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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, J08182613, 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 J08182613 and J1817+2729 to be 0:866 ± 0:002 and 0:408 ± 0:002, respectively. [ABSTRACT FROM AUTHOR]

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 data set of SNe that are not strongly lensed and a data set 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 SN population and the redshiftâ€"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 SN images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and 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. [ABSTRACT FROM AUTHOR]

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 data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) 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. [ABSTRACT FROM AUTHOR]

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 yr 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 data sets. The results in Rungs 1 and 2 show that methods that use only the point source positions tend to have lower precision (⁠|$10\!-\!20{{\ \rm per\ cent}}$|⁠) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic data sets can recover H 0 within the target accuracy (| A | < 2 per cent) and precision (<6 per cent per system), even in the presence of a 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. [ABSTRACT FROM AUTHOR]

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 H 0 = 73. 3 − 1.8 + 1.7 $ H_0 = 73.3^{+1.7}_{-1.8} $ km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) 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 H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 H 0 = 74. 5 − 6.1 + 5.6 $ H_0 = 74.5^{+5.6}_{-6.1} $ km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 H 0 = 67. 4 − 3.2 + 4.1 $ H_0 = 67.4^{+4.1}_{-3.2} $ km s−1 Mpc−1. This measurement assumes 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. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data. [ABSTRACT FROM AUTHOR]

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 yr of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution 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 |$6.6{{\ \rm per\ cent}}$|⁠. This translates to a Hubble constant |$H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$|⁠ , assuming a flat ΛCDM cosmology with a uniform prior on Ωm 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). [ABSTRACT FROM AUTHOR]

We present the measurement of the Hubble constant, H 0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) 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 PG 1115+080, |$H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$| for HE 0435−1223, and |$H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$| for RXJ 1131−1231. 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 these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ωm 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. [ABSTRACT FROM AUTHOR]

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 |$^{+5.4}_{-5.1}$|  km s−1 Mpc−1, assuming a flat Λ cold dark matter cosmology with uniform prior on Ωm 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 (footnote with link to www.h0licow.org). 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 |$^{+2.1}_{-2.3}$|  km s−1 Mpc−1. This measurement is independent of the distance ladder and other cosmological probes. [ABSTRACT FROM AUTHOR]

Strongly gravitational lensed quasars can be used to measure the so-called time-delay distance DΔt, and thus the Hubble constant H0 and other cosmological parameters. Stellar kinematics of the deflector galaxy play an essential role in this measurement by: (i) helping break the masssheet degeneracy; (ii) determining in principle the angular diameter distance Dd to the deflector and thus further improving the cosmological constraints. In this paper we simulate observations of lensed quasars with integral field spectrographs and show that spatially resolved kinematics of the deflector enables further progress by helping break the mass-anisotropy degeneracy. Furthermore, we use our simulations to obtain realistic error estimates with current/upcoming instruments like OSIRIS on Keck and NIRSPEC on the James Webb Space Telescope for both distances (typically ~6 per cent on DΔt and ~10 per cent on Dd). We use the error estimates to compute cosmological forecasts for the sample of nine lenses that currently have wellmeasured time delays and deep Hubble Space Telescope images and for a sample of 40 lenses that is projected to be available in a few years through follow-up of candidates found in ongoing wide field surveys. We find that H0 can be measured with 2 per cent (1 per cent) precision from nine (40) lenses in a flat Λcold dark matter cosmology. We study several other cosmological models beyond the flat Λcold dark matter model and find that time-delay lenses with spatially resolved kinematics can greatly improve the precision of the cosmological parameters measured by cosmic microwave background data. [ABSTRACT FROM AUTHOR]

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 yr of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution 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 |$6.6{{\ \rm per\ cent}}$|⁠. This translates to a Hubble constant |$H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$|⁠ , assuming a flat ΛCDM cosmology with a uniform prior on Ωm 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). [ABSTRACT FROM AUTHOR]