Stefan Schuldt

We present a strong-lensing analysis of the galaxy cluster MACS J0138.0−2155 ( z _l = 0.336), the first known cluster lens discovered to host two distinct multiply imaged type Ia supernovae (SNe): SN Requiem and SN Encore. Both transients are located in the massive, multiply imaged red galaxy MRG-M0138 at z _s = 1.949. The projected total mass distribution of this cluster has been investigated with several independent lens models, using a sample of 23 spectroscopically confirmed multiple images from eight background sources spanning 0.767 < z < 3.420, identified from Hubble Space Telescope and James Webb Space Telescope imaging, and VLT/MUSE spectroscopy. For this study, we developed a new lens model with the Bayesian parametric lens-modelling framework G RAVITY . JL , using the same strong-lensing dataset. Under a fiducial flat Lambda Cold Dark Matter cosmology, our reference mass model accurately reproduces the observed image positions, with an image-plane root-mean-square positional residual of Δ _rms = 0.15″. Assuming H ₀ = 70 km s ⁻¹ Mpc ⁻¹ , we predicted the future reappearances of highly delayed SN counter images, finding Δ t _1d,1a = 3122 ₋₇₀ ⁺⁷⁵ days (from approximately April–August 2032) for SN Encore and Δ t _2d,2a = 3122 ₋₇₂ ⁺⁶⁷ days (from approximately January–May 2027) for SN Requiem. By allowing the Hubble constant to vary and including the measured relative time delays of both SN Encore and SN Requiem, together with their statistical uncertainties, as observables, we inferred the value of H ₀ jointly with the lens-model parameters. We performed the cosmographic analysis with three alternative parametrisations of the large-scale cluster halo and combined the resulting H ₀ posteriors through Bayesian model averaging, using the corresponding Bayesian evidences as model weights. The resulting model-averaged constraint is H ₀ = 69.2 _−8.0 ^+9.6 km s ⁻¹ Mpc ⁻¹ , consistent with the value inferred from independent lens models of this cluster. The current uncertainty remains dominated by the relatively large fractional uncertainties of the measured SN time delays (≳10%), while the scatter among the mass parametrisations considered here is subdominant. The forthcoming long-baseline reappearance of SN Requiem offers an immediate opportunity to improve the statistical precision on the Hubble constant, provided that lens-model systematics are sufficiently controlled. Together, these results establish MACS J0138.0−2155 as a premier anchor for high-precision cluster-scale time-delay cosmography with multiply imaged SNe.

We present an end-to-end, iterative pipeline for efficient identification of strong galaxy-galaxy lensing systems, applied to the Euclid Q1 imaging data. Starting from the VIS catalogues, we rejected point sources, applied a magnitude cut ( I _E ≤ 24) on the deflectors, and ran a pixel-level artefact-and-noise filter to build 96 × 96 pixel cutouts. The VIS+NISP colour composites were constructed with a VIS-anchored luminance scheme that preserves VIS morphology and NISP colour contrast. A VIS-only seed classifier supplies clear positives and typical impostors, which we used to curate a morphology-balanced negative set and augment scarce positives. Among the six compact convolutional neural networks (CNNs) that had been studied initially, the modified VGG16 (GlobalAveragePooling + 256/128 dense layers with the last nine layers trainable) exhibited the best performance. In our run, the training set grew from 27 seed lenses (augmented 67× to 1809) plus 2000 negatives to a colour dataset of 30 686 images. After three rounds of iterative fine-tuning, a human grading of the top 4000 candidates ranked by the final model yielded 441 Grade A/B candidate lensing systems, including 311 overlapping with the existing Q1 strong-lens catalogue, and 130 additional A/B candidates (9 As and 121 Bs) not previously reported. Independently, the model recovered 740 out of 905 (81.8%) candidate Q1 lenses within its top 20 000 predictions, considering off-centred samples. Candidates span I _E ≃ 17–24 AB mag (median 21.3 AB mag) and are redder in Y _E − H _E than the parent population, consistent with massive early-type deflectors. Each training iteration required about a week for a small team and the approach can easily be scaled to future wide-area Euclid releases. Subsequent works will focus on calibrating the selection function via lens injection, extending recall through uncertainty-aware active learning, and exploring multi-scale or attention-based neural networks with fast post hoc vetters that incorporate lens models into the classification.

The Euclid Wide Survey (EWS) is expected to identify in the order of 100 000 galaxy-galaxy strong lenses across 14 000deg ² . The Euclid Quick Data Release (Q1) of 63.1deg ² Euclid images provides an excellent opportunity to test our lens-finding ability, and to verify the anticipated lens frequency in the EWS. Following the Q1 data release, eight machine learning networks from five teams were applied to approximately one million images. This was followed by a citizen science inspection of a subset of around 100 000 images, of which 65% received high network scores, with the remainder randomly selected. The top scoring outputs were inspected by experts to establish confident (grade A), likely (grade B), possible (grade C), and unlikely lenses. In this paper we combine the citizen science and machine learning classifiers into an ensemble, demonstrating that a combined approach can produce a purer and more complete sample than the original individual classifiers. Using the expert-graded subset as ground truth, we find that this ensemble can provide a purity of 52 ± 2% (grade A/B lenses) with 50% completeness (for context, due to the rarity of lenses a random classifier would have a purity of 0.05% and the best machine learning network in this work achieved 7.3% purity for the same completeness). We discuss future lessons for the first major Euclid data release (DR1), where the big-data challenges will become more significant and will require analysing more than ∼300 million galaxies, and thus the time investment of both experts and citizens must be carefully managed.

We present the first catalogue of strong-lensing galaxy clusters identified in the Euclid Quick Release 1 observations (covering 63.1 deg ² ). This catalogue is the result of the visual inspection of 1260 Euclid image cutouts of previously identified galaxy clusters. Each galaxy cluster was assigned a lensing score, 𝒫 _lens , derived from the aggregated votes of multiple visual inspectors, the majority of whom possess extensive expertise in strong gravitational lensing. Votes were assigned based on the assessed credibility and plausibility of the identified strong-lensing features. Specifically, we identified 83 gravitational lenses with 𝒫 _lens > 0.5, of which 14 have 𝒫 _lens = 1 and clearly exhibit secure strong-lensing features, such as giant tangential and radial arcs, and multiple images. Considering the measured number density of lensing galaxy clusters, approximately 0.3 deg ⁻² for 𝒫 _lens > 0.9, we predict that Euclid will likely observe more than 4500 strong-lensing clusters over the course of the mission. Notably, only three of the identified cluster-scale lenses had previously been observed from space. Thus, Euclid has provided the first high-resolution imaging for the remaining 80 strong-lensing galaxy cluster candidates, including those with the highest scores. The identified strong-lensing features will be used to train deep-learning models to automatically identify gravitational arcs and multiple images in the Euclid observations. This study confirms the great potential of Euclid for finding new strong-lensing clusters, enabling exciting new discoveries on the nature of dark matter and dark energy and the study of the high-redshift Universe.

Supermassive black holes and their host galaxies grow together over time, producing correlations between the black hole mass and various galaxy properties. Determining the evolution of these correlations requires precise measurements of the masses of distant black holes. We observed the gravitationally lensed quiescent galaxy MRG-M0138 at redshift 1.95 using James Webb Space Telescope integral field spectroscopy to spatially resolve the kinematics of stars within the black hole’s sphere of influence. By using a foreground lens model and fitting stellar dynamical models, we determined the mass of its inactive black hole to be M • = 6.0 − 1.7 + 2.1 × 10 9 solar masses. Comparing this measurement to local galaxies, we found that M • is higher than expected given the galaxy’s bulge mass but consistent with the correlation of M • with stellar velocity dispersion.

We conduct a search for strong gravitational lenses in the Dark Energy Survey (DES) Year 6 imaging data. We implement a pre-trained Vision Transformer (ViT) for our machine learning (ML) architecture and adopt interactive machine learning to construct a training sample with multiple classes to address common types of false positives. Our ML model reduces ∼236 million DES cutout images to 22,564 targets of interest, including ∼85% of previously reported galaxy–galaxy lens candidates discovered in DES. These targets were visually inspected by citizen scientists, who ruled out ∼90% as false positives. Of the remaining 2618 candidates, 149 were expert-classified as “definite” lenses and 516 as “probable” lenses, for a total of 665 systems, with 147 of these candidates being newly identified. Additionally, we trained a second ViT to find double-source plane lens systems, finding at least one double-source system. Our main ViT excels at identifying galaxy–galaxy lenses, consistently assigning high scores to candidates with high expert assessments. The top 800 ViT-scored images include ∼100 of our “definite” lens candidates. This selection is an order of magnitude higher in purity than previous convolutional neural-network-based lens searches and demonstrates the feasibility of applying our methodology for discovering large samples of lenses in future surveys.

Strong gravitational lensing by massive galaxy clusters offers rare opportunities to observe multiple images of distant ( z ≳ 2) Type Ia supernovae (SNe) and to resolve the properties of their host galaxies. A recent outstanding example is the Type Ia SN H0pe ( z = 1.78), which the James Webb Space Telescope (JWST) discovered in NIRCam images, when the galaxy cluster PLCK G165.7+67.0 (G165, z = 0.35) still produced three images of it. In this work, we build a new strong lensing model of G165, first using only the positions of multiple images of background galaxies. We then significantly increase the number of constraints around the position of SN H0pe by modeling the extended surface brightness of the SN host galaxy. Including extended image information reduces the average uncertainty on mass model parameters by more than an order of magnitude. We also study the spatial distribution of dust in the arc to estimate the dust extinction at the position of SN H0pe. We find good statistical agreement of the extinction estimate, at ≲1 σ , with three fully independent methods based on spectral energy distribution fitting. Moreover, our extended-image lens model of G165 allows us to map the dust distribution of the host galaxy from the image plane to the source plane. Supernova H0pe exploded in a region with a relatively high extinction ( A _V ≈ 0.9 mag) at around ∼1 kpc from its host center. This work shows that extended image modeling in lensing clusters simultaneously reduces the uncertainty on lens model parameters and enables spatially resolved analyses of lensed transients’ host galaxies. Such modeling advances are expected to play an important role in future cosmological analyses using strongly lensed SNe.

We provide a new measurement of the expansion history of the Universe at z = 0.54 based on the cosmic chronometer (CC) method, exploiting the high-quality spectroscopic VLT/MUSE data for three galaxy clusters in close-by redshift bins: SDSS J2222+2745 ( z = 0.49), MACS J1149.5+2223 ( z = 0.54), and SDSS J1029+2623 ( z = 0.59). The central one, MACS J1149.5+2223, hosts the well-known supernova Refsdal, which enabled H ₀ measurements via time delay cosmography. This represents the first step for a self-consistent probe combination, where different methods are applied to the same data sample. After selecting the most passive and massive cluster members (38 CCs), we derived their age and physical parameters via full spectrum fitting. We used the code Bagpipes , which was specifically modified to remove the cosmological prior on ages. On average, the CC sample shows super-solar metallicities ( Z / Z _⊙ = 1.3 ± 0.7) and a low dust extinction ( A _V = 0.3 ± 0.3 mag) and seems to have formed in short bursts ( τ = 0.6 ± 0.2 Gyr). We also observe both an ageing trend in redshift and a mass-downsizing pattern. From the age–redshift trend, implementing the CC method through a bootstrap approach, we derive a new H ( z ) measurement: H ( z = 0.542) = 66 ⁺⁸¹ ₋₂₉ (stat) ± 13 (syst) km/s/Mpc. We also simulated the impact of increased statistics and extended redshift coverage, finding that H ( z ) uncertainties can be reduced by up to a factor of 4 with ∼100 CCs and a slightly broader redshift range (d z ∼ 0.2).

Combining deep Hubble Space Telescope ( HST ) images and extensive data from the Multi-Unit Spectroscopic Explorer, we present new mass models of the cluster MACS J1149.5+2223, strongly lensing the supernova (SN) Refsdal, fully exploiting the source surface-brightness distribution of the SN host for the first time. In detail, we incorporated 77 000 HST pixels, in addition to the known 106 point-like multiple images, in our modeling. We considered four different models to explore the effect of the relative weighting of the point-like multiple image positions and flux distribution of the SN host on the model optimization. When the SN host’s extended image is included, we find that the statistical uncertainties of all 34 free model parameters are reduced by factors ranging from one to two orders of magnitude compared to the statistical uncertainty of the point-like only model, irrespective of the adopted different image weights. We quantified the remarkably increased level of precision with which the cluster’s total mass and the predicted time delays of the SN Refsdal multiple image positions can be reconstructed. We also show the delensed image of the SN host, a spiral galaxy at z _SN = 1.49, in multiple HST bands. In all those applications, we obtain a significant reduction of the statistical uncertainty, which is now below the level of even the small systematic uncertainty on the mass model that could be assessed by the different approaches. These results demonstrate that with extended image models of lensing clusters it is possible to measure the cluster’s total mass distribution, the values of the cosmological parameters, and the physical properties of high-redshift sources with an unparalleled precision, making the typically not-quantified systematic uncertainties now crucial.