Search

Strongly lensed supernovae (SNe) are a rare class of transient that can offer tight cosmological constraints that are complementary to methods from other astronomical events. We present a follow-up study of one recently-discovered strongly lensed SN, the quadruply-imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at z = 0.3544. We measure updated, template-subtracted photometry for SN Zwicky and derive improved time delays and magnifications. This is possible because SNe are transient, fading away after reaching their peak brightness. Specifically, we measure point spread function (PSF) photometry for all four images of SN Zwicky in three Hubble Space Telescope WFC3/UVIS passbands (F475W, F625W, F814W) and one WFC3/IR passband (F160W), with template images taken $\sim 11$ months after the epoch in which the SN images appear. We find consistency to within $2\sigma$ between lens model predicted time delays ($\lesssim1$ day), and measured time delays with HST colors ($\lesssim2$ days), including the uncertainty from chromatic microlensing that may arise from stars in the lensing galaxy. The standardizable nature of SNe Ia allows us to estimate absolute magnifications for the four images, with images A and C being elevated in magnification compared to lens model predictions by about $6\sigma$ and $3\sigma$ respectively, confirming previous work. We show that millilensing or differential dust extinction is unable to explain these discrepancies and find evidence for the existence of microlensing in images A, C, and potentially D, that may contribute to the anomalous magnification., Comment: Submitted to ApJ

We obtain spatially resolved kinematics with the Keck Cosmic Web Imager (KCWI) integral-field spectrograph for a sample of 14 massive (11 < log10 M* < 12) lensing early-type galaxies (ETGs) at redshifts z=0.15-0.35 from the Sloan Lens ACS (SLACS) survey. We integrate within the galaxy effective radius and examine the rotational and dispersion velocities, showing that 11/14 are quantitatively classified as slow rotators in comparison with local galaxy surveys. Of key interest is the ability of this data to enable the precision required for cosmological inference with lensing time delays on scales of 1-2% uncertainty. The dataset is unprecedented for galaxy-scale lens galaxies, in terms of signal-to-noise ratio, sampling, and calibration. We test sources of systematic error and identify primary contributions from choice of stellar template library and wavelength range of the spectral fit. Systematics are quantified at the spatial bin level, resulting in systematic error at 3% and positive spatial covariance of 2%. We examine the effects of integration of the kinematic maps within circular apertures of different sizes and compare with SDSS single-aperture velocity dispersions. The most recent velocity dispersion estimates from SDSS spectra are found to be biased by a factor of 5.3% with respect to KCWI data, and to underestimate uncertainties. We examine correlations between scaling relations and show the correlations to agree with previous SLACS analysis with no statistically significant disagreement. A follow-up paper will present Jeans modeling and discuss the context of these observations within broader studies of galaxy evolution and cosmology., Comment: 33 pages, 14 figures, submitted for publication in ApJ

We present a new measurement of the dark and luminous matter distribution of massive elliptical galaxies, and their evolution with redshift, by combining strong lensing and dynamical observables. Our sample of 58 lens galaxies covers a redshift range of $0.090\leq z_{\rm l}\leq0.884$. By combining new Hubble Space Telescope imaging with previously observed velocity dispersion and line-of-sight measurements, we decompose the luminous matter profile from the dark matter profile and perform a Bayesian hierarchical analysis to constrain the population-level properties of both profiles. We find that the inner slope of the dark matter density profile ("cusp"; $\rho_{\rm DM}\propto r^{-\gamma_{\rm in}}$) is slightly steeper ($\mu_{\gamma_{\rm in}}=1.18^{+0.03}_{-0.03}$ at $z=0.35$ with $\leq0.16$ intrinsic scatter) than a standard Navarro$-$Frenk$-$White (NFW; $\gamma_{\rm in}=1$), with an appreciable evolution with redshift ($d\log(\gamma_{\rm in})/dz=-0.33\pm0.13$) and is consistent with NFW-like distributions at higher redshifts ($z\geq0.56$ for $\leq1\sigma$ consistency). Additionally, we find the stellar mass-to-light ratio at the population level consistent with that of a Salpeter initial mass function, a small stellar mass-to-light gradient ($\kappa_{*}(r)\propto r^{-\eta}$, with $\overline{\eta}\leq9.4\times10^{-3}$), and isotropic stellar orbits. Our averaged total mass density profile is consistent with a power-law profile within $0.25-4$ Einstein radii ($\overline{\gamma}=2.14\pm0.06$), with an internal mass-sheet transformation parameter $\overline{\lambda}=1.02\pm0.01$ consistent with no mass sheet. Our findings confirm the validity of the standard mass models used for time-delay cosmography. However, our results are in strong tension with predictions from hydrodynamical simulations such as IllustrisTNG, highlighting the need to better understand the formation of massive galaxies., Comment: 28 pages, 20 figures

Like many areas of astrophysics and cosmology, the Vera C. Rubin Observatory will be transformational for almost all the applications of strong lensing, thanks to the dramatic increase in the number of known strong lenses by two orders of magnitude or more and the readily available time-domain data for the lenses with transient sources. In this article, we provide an overview of the forecasted number of discovered lenses of different types and describe the primary science cases these large lens samples will enable. We provide an updated forecast on the joint constraint for the dark energy equation-of-state parameters, $w_0$ and $w_a$, from combining all strong lensing probes of dark energy. We update the previous forecast from the Rubin Observatory Dark Energy Science Collaboration's Science Review Document by adding two new crucial strong lensing samples: lensed Type Ia supernovae and single-deflector lenses with measured stellar kinematics. Finally, we describe the current and near-future activities and collaborative efforts within the strong lensing community in preparation for the arrival of the first real dataset from Rubin in early 2026., Comment: 12 pages, 2 figures. Invited review for the Royal Society meeting "Multi-messenger Gravitational Lensing", submitted to Philosophical Transactions A. This version: updated references

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant ($H_{0}$). 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 obtain $D_{\Delta t} = 1.68^{+0.40}_{-0.38}$ Gpc 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 $\Lambda$CDM cosmology, we constrain the Hubble constant to be $H_{0} = 65^{+23}_{-14}\, \rm km\ s^{-1}\,Mpc^{-1}$. 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 the Vera C. Rubin Observatory'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., Comment: 8 pages, 5 figures, 3 tables; accepted for publication in Astronomy & Astrophysics

Observed evolution of the total mass distribution with redshift is crucial to testing galaxy evolution theories. To measure the total mass distribution, strong gravitational lenses complement the resolved dynamical observations currently limited to $z \lesssim 0.5$. Here we present the lens models for a pilot sample of seven galaxy-scale lenses from the ASTRO3D Galaxy Evolution with Lenses (AGEL) survey. The AGEL lenses, modeled using HST/WFC3-F140W images with Gravitational Lens Efficient Explorer (GLEE) software, have deflector redshifts between $0.3 < z_{\rm defl} < 0.9$. Assuming a power-law density profile with slope $\gamma$, we measure the total density profile for the deflector galaxies via lens modeling. We also measure the stellar velocity dispersions ($\sigma_{\rm obs}$) for four lenses and obtain $\sigma_{\rm obs}$ from SDSS-BOSS for the remaining lenses to test our lens models by comparing observed and model-predicted velocity dispersions. For the seven AGEL lenses, we measure an average density profile slope of $-1.95 \pm 0.09$ and a $\gamma$--$z$ relation that does not evolve with redshift at $z<1$. Although our result is consistent with some observations and simulations, it differs from other studies at $z<1$ that suggest the $\gamma$--$z$ relation evolves with redshift. The apparent conflicts among observations and simulations may be due to a combination of 1) systematics in the lensing and dynamical modeling; 2) challenges in comparing observations with simulations; and 3) assuming a simple power-law for the total mass distribution. By providing more lenses at $z_{\rm defl} > 0.5$, the AGEL survey will provide stronger constraints on whether the mass profiles evolve with redshift as predicted by current theoretical models., Comment: Accepted for publication in the Astrophysical Journal (ApJ) 24 Pages, 8 Figures, 3 Tables

A bright ($m_{\rm F150W,AB}$=24 mag), $z=1.95$ supernova (SN) candidate was discovered in JWST/NIRCam imaging acquired on 2023 November 17. The SN is quintuply-imaged as a result of strong gravitational lensing by a foreground galaxy cluster, detected in three locations, and remarkably is the second lensed SN found in the same host galaxy. The previous lensed SN was called "Requiem", and therefore the new SN is named "Encore". This makes the MACS J0138.0$-$2155 cluster the first known system to produce more than one multiply-imaged SN. Moreover, both SN Requiem and SN Encore are Type Ia SNe (SNe Ia), making this the most distant case of a galaxy hosting two SNe Ia. Using parametric host fitting, we determine the probability of detecting two SNe Ia in this host galaxy over a $\sim10$ year window to be $\approx3\%$. These observations have the potential to yield a Hubble Constant ($H_0$) measurement with $\sim10\%$ precision, only the third lensed SN capable of such a result, using the three visible images of the SN. Both SN Requiem and SN Encore have a fourth image that is expected to appear within a few years of $\sim2030$, providing an unprecedented baseline for time-delay cosmography., Comment: Accepted, ApJL

Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy-galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian Random Field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favoring a high frequency power spectrum across our lens population., Comment: 23 pages, 22 figures

We study the spatially resolved outflow properties of CSWA13, an intermediate mass ($M_*=10^{9}~\mathrm{M}_{\odot}$), gravitationally lensed star-forming galaxy at $z=1.87$. We use Keck/KCWI to map outflows in multiple rest-frame ultraviolet ISM absorption lines, along with fluorescent Si II$^*$ emission, and nebular emission from C III] tracing the local systemic velocity. The spatial structure of outflow velocity mirrors that of the nebular kinematics, which we interpret to be a signature of a young galactic wind that is pressurizing the ISM of the galaxy but is yet to burst out. From the radial extent of Si II$^*$ emission, we estimate that the outflow is largely encapsulated within $3.5$ kpc. We explore the geometry (e.g., patchiness) of the outflow by measuring the covering fraction at different velocities, finding that the maximum covering fraction is at velocities $v\simeq-150$ km$\,$s$^{-1}$. Using the outflow velocity ($v_{out}$), radius ($R$), column density ($N$), and solid angle ($\Omega$) based on the covering fraction, we measure the mass loss rate $\log\dot{m}_{out}/(\mathrm{M}_{\odot}\text{yr}^{-1}) = 1.73\pm0.23$ and mass loading factor $\log\eta = 0.04\pm0.34$ for the low-ionization outflowing gas in this galaxy. These values are relatively large and the bulk of the outflowing gas is moving with speeds less than the escape velocity of the galaxy halo, suggesting that the majority of outflowing mass will remain in the circumgalactic medium and/or recycle back into the galaxy. The results support a picture of high outflow rates transporting mass and metals into the inner circumgalactic medium, providing the gas reservoir for future star formation., Comment: Submitted to ApJ. Comments welcome (17 pages, 10 figures, 1 table)

The mass distribution in massive elliptical galaxies encodes their evolutionary history, thus providing an avenue to constrain the baryonic astrophysics in their evolution. The power-law assumption for the radial mass profile in ellipticals has been sufficient to describe several observables to the noise level, including strong lensing and stellar dynamics. In this paper, we quantitatively constrained any deviation, or the lack thereof, from the power-law mass profile in massive ellipticals through joint lensing-dynamics analysis of a large statistical sample with 77 galaxy-galaxy lens systems. We performed an improved and uniform lens modelling of these systems from archival Hubble Space Telescope imaging using the automated lens modelling pipeline dolphin. We combined the lens model posteriors with the stellar dynamics to constrain the deviation from the power law after accounting for the line-of-sight lensing effects, a first for analyses on galaxy-galaxy lenses. We find that the Sloan Lens ACS Survey (SLACS) lens galaxies with a mean redshift of 0.2 are consistent with the power-law profile within 1.1$\sigma$ (2.8$\sigma$) and the Strong Lensing Legacy Survey (SL2S) lens galaxies with a mean redshift of 0.6 are consistent within 0.8$\sigma$ (2.1$\sigma$), for a spatially constant (Osipkov-Merritt) stellar anisotropy profile. We adopted the spatially constant anisotropy profile as our baseline choice based on previous dynamical observables of local ellipticals. However, spatially resolved stellar kinematics of lens galaxies are necessary to differentiate between the two anisotropy models. Future studies will use our lens models to constrain the mass distribution individually in the dark matter and baryonic components., Comment: 31 pages, 20 figures, 9 tables. This version: accepted to MNRAS

Galaxy-scale strong lensing is a powerful tool in Astrophysics and Cosmology, enabling studies of massive galaxies' internal structure, their formation and evolution, stellar initial mass function, and cosmological parameters. In this conference proceeding, we highlight key findings from the past decade in astrophysical applications of strong lensing at the galaxy scale. We then briefly summarize the present status of discovery and analyses of new samples from recent or ongoing surveys. Finally, we offer insights into anticipated developments in the upcoming era of big data shaping the future of this field, thanks to the Rubin, Euclid, and Roman observatories., Comment: Invited review for the Proceedings of IAU Symposium 381: "Strong gravitational lensing in the era of Big Data", H. Stacey, C. Grillo, and A. Sonnenfeld eds. 7 pages, 4 figures

Galaxy-scale gravitational lenses are often modeled with two-component mass profiles where one component represents the stellar mass and the second is an NFW profile representing the dark matter. Outside of the spherical case, the NFW profile is costly to implement, and so it is approximated via two different methods; ellipticity can be introduced via the lensing potential (NFWp) or via the mass by approximating the NFW profile as a sum of analytical profiles (NFWm). While the NFWp method has been the default for lensing applications, it gives a different prescription of the azimuthal structure, which we show introduces ubiquitous gradients in ellipticity and boxiness in the mass distribution rather than having a constant elliptical shape. Because unmodeled azimuthal structure has been shown to be able to bias lens model results, we explore the degree to which this introduced azimuthal structure can affect the model accuracy. We construct input profiles using composite models using both the NFWp and NFWm methods and fit these mocks with a power-law elliptical mass distribution (PEMD) model with external shear. As a measure of the accuracy of the recovered lensing potential, we calculate the value of the Hubble parameter $H_0$ one would determine from the lensing fit. We find that the fits to the NFWp input return $H_0$ values which are systematically biased by about $3\%$ lower than the NFWm counterparts. We explore whether such an effect is attributable to the mass sheet transformation (MST) by using an MST-independent quantity, $\xi_2$. We show that, as expected, the NFWm mocks are degenerate with PEMD through an MST. For the NFWp, an additional bias is found beyond the MST due to azimuthal structures {\it exterior to the Einstein radius}. We recommend modelers use an NFWm prescription in the future, such that azimuthal structure can be introduced explicitly rather than implicitly., Comment: 15 pages, 8 figures

Time delays from strong gravitational lensing provide a one-step absolute distance measurement. Thus, they measure $H_0$ independently of all other probes. We first review the foundations and history of time-delay cosmography. Then, we illustrate the current state of the art by means of two recent case studies that have been real breakthroughs: i) the quadruply imaged quasar lensed by a galaxy-scale deflector RXJ1131$-$1231, for which spatially resolved stellar kinematics is available; ii) the multiply imaged supernova "Refsdal", the first with measured time delays, lensed by cluster MACS1149.5$+$2223. We conclude by discussing the exciting future prospects of time-delay cosmography in the coming decade., Comment: Invited chapter for the edited book "Hubble Constant Tension" (Eds. E. Di Valentino and D. Brout, Springer Singapore, expected in 2024)

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, $\alpha_{sps}$, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of $0.5''$, the strong lensing bias in $\alpha_{sps}$ is $10\%$, while that in the central dark matter mass is $5\%$. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. Time-delay measurements of $H_0$ from lensed quasars can take advantage of prior information obtained from galaxy-galaxy lenses with similar Einstein radii., Comment: Published on Astronomy & Astrophysics. A two-minute summary video of this paper is available at https://youtu.be/UmS9jRHTmZU

Strong-lensing time delays enable 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 $D_{\rm d} = 865_{-81}^{+85}$ Mpc and the time-delay distance $D_{\Delta t} = 2180_{-271}^{+472}$ Mpc, giving $H_0 = 77.1_{-7.1}^{+7.3}$ km s$^{-1}$ Mpc$^{-1}$ - for a flat $\Lambda$ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the 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 ($H_0 = 78.3^{+3.4}_{-3.3}$ 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., Comment: 21 pages, 22 figures, 1 table. Accepted by A&A (this version: language improvements only)

Supernovae (SNe) that have been multiply-imaged by gravitational lensing are rare and powerful probes for cosmology. Each detection is an opportunity to develop the critical tools and methodologies needed as the sample of lensed SNe increases by orders of magnitude with the upcoming Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope. The latest such discovery is of the quadruply-imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at $z=0.3544$. SN Zwicky was discovered by the Zwicky Transient Facility (ZTF) in spatially unresolved data. Here we present follow-up Hubble Space Telescope observations of SN Zwicky, the first from the multi-cycle "LensWatch" program. We measure photometry for each of the four images of SN Zwicky, which are resolved in three WFC3/UVIS filters (F475W, F625W, F814W) but unresolved with WFC3/IR~F160W, and present an analysis of the lensing system using a variety of independent lens modeling methods. We find consistency between lens model predicted time delays ($\lesssim1$ day), and delays estimated with the single epoch of HST colors ($\lesssim3.5$ days), including the uncertainty from chromatic microlensing ($\sim1$-$1.5$ days). Our lens models converge to an Einstein radius of $\theta_E=(0.168^{+0.009}_{-0.005})\prime\prime$, the smallest yet seen in a lensed SN system. The "standard candle" nature of SN Zwicky provides magnification estimates independent of the lens modeling that are brighter than predicted by $\sim1.7^{+0.8}_{-0.6}$mag and $\sim0.9^{+0.8}_{-0.6}$mag for two of the four images, suggesting significant microlensing and/or additional substructure beyond the flexibility of our image-position mass models.

Multiply lensed sources experience a relative time delay in the arrival of photons. This effect can be used to measure absolute distances and the Hubble constant ($H_0$) and is known as time-delay cosmography. The methodology is independent of the local distance ladder and early-universe physics and provides a precise and competitive measurement of $H_0$. With upcoming observatories, time-delay cosmography can provide a 1% precision measurement of $H_0$ and can decisively shed light on the current reported 'Hubble tension'. This paper presents the theoretical background and the current techniques applied for time-delay cosmographic studies and the measurement of the Hubble constant. The paper describes the challenges and systematics in the different components of the analysis and strategies to mitigate them. The current measurements are discussed in context and the opportunities with the anticipated data sets in the future are laid out., Comment: 30 pages, 11 figures, accepted to Space Science Reviews, Topical Collection 'Strong Gravitational Lensing', eds. J. Wambsganss et al

We perform a search for galaxy-galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey (DELVE), which contains $\sim 520$ million astronomical sources covering $\sim 4,000$ $\mathrm{deg}^2$ of the southern sky to a $5\sigma$ point-source depth of $g=24.3$, $r=23.9$, $i=23.3$, and $z=22.8$ mag. Following the methodology of similar searches using DECam data, we apply color and magnitude cuts to select a catalog of $\sim 11$ million extended astronomical sources. After scoring with our CNN, the highest scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (definitely not a lens) to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap ($b > 10$ deg) and southern celestial hemisphere (${\rm Dec.}<0$ deg), our candidate list has little overlap with other existing ground-based searches. Where our search footprint does overlap with other searches, we find a significant number of high-quality candidates which were previously unidentified, indicating a degree of orthogonality in our methodology. We report properties of our candidates including apparent magnitude and Einstein radius estimated from the image separation., Comment: 24 pages; published version (ApJ)

Strong gravitational lensing at the galaxy scale is a valuable tool for various applications in astrophysics and cosmology. The primary uses of galaxy-scale lensing are to study elliptical galaxies' mass structure and evolution, constrain the stellar initial mass function, and measure cosmological parameters. Since the discovery of the first galaxy-scale lens in the 1980s, this field has made significant advancements in data quality and modeling techniques. In this review, we describe the most common methods for modeling lensing observables, especially imaging data, as they are the most accessible and informative source of lensing observables. We then summarize the primary findings from the literature on the astrophysical and cosmological applications of galaxy-scale lenses. We also discuss the current limitations of the data and methodologies and provide an outlook on the expected improvements in both areas in the near future., Comment: Submitted to Space Science Reviews, Topical Collection "Strong Gravitational Lensing", eds. J. Wambsganss et al. This version: updated after peer review

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 $0.866 \pm 0.002$ and $0.408 \pm 0.002$, respectively., Comment: 13 pages, 6 figures, 3 tables; accepted in A&A

To use strong gravitational lenses as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for uniform modeling of strongly lensed quasars with GLEE, a lens modeling software, for high-resolution multi-band data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the lensed quasar host galaxy, we obtain a model of the mass distribution of the lens galaxy. We apply this uniform modeling pipeline to a sample of nine strongly lensed quasars with HST WFC 3 images. The models show in most cases well reconstructed light components and a good alignment between mass and light centroids. We find that the automated modeling code significantly reduces the user input time during the modeling process. The preparation time of required input files is reduced significantly. This automated modeling pipeline can efficiently produce uniform models of extensive lens system samples which can be used for further cosmological analysis. A blind test through a comparison with the results of an independent automated modeling pipeline based on the modeling software Lenstronomy reveals important lessons. Quantities such as Einstein radius, astrometry, mass flattening and position angle are generally robustly determined. Other quantities depend crucially on the quality of the data and the accuracy of the PSF reconstruction. Better data and/or more detailed analysis will be necessary to elevate our automated models to cosmography grade. Nevertheless, our pipeline enables the quick selection of lenses for follow-up monitoring and further modeling, significantly speeding up the construction of cosmography-grade models. This is an important step forward to take advantage of the orders of magnitude increase in the number of lenses expected in the coming decade., Comment: 37 pages, 14 figures, published in A&A

Gravitational time delays provide a powerful one step measurement of $H_0$, 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 (10$^{5-6}$ CPU hours and $\sim$ 0.5-1 year, respectively). Major improvements in modeling 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, building on the work by Shajib et al. (2019), we develop an automated modeling pipeline and apply it to a sample of 30 quadruply imaged quasars and one lensed compact galaxy, 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 Fermat potential (proportional to time delay) w.r.t. modeling choices. We find that for 10/30 lenses our models are cosmography or nearly cosmography grade (<3% and 3-5% variations). For 6/30 lenses the models are close to cosmography grade (5-10%). These results are based on informative priors and will need to be confirmed by further analysis. However, they are also likely to improve by extending the pipeline modeling sequence and options. In conclusion, we show that uniform cosmography grade modeling of large strong lens samples is within reach., Comment: 40 pages, 24 figures, 11 tables. Submitted to MNRAS

Gravitationally lensed supernovae (LSNe) are important probes of cosmic expansion, but they remain rare and difficult to find. Current cosmic surveys likely contain and 5-10 LSNe in total while next-generation experiments are expected to contain several hundreds to a few thousands of these systems. We search for these systems in observed Dark Energy Survey (DES) 5-year SN fields -- 10 3-sq. deg. regions of sky imaged in the $griz$ bands approximately every six nights over five years. To perform the search, we utilize the DeepZipper approach: a multi-branch deep learning architecture trained on image-level simulations of LSNe that simultaneously learns spatial and temporal relationships from time series of images. We find that our method obtains a LSN recall of 61.13% and a false positive rate of 0.02% on the DES SN field data. DeepZipper selected 2,245 candidates from a magnitude-limited ($m_i$ $<$ 22.5) catalog of 3,459,186 systems. We employ human visual inspection to review systems selected by the network and find three candidate LSNe in the DES SN fields., Comment: Accepted by ApJ

Imaging data is the principal observable required to use galaxy-scale strong lensing in a multitude of applications in extragalactic astrophysics and cosmology. In this paper, we develop Lensing Exposure Time Calculator (LensingETC) to optimize the efficiency of telescope time usage when planning multi-filter imaging campaigns for galaxy-scale strong lenses. This tool simulates realistic data tailored to specified instrument characteristics and then automatically models them to assess the power of the data in constraining lens model parameters. We demonstrate a use case of this tool by optimizing a two-filter observing strategy (in IR and UVIS) within the limited exposure time per system allowed by a Hubble Space Telescope (HST) Snapshot program. We find that higher resolution is more advantageous to gain constraining power on the lensing observables, when there is a trade-off between signal-to-noise ratio and resolution; e.g., between the UVIS and IR filters of the HST. We also find that, whereas a point spread function (PSF) with sub-Nyquist sampling allows the sample mean for a model parameter to be robustly recovered for both galaxy-galaxy and point-source lensing systems, a sub-Nyquist sampled PSF introduces a larger scatter than a Nyquist sampled one in the deviation from the ground truth for point-source lens systems., Comment: 10 pages, 7 figures, 3 tables

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: GLEE and LENSTRONOMY. 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 $1.2\sigma$, implying that once the time delay is measured the inferred Hubble constant will also be mutually consistent. However, there is a $\sim$4$\sigma$ discrepancy 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 $\sim$0.6$\sigma$, 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., Comment: Accepted version by A&A. 34 pages, 26 figures, 3 tables

The dominant uncertainty in the current measurement of the Hubble constant ($H_0$) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a dataset of SNe that are not strongly lensed and a dataset of strongly lensed SNe with measured time delays. We jointly constrain (i) $H_0$ using the time delays as an absolute distance indicator, (ii) the lens model profiles using the magnification ratio of lensed and unlensed fluxes on the population level and (iii) the unlensed apparent magnitude distribution of the SNe population and the redshift-luminosity relation of the relative expansion history of the Universe. We apply our joint inference framework on a future expected data set of glSNe, and forecast that a sample of 144 glSNe of Type~Ia with well measured time series and imaging data will measure $H_0$ to 1.5\%. We discuss strategies to mitigate systematics associated with using absolute flux measurements of glSNe to constrain the mass density profiles. Using the magnification of SNe images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and \textit{Roman} observatories, will be able to discover the necessary number of glSNe, and with additional follow-up observations this methodology will provide precise constraints on mass profiles and $H_0$., Comment: 23 pages, 7 figures, to be submitted to AAS journal. comments welcome

lenstronomy is an Astropy-affiliated Python package for gravitational lensing simulations and analyses. lenstronomy was introduced by Birrer and Amara (2018) and is based on the linear basis set approach by Birrer et a. (2015). The user and developer base of lenstronomy has substantially grown since then, and the software has become an integral part of a wide range of recent analyses, such as measuring the Hubble constant with time-delay strong lensing or constraining the nature of dark matter from resolved and unresolved small scale lensing distortion statistics. The modular design has allowed the community to incorporate innovative new methods, as well as to develop enhanced software and wrappers with more specific aims on top of the lenstronomy API. Through community engagement and involvement, lenstronomy has become a foundation of an ecosystem of affiliated packages extending the original scope of the software and proving its robustness and applicability at the forefront of the strong gravitational lensing community in an open source and reproducible manner., Comment: published by JOSS. Software available at https://github.com/sibirrer/lenstronomy. Comments, issues and pull requests welcome!

Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant ($H_0$) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: the lensed host galaxy can be observed before or after the transient's appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock datasets of 48 quasar lensing systems (i.e., adding AGN in the galaxy center) and 48 galaxy-galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and $H_0$. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of $H_0$ precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which in turn plays a key role in breaking the mass-sheet degeneracy and constraining $H_0$., Comment: 9 pages, 4 figures, MNRAS accepted, comments welcome

We report upon three years of follow-up and confirmation of doubly imaged quasar lenses through imaging campaigns from 2016-2018 with the Near-Infrared Camera2 (NIRC2) on the W. M. Keck Observatory. A sample of 57 quasar lens candidates are imaged in adaptive-optics-assisted or seeing-limited $K^\prime$-band observations. Out of these 57 candidates, 15 are confirmed as lenses. We form a sample of 20 lenses adding in a number of previously-known lenses that were imaged with NIRC2 in 2013-14 as part of a pilot study. By modelling these 20 lenses, we obtain $K^\prime$-band relative photometry and astrometry of the quasar images and the lens galaxy. We also provide the lens properties and predicted time delays to aid planning of follow-up observations necessary for various astrophysical applications, e.g., spectroscopic follow-up to obtain the deflector redshifts for the newly confirmed systems. We compare the departure of the observed flux ratios from the smooth-model predictions between doubly and quadruply imaged quasar systems. We find that the departure is consistent between these two types of lenses if the modelling uncertainty is comparable., Comment: 11 pages, 8 figures, 5 tables. This version: accepted to MNRAS

We investigate the internal structure of elliptical galaxies at $z\sim 0.2$ from a joint lensing-dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy-galaxy lenses selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median $2.08\pm0.03$ and intrinsic scatter $0.13 \pm 0.02$, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) halos. We find that the DM halos are well described by a standard Navarro-Frenk-White halo with no contraction on average for both of a constant stellar mass-to-light ratio ($M/L$) model and a stellar $M/L$ gradient model. For the $M/L$ gradient model, we find that most galaxies are consistent with no $M/L$ gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM halos., Comment: 26 pages, 19 figures, 3 tables. This version: accepted to MNRAS

The current cosmological probes have provided a fantastic confirmation of the standard $\Lambda$ Cold Dark Matter cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the $4.4\sigma$ tension between the Planck estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting new physics models that could solve this tension and discuss how the next decade experiments will be crucial., Comment: Snowmass2021 - Letter of Interest

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $\Lambda$CDM model., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant $H_0$ value, the $\sigma_8 - S_8$ tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth, that will be of crucial importance to address all these questions., Comment: Snowmass2021 - Letter of Interest

The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in $H_0$. We quantify any potential effect of the MST with flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by stellar kinematics. The approach is validated on hydrodynamically simulated lenses. We apply the method to the TDCOSMO sample of 7 lenses (6 from H0LiCOW) and measure $H_0=74.5^{+5.6}_{-6.1}$ km s$^{-1}{\rm Mpc}^{-1}$. In order to further constrain the deflector mass profiles, we then add imaging and spectroscopy for 33 strong gravitational lenses from the SLACS sample. For 9 of the SLAC lenses we use resolved kinematics to constrain the stellar anisotropy. From the joint analysis of the TDCOSMO+SLACS sample, we measure $H_0=67.4^{+4.1}_{-3.2}$ km s$^{-1}{\rm Mpc}^{-1}$, assuming that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. While our new analysis does not statistically invalidate the mass profile assumptions by H0LiCOW, and thus their $H_0$ measurement relying on those, it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on $H_0$ derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data, chiefly spatially resolved kinematics of lens galaxies., Comment: accepted by A&A. Full analysis available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public updated permanent analysis script links

In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant $H_0$. However, published state-of-the-art analyses require of order 1 year of expert investigator time and up to a million hours of computing time per system. Furthermore, as precision improves, it is crucial to identify and mitigate systematic uncertainties. With this time delay lens modelling challenge we aim to assess the level of precision and accuracy of the modelling techniques that are currently fast enough to handle of order 50 lenses, via the blind analysis of simulated datasets. The results in Rung 1 and Rung 2 show that methods that use only the point source positions tend to have lower precision ($10 - 20\%$) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic datasets can recover $H_0$ within the target accuracy ($ |A| < 2\%$) and precision ($< 6\%$ per system), even in the presence of poorly known point spread function and complex source morphology. A post-unblinding analysis of Rung 3 showed the numerical precision of the ray-traced cosmological simulations to be insufficient to test lens modelling methodology at the percent level, making the results difficult to interpret. A new challenge with improved simulations is needed to make further progress in the investigation of systematic uncertainties. For completeness, we present the Rung 3 results in an appendix, and use them to discuss various approaches to mitigating against similar subtle data generation effects in future blind challenges., Comment: 23 pages, 12 figures, 6 tables, MNRAS accepted

In time-delay cosmography, three of the key ingredients are 1) determining the velocity dispersion of the lensing galaxy, 2) identifying galaxies and groups along the line of sight with sufficient proximity and mass to be included in the mass model, and 3) estimating the external convergence $\kappa_\mathrm{ext}$ from less massive structures that are not included in the mass model. We present results on all three of these ingredients for two time-delay lensed quasar systems, DES J0408-5354 and WGD 2038-4008. We use the Gemini, Magellan and VLT telescopes to obtain spectra to both measure the stellar velocity dispersions of the main lensing galaxies and to identify the line-of-sight galaxies in these systems. Next, we identify 10 groups in DES J0408-5354 and 2 groups in WGD 2038-4008using a group-finding algorithm. We then identify the most significant galaxy and galaxy-group perturbers using the "flexion shift" criterion. We determine the probability distribution function of the external convergence $\kappa_\mathrm{ext}$ for both of these systems based on our spectroscopy and on the DES-only multiband wide-field observations. Using weighted galaxy counts, calibrated based on the Millennium Simulation, we find that DES J0408-5354 is located in a significantly underdense environment, leading to a tight (width $\sim3\%$), negative-value $\kappa_\mathrm{ext}$ distribution. On the other hand, WGD 2038-4008 is located in an environment of close to unit density, and its low source redshift results in a much tighter $\kappa_\mathrm{ext}$ of $\sim1\%$, as long as no external shear constraints are imposed., Comment: 40 pages, 18 figures Added missing author to the author list

Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, $H_0$. As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic change of 10% of measured velocity dispersion leads to only a 0.7% shift on $H_0$ from the seven lenses analyzed by TDCOSMO. Second, we find no bias to arise from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in $H_0$ values. However, the TDCOSMO procedures that model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the "bulge-halo" conspiracy, $H_0$ is recovered precisely and accurately by both models. If the two models disagree, as in the case of some pathological models illustrated here, the TDCOSMO procedure either discriminates between them through the goodness of fit, or it accounts for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of six of the TDCOSMO (real) lenses: the composite model yields $74.0^{+1.7}_{-1.8}$ $km.s^{-1}.Mpc^{-1}$, while the power-law model yields $H_0=74.2^{+1.6}_{-1.6}$ $km.s^{-1}.Mpc^{-1}$. In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO., Comment: 19 pages, 9 figures, 4 tables, published in A&A

We present a blind time-delay cosmographic analysis for the lens system DES J0408$-$5354. This system is extraordinary for the presence of two sets of multiple images at different redshifts, which provide the opportunity to obtain more information at the cost of increased modelling complexity with respect to previously analyzed systems. We perform detailed modelling of the mass distribution for this lens system using three band Hubble Space Telescope imaging. We combine the measured time delays, line-of-sight central velocity dispersion of the deflector, and statistically constrained external convergence with our lens models to estimate two cosmological distances. We measure the "effective" time-delay distance corresponding to the redshifts of the deflector and the lensed quasar $D_{\Delta t}^{\rm eff}=3382^{+146}_{-115}$ Mpc and the angular diameter distance to the deflector $D_{\rm d}=1711^{+376}_{-280}$ Mpc, with covariance between the two distances. From these constraints on the cosmological distances, we infer the Hubble constant $H_0 = 74.2^{+2.7}_{-3.0}$ km s$^{-1}$ Mpc$^{-1}$ assuming a flat $\Lambda$CDM cosmology and a uniform prior for $\Omega_{\rm m}$ as $\Omega_{\rm m} \sim \mathcal{U}(0.05, 0.5)$. This measurement gives the most precise constraint on $H_0$ to date from a single lens. Our measurement is consistent with that obtained from the previous sample of six lenses analyzed by the $H_0$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) collaboration. It is also consistent with measurements of $H_0$ based on the local distance ladder, reinforcing the tension with the inference from early Universe probes, for example, with 2.2$\sigma$ discrepancy from the cosmic microwave background measurement., Comment: 32 pages, 17 figures, 10 tables. Accepted by MNRAS

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $\Lambda$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1\sigma$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3\sigma$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $\Lambda$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $\Lambda$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints., Comment: Accepted for publication in MNRAS; 23 pages, 13 figures, 8 tables

We present the measurement of the Hubble Constant, $H_0$, with three strong gravitational lens systems. We describe a blind analysis of both PG1115+080 and HE0435-1223 as well as an extension of our previous analysis of RXJ1131-1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL measured time delays in these systems to determine $H_{0}$. We do both an AO-only and an AO+HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rm km\,s^{-1}\,Mpc^{-1}$ for PG1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rm km\,s^{-1}\,Mpc^{-1}$ for HE0435-1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rm km\,s^{-1}\,Mpc^{-1}$ for RXJ1131-1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\,s^{-1}\,Mpc^{-1}$. The joint result of the AO+HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rm km\,s^{-1}\,Mpc^{-1}$. All of the above results assume a flat $\Lambda$ cold dark matter cosmology with a uniform prior on $\Omega_{\textrm{m}}$ in [0.05, 0.5] and $H_{0}$ in [0, 150] $\rm km\,s^{-1}\,Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of $H_0$. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper., Comment: 33 pages, 23 figures

We demonstrate an efficient method to compute the strong-gravitational-lensing deflection angle and magnification for any elliptical surface-density profile. This method solves a numerical hurdle in lens modelling that has lacked a general solution for nearly three decades. The hurdle emerges because it is prohibitive to derive analytic expressions of the lensing quantities for most elliptical mass profiles. In our method, we first decompose an elliptical mass profile into Gaussian components. We introduce an integral transform that provides us with a fast and accurate algorithm for the Gaussian decomposition. We derive analytic expressions of the lensing quantities for a Gaussian component. As a result, we can compute these quantities for the total mass profile by adding up the contributions from the individual components. This lensing analysis self-consistently completes the kinematic description in terms of Gaussian components presented by Cappellari (2008). Our method is general without extra computational burden unlike other methods currently in use., Comment: 11 pages + appendices, 6 figures, submitted to MNRAS. An interactive jupyter notebook version of this paper is accessible on Google colab at https://colab.research.google.com/drive/10jw5T07mhvdP0hp60HqVqNqWK49Cfzby

Context. The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constant $H_0$, is one of the most pressing challenges in modern cosmology. Assuming flat $\Lambda$CDM, $H_0$ inference at high redshift using cosmic-microwave-background data from Planck disagrees at the 4.4$\sigma$ level with measurements based on the local distance ladder made up of parallaxes, Cepheids and Type Ia supernovae (SNe Ia), often referred to as "Hubble tension". Independent, cosmological-model-insensitive ways to infer $H_0$ are of critical importance. Aims. We apply an inverse-distance-ladder approach, combining strong-lensing time-delay-distance measurements with SN Ia data. By themselves, SNe Ia are merely good relative distance indicators, but by anchoring them to strong gravitational lenses one can obtain an $H_0$ measurement that is relatively insensitive to other cosmological parameters. Methods. A cosmological parameter estimate is performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets. Results. The cosmological-model dependence of strong-lensing $H_0$ measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferred $H_0$ consistently lies around 73-74 km s$^{-1}$ Mpc$^{-1}$, regardless of the assumed cosmological background model. Our results agree nicely with those from the local distance ladder, but there is a >2$\sigma$ tension with Planck results, and a ~1.5$\sigma$ discrepancy with results from an inverse distance ladder including Planck, Baryon Acoustic Oscillations and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties in $H_0$ from our inverse distance ladder., Comment: 5 pages, 3 figures, A&A letters accepted version

We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033-4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 years of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution $\textit{Hubble Space Telescope}$ imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average precision of $6.6\%$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat $\Lambda$CDM cosmology with a uniform prior on $\Omega_\mathrm{m}$ in the range [0.05, 0.5]. This work is part of the $H_0$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII)., Comment: Version accepted by MNRAS. 29 pages including appendix, 17 figures, 6 tables. arXiv admin note: text overlap with arXiv:1607.01403

Galaxies and galaxy groups located along the line of sight towards gravitationally lensed quasars produce high-order perturbations of the gravitational potential at the lens position. When these perturbation are too large, they can induce a systematic error on $H_0$ of a few-percent if the lens system is used for cosmological inference and the perturbers are not explicitly accounted for in the lens model. In this work, we present a detailed characterization of the environment of the lens system WFI2033-4723 ($z_{\rm src} = 1.662$, $z_{\rm lens}$ = 0.6575), one of the core targets of the H0LICOW project for which we present cosmological inferences in a companion paper (Rusu et al. 2019). We use the Gemini and ESO-Very Large telescopes to measure the spectroscopic redshifts of the brightest galaxies towards the lens, and use the ESO-MUSE integral field spectrograph to measure the velocity-dispersion of the lens ($\sigma_{\rm {los}}= 250^{+15}_{-21}$ km/s) and of several nearby galaxies. In addition, we measure photometric redshifts and stellar masses of all galaxies down to $i < 23$ mag, mainly based on Dark Energy Survey imaging (DR1). Our new catalog, complemented with literature data, more than doubles the number of known galaxy spectroscopic redshifts in the direct vicinity of the lens, expanding to 116 (64) the number of spectroscopic redshifts for galaxies separated by less than 3 arcmin (2 arcmin) from the lens. Using the flexion-shift as a measure of the amplitude of the gravitational perturbation, we identify 2 galaxy groups and 3 galaxies that require specific attention in the lens models. The ESO MUSE data enable us to measure the velocity-dispersions of three of these galaxies. These results are essential for the cosmological inference analysis presented in Rusu et al. (2019)., Comment: Matches the version accepted for publication by MNRAS. Note that this paper previously appeared as H0LICOW XI

Many of the fundamental physical constants in Physics, as a discipline, are measured to exquisite levels of precision. The fundamental constants that define Cosmology, however, are largely determined via a handful of independent techniques that are applied to even fewer datasets. The history of the measurement of the Hubble Constant (H0), which serves to anchor the expansion history of the Universe to its current value, is an exemplar of the difficulties of cosmological measurement; indeed, as we approach the centennial of its first measurement, the quest for H0 still consumes a great number of resources. In this white paper, we demonstrate how the approaching era of Extremely Large Telescopes (ELTs) will transform the astrophysical measure of H0 from the limited and few into a fundamentally new regime where (i) multiple, independent techniques are employed with modest use of large aperture facilities and (ii) 1% or better precision is readily attainable. This quantum leap in how we approach H0 is due to the unparalleled sensitivity and spatial resolution of ELT's and the ability to use integral field observations for simultaneous spectroscopy and photometry, which together permit both familiar and new techniques to effectively by-pass the conventional 'ladder' framework to minimize total uncertainty. Three independent techniques are discussed -- (i) standard candles via a two-step distance ladder applied to metal, poor stellar populations, (ii) standard clocks via gravitational lens cosmography, and (iii) standard sirens via gravitational wave sources -- each of which can reach 1% with relatively modest investment from 30-m class facilities., Comment: Submitted as an Astro2020 White Paper. Please send comments to both Rachael Beaton & Simon Birrer. Development of this paper occurred as part of the The US Extremely Large Telescope Program Workshop in Oct 2018. We wish to acknowledge NOAO for bringing the co-authors together, in particular the enthusiasm and tireless leadership of Mark Dickinson

We present a blind time-delay strong lensing (TDSL) cosmographic analysis of the doubly imaged quasar SDSS 1206+4332. We combine the relative time delay between the quasar images, Hubble Space Telescope imaging, the Keck stellar velocity dispersion of the lensing galaxy, and wide-field photometric and spectroscopic data of the field to constrain two angular diameter distance relations. The combined analysis is performed by forward modelling the individual data sets through a Bayesian hierarchical framework, and it is kept blind until the very end to prevent experimenter bias. After unblinding, the inferred distances imply a Hubble constant $H_0 = 68.8^{+5.4}_{-5.1}$ kms$^{-1}$Mpc$^{-1}$, assuming a flat Lambda cold dark matter cosmology with uniform prior on $\Omega_{\rm m}$ in [0.05, 0.5]. The precision of our cosmographic measurement with the doubly imaged quasar SDSS 1206+4332 is comparable with those of quadruply imaged quasars and opens the path to perform on selected doubles the same analysis as anticipated for quads. Our analysis is based on a completely independent lensing code than our previous three H0LiCOW systems and the new measurement is fully consistent with those. We provide the analysis scripts paired with the publicly available software to facilitate independent analysis. The consistency between blind measurements with independent codes provides an important sanity check on lens modelling systematics. By combining the likelihoods of the four systems under the same prior, we obtain $H_0 = 72.5^{+2.1}_{-2.3}$kms$^{-1}$Mpc$^{-1}$. This measurement is independent of the distance ladder and other cosmological probes., Comment: 30 pages, 17 figures, MNRAS published likelihood available here: http://shsuyu.github.io/H0LiCOW/site/notebooks/H0_from_lenses.html, all modeling and analysis scripts available upon request

Strong-gravitational lens systems with quadruply-imaged quasars (quads) are unique probes to address several fundamental problems in cosmology and astrophysics. Although they are intrinsically very rare, ongoing and planned wide-field deep-sky surveys are set to discover thousands of such systems in the next decade. It is thus paramount to devise a general framework to model strong-lens systems to cope with this large influx without being limited by expert investigator time. We propose such a general modelling framework (implemented with the publicly available software Lenstronomy) and apply it to uniformly model three-band Hubble Space Telescope Wide Field Camera 3 images of 13 quads. This is the largest uniformly modelled sample of quads to date and paves the way for a variety of studies. To illustrate the scientific content of the sample, we investigate the alignment between the mass and light distribution in the deflectors. The position angles of these distributions are well-aligned, except when there is strong external shear. However, we find no correlation between the ellipticity of the light and mass distributions. We also show that the observed flux-ratios between the images depart significantly from the predictions of simple smooth models. The departures are strongest in the bluest band, consistent with microlensing being the dominant cause in addition to millilensing. Future papers will exploit this rich dataset in combination with ground based spectroscopy and time delays to determine quantities such as the Hubble constant, the free streaming length of dark matter, and the normalization of the initial stellar mass function., Comment: 22 pages, 9 figures, 8 tables, Accepted to MNRAS. This version: updated Table 4 from the erratum