arXiv subjects

Wolfgang J. R. Enzi

Publications and source records attributed to Wolfgang J. R. Enzi.

9 recordsLinked to original sources

arXiv2026

Harnessing stellar kinematics to constrain dark energy with the double-source-plane gravitational lens SDSS J0946+1006

SDSS J0946+1006 is an attractive target for measuring cosmological parameters through lens modelling. It is the best-studied galaxy-scale strong gravitational lens with multiple sources whose redshift separations are well-suited to constraining the dark energy equation of state. However, multi-plane lens models with free cosmological parameters risk a multi-plane mass-sheet degeneracy, although this can be lifted by a non-lensing deflector density profile tracer. We simultaneously reconstruct near-infrared and near-ultraviolet HST imaging whilst including a velocity dispersion measurement from VLT-MUSE to constrain the foreground deflector. Imaging is reconstructed faithfully regardless of whether the inferred kinematics are realistic, though we find the kinematic constraint essential for shifting the preferred cosmology into a region not in significant tension with other dark energy probes. Deflector density profile perturbations, via substructure and multipolar halo shape deformations, have only a modest effect on inferred cosmology. Combining our fiducial model with Planck CMB data yields $w=-1.01^{+0.08}_{-0.13}$; or, combined with Pantheon SNe Ia, $w=-0.99^{+0.13}_{-0.15}$. We further show that this system proves a remarkably valuable complementary probe in the $w_{0}$-$w_{a}$ plane of an evolving dark energy model, and that the DESI BAO tension with $Λ$CDM seen when combined with other datasets is not reproduced when combined with this lens, yielding $(w_{0}, w_{a})=(-0.87^{+0.10}_{-0.11}, -0.22^{+0.28}_{-0.25})$. The system's third source, visible with MUSE, only weakly constrains $w$CDM but may strengthen $w_{0}w_{a}$CDM constraints, though further mass-model complexity along its line of sight is required. Overall, kinematics-informed multi-plane lens modelling is a robust route to competitive dark energy constraints, even with a single system.

astro-ph.CO↗

arXiv2026

Disentangling the dark and stellar mass through precise lens modelling of the JWST observation of lensed quasar WFI2033--4723

We use high-resolution JWST/NIRCam imaging and measured time delays to model the quadruply imaged quasar WFI2033--4723 with a composite stellar plus dark-matter mass model. We first construct an elliptical power-law baseline model and recover Fermat-potential differences (fpd) consistent with previous HST-based and JWST-based analyses, providing a reference scale for composite modelling. We then replace the total mass profile with a physically motivated decomposition in which the stellar mass follows a multi-Gaussian expansion of the lens light, with a free radial mass-to-light gradient, and the dark matter is described by a generalized Navarro--Frenk--White (gNFW) halo. Using two external cosmological priors, Planck+DESI and Pantheon+SH0ES, the measured time delays constrain the mass-sheet-transformation freedom that would otherwise damage the stellar--dark-matter decomposition. In both cosmological cases, the stellar normalization lies between the expectations for Chabrier and Salpeter initial mass functions, while the radial mass-to-light gradient is not strongly required by the data (mildly positive). The dark matter halo has an inner slope $γ_{\rm in}\simeq1.3$, steeper than a standard NFW cusp, and the main astrophysical conclusions are insensitive to the adopted cosmological prior. This work shows that composite time-delay lens modelling can effectively separate baryons from dark matter. As a qualitative check, we reverse the logic and use our composite lens model without kinematic information to infer the cosmology instead. However, the strong degeneracy between $H_0$ and the halo scale radius $R_s$ prevents a robust standalone constraint.

astro-ph.GA↗

arXiv2026

A Salpeter IMF and an NFW halo: Disentangling the dark and stellar mass of an elliptical galaxy through precise lens modelling of a double-source-plane system

We present a strong lensing analysis of the double source plane lens J0946+1006 (colloquially "Jackpot" lens) to measure the inner dark matter density profile, the stellar-to-halo mass ratio, and the stellar initial mass function normalisation using a two component stellar plus dark matter mass model. The stellar mass follows a multi-Gaussian expansion light model with a free global mass-to-light ratio and an allowed radial $M/L$ gradient, while the dark matter is described by an elliptical generalised NFW halo. The double-source-plane geometry provides additional leverage against the mass-sheet transformation and helps constrain the radial mass profile. Despite allowing both a radial stellar $M/L$ gradient and a generalised NFW halo, the data prefer the canonical picture: an approximately constant stellar mass-to-light ratio with a Salpeter-like IMF normalisation, and a dark matter halo consistent with NFW. We infer $M_{\star} = 4.4^{+0.25}_{-0.39}\times 10^{11}\,M_{\odot}$ and an inner halo slope $γ_{\rm in}^{\rm halo} = 1.04^{+0.10}_{-0.14}$. The halo mass is $M_{200}^{\rm halo} = 1.11^{+0.37}_{-0.32}\times 10^{13}\,M_{\odot}$, implying $\log_{10}(M_{200}/M_{\star})=1.41^{+0.13}_{-0.14}$. At fixed halo mass, the inferred stellar mass lies $\sim0.1$ dex above typical literature stellar halo mass relations at similar redshift, which is comparable to the intrinsic scatter of these relations. We expect this approach to provide a practical template for future dark matter studies with the large double-source-plane lens samples from Euclid.

astro-ph.GA↗

arXiv2026

Gaussian processes on ray-guided transformed uniform grids for fast, flexible, and auto-differentiable adaptive source reconstruction in lens modelling

Strong gravitational lensing constrains cosmology and dark matter, but robust inference requires accurate source reconstruction. The achievable source resolution is highly position-dependent. Adaptive meshes can place resolution where needed, but typically rely on discontinuous operations, such as Delaunay tessellations or Voronoi binning, which can restrict regularization choices and break differentiability. In this paper, we present a novel approach for modelling the source on a ray-guided transformed uniform grid (RTU grid), that is adaptive to the lens mass model, auto-differentiable and flexible with respect to the regularization by allowing for an arbitrary choice of power spectrum. We achieve this by defining the source as a Gaussian process on a uniform grid, which is then transformed based on the cumulative distributions of rays traced back to the source plane. This approach ensures that source pixels contain a more uniform number of rays. The approach is fast by leveraging the fast Fourier transform to describe the Gaussian process in Fourier space. We apply this new approach to mock data and show that it achieves comparable fit quality with fewer source pixels, typically corresponding to about a factor of two fewer pixels per dimension, and increases Evidence Lower Bounds (ELBOs) for the same number of pixels. Using the RTU grid only mildly affects the difference in ELBO for models with and without substructures within lens galaxies. A fast, flexible, and auto-differentiable source reconstruction can greatly benefit the analysis of large samples of lens systems, e.g. those found within the Euclid survey

astro-ph.IM↗

arXiv2026

Lensed stars in galaxy-galaxy strong lensing -- a JWST prediction for the Cosmic Horseshoe

We explore for the first time the possibility of detecting lensed star transients in galaxy-galaxy strong lensing systems upon repeated, deep imaging using the {\it James-Webb Space Telescope} ({\it JWST}). Our calculation predicts that the extremely high recent star formation rate of $\sim 140\,M_{\odot}\textrm{yr}^{-1}$ over the last 50 Myr (not accounting for image multiplicity) in the ``Cosmic Horseshoe'' lensed system ($z = 2.381$) generates many young, bright stars, of which their large abundance is expected to lead to a detection rate of $\sim 60$ transients per pointing in {\it JWST} observations with a $5σ$ limiting magnitude of $\sim 29\,m_{AB}$. With the high expected detection rate and little room for uncertainty for the lens model compared with cluster lenses, our result suggests that the Cosmic Horseshoe could be an excellent tool to test the nature of dark matter based on the spatial distribution of transients, and can be used to constrain axion mass if dark matter is constituted of ultra-light axions. We also argue that the large distance modulus of $\sim46.5\,$mag at $z \approx 2.4$ can act as a filter to screen out less massive stars as transients and allow one to better constrain the high-mass end of the stellar initial mass function based on the transient detection rate. Follow-up {\it JWST} observations of the Cosmic Horseshoe would allow one to better probe the nature of dark matter and the star formation properties, such as the initial mass function at the cosmic noon, via lensed star transients.

astro-ph.CO↗

arXiv2025

Unveiling a 36 Billion Solar Mass Black Hole at the Centre of the Cosmic Horseshoe Gravitational Lens

Supermassive black holes (SMBHs) are found at the centre of every massive galaxy, with their masses tightly connected to their host galaxies through a co-evolution over cosmic time. For massive ellipticals, the SMBH mass ($M_\text{BH}$) strongly correlates with the central stellar velocity dispersion ($σ_e$), via the $M_\text{BH}-σ_e$ relation. However, SMBH mass measurements have traditionally relied on central stellar dynamics in nearby galaxies ($z < 0.1$), limiting our ability to explore the SMBHs across cosmic time. In this work, we present a self-consistent analysis combining 2D stellar dynamics and lens modelling of the Cosmic Horseshoe gravitational lens system ($z = 0.44$), one of the most massive galaxies ever observed. Using integral-field spectroscopic data from MUSE and high-resolution imaging from HST, we model the radial arc and stellar kinematics, constraining the galaxy's central mass distribution and SMBH mass. Bayesian model comparison yields a $5σ$ detection of an ultramassive black hole (UMBH) with $\log_{10}(M_\text{BH}/M_{\odot}) = 10.56^{+0.07}_{-0.08} \pm (0.12)^\text{sys}$, consistent across various systematic tests. Our findings place the Cosmic Horseshoe $\sim$$1.5σ$ above the $M_\text{BH}-σ_e$ relation, supporting an emerging trend observed in BGCs and other massive galaxies. This suggests a steeper $M_\text{BH}-σ_e$ relationship at the highest masses, potentially driven by a different co-evolution of SMBHs and their host galaxies. Future surveys will uncover more radial arcs, enabling the detection of SMBHs over a broader redshift and mass range. These discoveries will further refine our understanding of the $M_\text{BH}-σ_e$ relation and its evolution across cosmic time.

astro-ph.GA↗

arXiv2024

The overconcentrated dark halo in the strong lens SDSS J0946+1006 is a subhalo: evidence for self interacting dark matter?

The nature of dark matter is poorly constrained on subgalactic scales. Alternative models to cold dark matter, such as warm dark matter or self-interacting dark matter, could produce very different dark haloes on these scales. One of the few known dark haloes smaller than a galaxy was discovered in the triple source plane strong lens system J0946+1006. Previous studies have found that this structure is much more concentrated than expected in $Λ$CDM, but have assumed the dark halo is at the same redshift as the main deflector ($z_{\rm main}=0.222$). In this paper, we fit for the redshift of this dark halo. We reconstruct the first two sources in the system using a forward modelling approach, allowing for additional complexity from multipole perturbations. We find that the perturber redshift is $z_{\rm halo} = {0.207}^{+0.019}_{-0.019}$, and lower bounds on the evidence strongly prefer a subhalo over a line-of-sight structure. Whilst modelling both background sources does not improve constraints on the redshift of the subhalo, it breaks important degeneracies affecting the reconstruction of multipole perturbations. We find that the subhalo is a more than $5σ$ outlier from the $Λ$CDM $v_{\rm max}$-$r_{\rm max}$ relation and has a steep profile with an average slope of $γ_{\rm 2D} = {-1.81}^{+0.15}_{-0.11}$ for radii between $0.75-1.25$ kpc. This steep slope might indicate dark matter self-interactions causing the subhalo to undergo gravothermal collapse; such collapsed haloes are expected to have $γ_{\rm 2D} \approx -2$.

astro-ph.CO↗

arXiv2024

Find the haystacks, then look for needles: The rate of strongly lensed transients in galaxy-galaxy strong gravitational lenses

The time delay between appearances of multiple images of a gravitationally lensed supernova (glSN) is sensitive to the Hubble constant, $H_0$. As well as time delays, a lensed host galaxy is needed to enable precise inference of $H_0$. In this work we investigate the connection between discoverable lensed transients and their host galaxies. We find that LSST will discover 88 glSNe per year, of which $54\%$ will also have a strongly lensed host. The rates can change by approximately 30 percent uncertainty depending primarily on the choice of unlensed SN population and uncertainties in the redshift evolution of the deflector population, but the fraction of glSNe with a lensed host is consistently around a half. LSST will discover 20 glSNe per year in systems that could plausibly have been identified by Euclid as galaxy-galaxy lenses before the discovery of the glSN. Such systems have preferentially longer time delays and therefore are well suited for cosmography. We define a golden sample of glSNe Ia with time delays over 10 days, image separations greater than 0.8 arcseconds, and a multiply imaged host. For this golden sample, we find $91\%$ occur in systems that should already be discoverable as galaxy-galaxy lenses in Euclid. For cosmology with glSNe, monitoring Euclid lenses is a plausible alternative to searching the entire LSST alert stream.

astro-ph.CO↗

arXiv2024

Gravitational imaging through a triple source plane lens: revisiting the $Λ$CDM-defying dark subhalo in SDSSJ0946+1006

The $Λ$CDM paradigm successfully explains the large-scale structure of the Universe, but is less well constrained on sub-galactic scales. Gravitational lens modelling has been used to measure the imprints of dark substructures on lensed arcs, testing the small-scale predictions of $Λ$CDM. However, the methods required for these tests are subject to degeneracies among the lens mass model and the source light profile. We present a case study of the unique compound gravitational lens SDSSJ0946+1006, wherein a dark, massive substructure has been detected, whose reported high concentration would be unlikely in a $Λ$CDM universe. For the first time, we model the first two background sources in both I- and U-band HST imaging, as well as VLT-MUSE emission line data for the most distant source. We recover a lensing perturber at a $5.9σ$ confidence level with mass $\log_{10}(M_\mathrm{sub}/M_{\odot})=9.2^{+0.4}_{-0.1}$ and concentration $\log_{10}c=2.4^{+0.5}_{-0.3}$. The concentration is more consistent with CDM subhalos than previously reported, and the mass is compatible with that of a dwarf satellite galaxy whose flux is undetectable in the data at the location of the perturber. A wandering black hole with mass $\log_{10}(M_\mathrm{BH}/M_{\odot})=8.9^{+0.2}_{-0.1}$ is a viable alternative model. We systematically investigate alternative assumptions about the complexity of the mass distribution and source reconstruction; in all cases the subhalo is detected at around the $\geq5σ$ level. However, the detection significance can be altered substantially (up to $11.3σ$) by alternative choices for the source regularisation scheme.

astro-ph.CO↗