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Gravitational lensing is a powerful tool for constraining substructure in the mass distribution of galaxies, be it from the presence of dark matter sub-haloes or due to physical mechanisms affecting the baryons throughout galaxy evolution. Such substructure is hard to model and is either ignored by traditional, smooth modelling, approaches, or treated as well-localized massive perturbers. In this work, we propose a deep learning approach to quantify the statistical properties of such perturbations directly from images, where only the extended lensed source features within a mask are considered, without the need of any lens modelling. Our training data consist of mock lensed images assuming perturbing Gaussian Random Fields permeating the smooth overall lens potential, and, for the first time, using images of real galaxies as the lensed source. We employ a novel deep neural network that can handle arbitrary uncertainty intervals associated with the training data set labels as input, provides probability distributions as output, and adopts a composite loss function. The method succeeds not only in accurately estimating the actual parameter values, but also reduces the predicted confidence intervals by 10 per cent in an unsupervised manner, i.e. without having access to the actual ground truth values. Our results are invariant to the inherent degeneracy between mass perturbations in the lens and complex brightness profiles for the source. Hence, we can quantitatively and robustly quantify the smoothness of the mass density of thousands of lenses, including confidence intervals, and provide a consistent ranking for follow-up science. [ABSTRACT FROM AUTHOR]

The central dark-matter fraction of galaxies is sensitive to feedback processes during galaxy formation. Strong gravitational lensing has been effective in the precise measurement of the dark-matter fraction inside massive early-type galaxies. Here, we compare the projected dark-matter fraction of early-type galaxies inferred from the SLACS (Sloan Lens ACS Survey) strong-lens survey with those obtained from the Evolution and Assembly of GaLaxies and their Environment (EAGLE), Illustris, and IllustrisTNG hydrodynamical simulations. Previous comparisons with some simulations revealed a large discrepancy, with considerably higher inferred dark-matter fractions – by factors of ≈2–3 – inside half of the effective radius in observed strong-lens galaxies as compared to simulated galaxies. Here, we report good agreement between EAGLE and SLACS for the dark-matter fractions inside both half of the effective radius and the effective radius as a function of the galaxy's stellar mass, effective radius, and total mass-density slope. However, for IllustrisTNG and Illustris, the dark-matter fractions are lower than observed. This work consistently assumes a Chabrier initial mass function (IMF), which suggests that a different IMF (although not excluded) is not necessary to resolve this mismatch. The differences in the stellar feedback model between EAGLE and Illustris and IllustrisTNG are likely the dominant cause of the difference in their dark-matter fraction and density slope. [ABSTRACT FROM AUTHOR]

We use nine different galaxy formation scenarios in ten cosmological simulation boxes from the EAGLE (Evolution and Assembly of GaLaxies and their Environments) suite of Lambda cold dark matter hydrodynamical simulations to assess the impact of feedback mechanisms in galaxy formation and compare these to observed strong gravitational lenses. To compare observations with simulations, we create strong lenses with M * > 1011 M⊙ with the appropriate resolution and noise level, and model them with an elliptical power-law mass model to constrain their total mass density slope. We also obtain the mass–size relation of the simulated lens-galaxy sample. We find significant variation in the total mass density slope at the Einstein radius and in the projected stellar mass–size relation, mainly due to different implementations of stellar and active galactic nucleus (AGN) feedback. We find that for lens-selected galaxies, models with either too weak or too strong stellar and/or AGN feedback fail to explain the distribution of observed mass density slopes, with the counter-intuitive trend that increasing the feedback steepens the mass density slope around the Einstein radius (≈3–10 kpc). Models in which stellar feedback becomes inefficient at high gas densities, or weaker AGN feedback with a higher duty cycle, produce strong lenses with total mass density slopes close to isothermal [i.e. −dlog (ρ)/dlog (r) ≈ 2.0] and slope distributions statistically agreeing with observed strong-lens galaxies in Sloan Lens ACS Survey and BOSS (Baryon Oscillation Spectroscopic Survey) Emission-Line Lens Survey. Agreement is only slightly worse with the more heterogeneous Strong Lensing Legacy Survey lens-galaxy sample. Observations of strong-lens-selected galaxies thus appear to favour models with relatively weak feedback in massive galaxies. [ABSTRACT FROM AUTHOR]

In this paper we introduce the SEAGLE (i.e. Simulating EAGLE LEnses) programme, which approaches the study of galaxy formation through strong gravitational lensing, using a suite of high-resolution hydrodynamic simulations, Evolution and Assembly of GaLaxies and their Environments (EAGLE) project. We introduce the simulation and analysis pipeline and present the first set of results from our analysis of early-type galaxies. We identify and extract an ensemble of simulated lens galaxies and use the glamer ray-tracing lensing code to create mock lenses similar to those observed in the Sloan Lens ACS Survey (SLACS) and SL2S surveys, using a range of source parameters and galaxy orientations, including observational effects such as the point spread function, pixelization, and noise levels, representative of single-orbit observations with the Hubble Space Telescope (HST) using the ACS- F 814 W filter. We subsequently model these mock lenses using the code lensed, treating them in the same way as observed lenses. We also estimate the mass model parameters directly from the projected surface mass density of the simulated galaxy, using an identical mass model family. We perform a three-way comparison of all the measured quantities with real lenses. We find the average total density slope of EAGLE lenses, $$t=2.26\,\, (0.25\,\, {\rm rms})$$ to be higher than SL2S, t  = 2.16 or SLACS, t  = 2.08. We find a very strong correlation between the external shear (γ) and the complex ellipticity (ε), with γ ∼ ε/4. This correlation indicates a degeneracy in the lens mass modelling. We also see a dispersion between lens modelling and direct fitting results, indicating systematical biases. [ABSTRACT FROM AUTHOR]