and replacing those with observations of stellar kinematics

Helens: JAX-based lens equation solver for strong lensing applications

&lt;p&gt;Lens equation solver written in Python, compatible with JAX auto-differentiation, JIT-compilation and GPU parallelization. Designed for strong lens modeling and simulation applications with any JAX-baxed software package.&lt;/p&gt; &lt;p&gt;The solver was originally developped by Austin Peel within the software package &lt;a href="https://github.com/Herculens/herculens"&gt;Herculens&lt;/a&gt;.&lt;/p&gt