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The origin of the tight scaling relation between the mass of supermassive black holes (SMBHs; MBH) and their host-galaxy properties remains unclear. Active galactic nuclei (AGNs) probe phases of ongoing SMBH growth and offer the only opportunity to measure MBH beyond the local Universe. However, determining an AGN's host galaxy's stellar velocity dispersion, σå, and its galaxy dynamical mass, Mdyn, is complicated by AGN contamination, aperture effects, and different host-galaxy morphologies. We select a sample of AGNs for which MBH has been independently determined to high accuracy by state-of-the-art techniques: dynamical modeling of the reverberation signal and spatially resolving the broad-line region with the Very Large Telescope Interferometer/GRAVITY. Using integral-field spectroscopic observations, we spatially map the host-galaxy stellar kinematics across the galaxy and bulge effective radii. We find that the dynamically hot component of galaxy disks correlates with MBH; however, the correlations are tightest for aperture-integrated σå measured across the bulge. Accounting for the different MBH distributions, we demonstrate—for the first time—that AGNs follow the same MBH–σ and MBH–M_bulge,dyn relations as quiescent galaxies. We confirm that the classical approach of determining the virial factor as a sample average, yielding log f = 0.65 +/- 0.18, is consistent with the average f from individual measurements. The similarity between the underlying scaling relations of AGNs and quiescent galaxies implies that the current AGN phase is too short to have altered black hole masses on a population level. These results strengthen the local calibration of f for measuring single-epoch MBH in the distant Universe. 

This is the second in a series of papers in which we use JWST MIRI multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of 9 systems. The warm dust region is compact and sensitive to perturbations by populations of halos down to masses ∼106 M⊙. Using these warm dust flux-ratio measurements in combination with 5 previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhalos. We constrain a WDM model and find an upper limit on the half-mode mass of 107.6M⊙ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Lyα forest and Milky Way satellite galaxies. 

We introduce the rapidly emerging field of multi-messenger gravitational lensing—the discovery and science of gravitationally lensed phenomena in the distant universe through the combination of multiple messengers. This is framed by gravitational lensing phenomenology that has grown since the first discoveries in the twentieth century, messengers that span 30 orders of magnitude in energy from high-energy neutrinos to gravitational waves, and powerful ‘survey facilities’ that are capable of continually scanning the sky for transient and variable sources. Within this context, the main focus is on discoveries and science that are feasible in the next 5–10 years with current and imminent technology including the LIGO–Virgo–KAGRA network of gravitational wave detectors, the Vera C. Rubin Observatory and contemporaneous gamma/X-ray satellites and radio surveys. The scientific impact of even one multi-messenger gravitational lensing discovery will be transformational and reach across fundamental physics, cosmology and astrophysics. We describe these scientific opportunities and the key challenges along the path to achieving them. This article therefore describes the consensus that emerged at the eponymous Theo Murphy meeting in March 2024, and also serves as an introduction to this Theo Murphy meeting issue. This article is part of the Theo Murphy meeting issue ‘Multi-messenger gravitational lensing (Part 2)’. 

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H₀). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtainD_Δt = 1.68_−0.38^+0.40Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to beH₀ = 65₋₁₄⁺²³km s⁻¹Mpc⁻¹. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of theVera C. RubinObservatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future. 

ABSTRACT One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images – the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1. 

Abstract Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<10¹⁰M_⊙) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys. 

Strong-lensing time delays enable the measurement of the Hubble constant ( H 0 ) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H 0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H 0 , effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy D d  = 865 −81 +85 Mpc and the time-delay distance D Δt  = 2180 −271 +472 Mpc, giving H 0  = 77.1 −7.1 +7.3 km s −1 Mpc −1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ( H 0  = 78.3 −3.3 +3.4 km s −1 Mpc −1 ) and for seven lenses ( H 0  = 74.2 −1.6 +1.6 km s −1 Mpc −1 ), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H 0  = 73.3 −5.8 +5.8 km s −1 Mpc −1 ). This agreement corroborates the methodology of time-delay cosmography. 

Strong lensing time delays can measure the Hubble constant H 0 independently of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2% precision has been achieved with seven Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H 0 from the cosmic microwave background. However, without assumptions on the radial mass density profile – and relying exclusively on stellar kinematics to break the mass-sheet degeneracy – the precision drops to 8% with the current data obtained using the seven TDCOSMO lenses, which is insufficient to resolve the H 0 tension. With the addition of external information from 33 Sloan Lens ACS (SLACS) lenses, the precision improves to 5% if the deflectors of TDCOSMO and SLACS lenses are drawn from the same population. We investigate the prospect of improving the precision of time-delay cosmography without relying on mass profile assumptions to break the mass-sheet degeneracy. Our forecasts are based on a previously published hierarchical framework. With existing samples and technology, 3.3% precision on H 0 can be reached by adding spatially resolved kinematics of the seven TDCOSMO lenses. The precision improves to 2.5% with the further addition of kinematics for 50 nontime-delay lenses from SLACS and the Strong Lensing Legacy Survey. Expanding the samples to 40 time-delay and 200 nontime-delay lenses will improve the precision to 1.5% and 1.2%, respectively. Time-delay cosmography can reach sufficient precision to resolve the Hubble tension at 3–5 σ , without assumptions on the radial mass profile of lens galaxies. By obtaining this precision with and without external datasets, we will test the consistency of the samples and enable further improvements based on even larger future samples of time-delay and nontime-delay lenses (e.g., from the Rubin , Euclid , and Roman Observatories).