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Multiply imaged time-variable sources can be used to measure absolute distances as a function of redshifts and thus determine cosmological parameters, chiefly the Hubble Constant H$$_0$$${}_0$. In the two decades up to 2020, through a number of observational and conceptual breakthroughs, this so-called time-delay cosmography has reached a precision sufficient to be an important independent voice in the current “Hubble tension” debate between early- and late-universe determinations of H$$_0$$${}_0$. The 2020s promise to deliver major advances in time-delay cosmography, owing to the large number of lenses to be discovered by new and upcoming surveys and the vastly improved capabilities for follow-up and analysis. In this review, after a brief summary of the foundations of the method and recent advances, we outline the opportunities for the decade and the challenges that will need to be overcome in order to meet the goal of the determination of H$$_0$$${}_0$from time-delay cosmography with 1% precision and accuracy.

 

We report the spectroscopic follow-up of 175 lensed quasar candidates selected using Gaia Data Release 2 observations following Paper III of this series. Systems include 86 confirmed lensed quasars and a further 17 likely lensed quasars based on imaging and/or similar spectra. We also confirm 11 projected quasar pairs and 11 physical quasar pairs, while 25 systems are left as unclassified quasar pairs – pairs of quasars at the same redshift, which could be either distinct quasars or potential lensed quasars. Especially interesting objects include eight quadruply imaged quasars of which two have BAL sources, an apparent triple, and a doubly lensed LoBaL quasar. The source redshifts and image separations of these new lenses range between 0.65–3.59 and 0.78–6.23 arcsec, respectively. We compare the known population of lensed quasars to an updated mock catalogue at image separations between 1 and 4 arcsec, showing a very good match at z < 1.5. At z > 1.5, only 47 per cent of the predicted number are known, with 56 per cent of these missing lenses at image separations below 1.5 arcsec. The missing higher redshift, small-separation systems will have fainter lensing galaxies, and are partially explained by the unclassified quasar pairs and likely lenses presented in this work, which require deeper imaging. Of the 11 new reported projected quasar pairs, 5 have impact parameters below 10 kpc, almost tripling the number of such systems, which can probe the innermost regions of quasar host galaxies through absorption studies. We also report four new lensed galaxies discovered through our searches, with source redshifts ranging from 0.62 to 2.79.

 

In late 2014, four images of supernova (SN) “Refsdal,” the first known example of a strongly lensed SN with multiple resolved images, were detected in the MACS J1149 galaxy-cluster field. Following the images’ discovery, the SN was predicted to reappear within hundreds of days at a new position ∼8″ away in the field. The observed reappearance in late 2015 makes it possible to carry out Refsdal’s original proposal to use a multiply imaged SN to measure the Hubble constantH₀, since the time delay between appearances should vary inversely withH₀. Moreover, the position, brightness, and timing of the reappearance enable a novel test of the blind predictions of galaxy-cluster models, which are typically constrained only by the positions of multiply imaged galaxies. We have developed a new photometry pipeline that usesDOLPHOTto measure the fluxes of the five images of SN Refsdal from difference images. We apply four separate techniques to perform a blind measurement of the relative time delays and magnification ratios between the last image SX and the earlier images S1–S4. We measure the relative time delay of SX–S1 to be${\displaystyle {376.0}_{-5.5}^{+5.6}}$days and the relative magnification to be${\displaystyle {0.30}_{-0.3}^{+0.5}}$. This corresponds to a 1.5% precision on the time delay and 17% precision for the magnification ratios and includes uncertainties due to millilensing and microlensing. In an accompanying paper, we place initial and blind constraints on the value of the Hubble constant.

 

Gravitational time delays provide a powerful one-step measurement of H0, independent of all other probes. One key ingredient in time-delay cosmography are high-accuracy lens models. Those are currently expensive to obtain, both, in terms of computing and investigator time (105–106 CPU hours and ∼0.5–1 yr, respectively). Major improvements in modelling speed are therefore necessary to exploit the large number of lenses that are forecast to be discovered over the current decade. In order to bypass this roadblock, we develop an automated modelling pipeline and apply it to a sample of 31 lens systems, observed by the Hubble Space Telescope in multiple bands. Our automated pipeline can derive models for 30/31 lenses with few hours of human time and <100 CPU hours of computing time for a typical system. For each lens, we provide measurements of key parameters and predictions of magnification as well as time delays for the multiple images. We characterize the cosmography-readiness of our models using the stability of differences in the Fermat potential (proportional to time delay) with respect to modelling choices. We find that for 10/30 lenses, our models are cosmography or nearly cosmography grade (<3 per cent and 3–5 per cent variations). For 6/30 lenses, the models are close to cosmography grade (5–10 per cent). These results utilize informative priors and will need to be confirmed by further analysis. However, they are also likely to improve by extending the pipeline modelling sequence and options. In conclusion, we show that uniform cosmography grade modelling of large strong lens samples is within reach.

 

Strongly lensed quasars can provide measurements of the Hubble constant (H0) independent of any other methods. One of the key ingredients is exquisite high-resolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptive-optics (AO) imaging from ground-based telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three time-delay lenses with AO imaging (RX J1131−1231, HE 0435−1223, and PG 1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck telescope, obtained as part of the Strong lensing at High Angular Resolution Program (SHARP) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat Λ cold dark matter (ΛCDM) model with fixed Ωm = 0.3, we show that by marginalizing over two different kinds of mass models (power-law and composite models) and their transformed mass profiles via a mass-sheet transformation, we obtain $\Delta t_{\rm BA}=6.89\substack{+0.8\\-0.7}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, $\Delta t_{\rm CA}=10.7\substack{+1.6\\-1.2}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, and $\Delta t_{\rm DA}=7.70\substack{+1.0\\-0.9}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, where $h=H_{0}/100\,\rm km\, s^{-1}\, Mpc^{-1}$ is the dimensionless Hubble constant and $\hat{\sigma }_{v}=\sigma ^{\rm ob}_{v}/(280\,\rm km\, s^{-1})$ is the scaled dimensionless velocity dispersion. Future measurements of time delays with 10 per cent uncertainty and velocity dispersion with 5 per cent uncertainty would yield a H0 constraint of ∼15 per cent precision.

 

The gravitationally lensed supernova Refsdal appeared in multiple images produced through gravitational lensing by a massive foreground galaxy cluster. After the supernova appeared in 2014, lens models of the galaxy cluster predicted that an additional image of the supernova would appear in 2015, which was subsequently observed. We use the time delays between the images to perform a blinded measurement of the expansion rate of the Universe, quantified by the Hubble constant (H₀). Using eight cluster lens models, we infer$H_0={64.8}_{-4.3}^{+4.4}\text{ kilometers per second per megaparsec}$. Using the two models most consistent with the observations, we find$H_0={66.6}_{-3.3}^{+4.1}\text{ kilometers per second per megaparsec}$. The observations are best reproduced by models that assign dark-matter halos to individual galaxies and the overall cluster.

 

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. 

When strong gravitational lenses are to be used as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for the uniform modeling of strongly lensed quasars withGLEE, a lens-modeling software for multiband data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the host galaxy of the lensed quasar, we obtain a model of the mass distribution of the lens galaxy. We applied this uniform modeling pipeline to a sample of nine strongly lensed quasars for which images were obtained with the Wide Field Camera 3 of theHubbleSpace Telescope. The models show well-reconstructed light components and a good alignment between mass and light centroids in most cases. We find that the automated modeling code significantly reduces the input time during the modeling process for the user. The time for preparing the required input files is reduced by a factor of 3 from ~3 h to about one hour. The active input time during the modeling process for the user is reduced by a factor of 10 from ~ 10 h to about one hour per lens system. This automated uniform modeling pipeline can efficiently produce uniform models of extensive lens-system samples that can be used for further cosmological analysis. A blind test that compared our results with those of an independent automated modeling pipeline based on the modeling softwareLenstronomyrevealed important lessons. Quantities such as Einstein radius, astrometry, mass flattening, and position angle are generally robustly determined. Other quantities, such as the radial slope of the mass density profile and predicted time delays, depend crucially on the quality of the data and on the accuracy with which the point spread function is reconstructed. Better data and/or a more detailed analysis are necessary to elevate our automated models to cosmography grade. Nevertheless, our pipeline enables the quick selection of lenses for follow-up and further modeling, which significantly speeds up the construction of cosmography-grade models. This important step forward will help us to take advantage of the increase in the number of lenses that is expected in the coming decade, which is an increase of several orders of magnitude.

 

We have measured the redshifts and single-aperture velocity dispersions of eight lens galaxies using the data collected by the Echellette Spectrograph and Imager (ESI) and Low Resolution Imaging Spectrometer (LRIS) at W.M. Keck observatory on different observing nights spread over three years (2018–2020). These results, combined with other ancillary data, such as high-resolution images of the lens systems, and time delays, are necessary to increase the sample size of the quasar-galaxy lens systems for which the Hubble constant can be measured, using the time-delay strong lensing method, hence increasing the precision of its inference. Typically, the 2D spectra of the quasar-galaxy lens systems get spatially blended due to seeing by ground-based observations. As a result, the extracted lensing galaxy (deflector) spectra become significantly contaminated by quasar light, which affects the ability to extract meaningful information about the deflector. To account for spatial blending and extract less contaminated and higher signal-to-noise ratio (S/N) 1D spectra of the deflectors, a forward modeling method has been implemented. From the extracted spectra, we have measured redshifts using prominent absorption lines and single aperture velocity dispersions using the penalized pixel fitting code pPXF. In this paper, we report the redshifts and single aperture velocity dispersions of eight lens galaxies – J0147+4630, B0445+123, B0631+519, J0659+1629, J0818−2613, J0924+0219, J1433+6007, and J1817+2729. Among these systems, six do not have previously measured velocity dispersions; for the other two, our measurements are consistent with previously reported values. Additionally, we have measured the previously unknown redshifts of the deflectors in J0818−2613 and J1817+2729 to be 0.866 ± 0.002 and 0.408 ± 0.002, respectively.

 

The importance of alternative methods for measuring the Hubble constant, such as time-delay cosmography, is highlighted by the recent Hubble tension. It is paramount to thoroughly investigate and rule out systematic biases in all measurement methods before we can accept new physics as the source of this tension. In this study, we perform a check for systematic biases in the lens modelling procedure of time-delay cosmography by comparing independent and blind time-delay predictions of the system WGD 2038−4008 from two teams using two different software programs:GLEEandLENSTRONOMY. The predicted time delays from the two teams incorporate the stellar kinematics of the deflector and the external convergence from line-of-sight structures. The un-blinded time-delay predictions from the two teams agree within 1.2σ, implying that once the time delay is measured the inferred Hubble constant will also be mutually consistent. However, there is a ∼4σdiscrepancy between the power-law model slope and external shear, which is a significant discrepancy at the level of lens models before the stellar kinematics and the external convergence are incorporated. We identify the difference in the reconstructed point spread function (PSF) to be the source of this discrepancy. When the same reconstructed PSF was used by both teams, we achieved excellent agreement, within ∼0.6σ, indicating that potential systematics stemming from source reconstruction algorithms and investigator choices are well under control. We recommend that future studies supersample the PSF as needed and marginalize over multiple algorithms or realizations for the PSF reconstruction to mitigate the systematics associated with the PSF. A future study will measure the time delays of the system WGD 2038−4008 and infer the Hubble constant based on our mass models.