arXiv subjects

Philip J. Marshall

Publications and source records attributed to Philip J. Marshall.

At least 19 recordsLinked to original sources

arXiv2026

Lens Modeling and Cosmological Inference from an Impure Sample of Galaxy-Galaxy Strong Lenses

The start of the Legacy Survey of Space and Time marks a new era for strong lensing science, where the number of strong lenses identified is expected to increase to $\mathcal{O}(10^5)$. In this paper we use a neural network to determine the precision with which lens parameters can be determined, using realistic simulated LSST lensed systems. We find that the Einstein radius can be measured with a mean precision of $3.7\%$ with calibrated uncertainties accurately reflecting the corresponding measurement error. Based on the performance of current strong lens classifiers, the $\sim 100,000$ detectable strong lenses are expected to be accompanied by a similar or larger number of false positives (non-lenses). In readiness for this we introduce a formalism, termed `COSMIC-BEAMS', to infer cosmological parameters while accounting for contamination by false positives. As a proof-of-concept, using simulated LSST measurements of the Einstein radii of a realistic and impure sample of photometric lens systems, i.e. those without spectroscopic confirmation, we find that the cosmological parameters $Ω_m$, $Ω_Λ$, and $w$ can be measured to a precision of $0.1$, $0.03$ and $0.15$ respectively for a $w$CDM cosmology. We demonstrate that unbiased cosmological parameters can be inferred even in strong lens samples contaminated by $50\%$ false positives, and that the photometric dataset of $100\,000$ strong lenses will provide equivalent $w$-precision to $2500-3500$ spectroscopic systems.

astro-ph.CO↗

arXiv2025

A halo model approach for mock catalogs of time-variable strong gravitational lenses

Time delays in both galaxy- and cluster-scale strong gravitational lenses have recently attracted a lot of attention in the context of the Hubble tension. Future wide-field cadenced surveys, such as the LSST, are anticipated to discover strong lenses across various scales. We generate mock catalogs of strongly lensed QSOs and SNe on galaxy-, group-, and cluster-scales based on a halo model that incorporates dark matter halos, galaxies, and subhalos. For the upcoming LSST survey, we predict that approximately 4000 lensed QSOs and 200 lensed SNe with resolved multiple images will be discovered. Among these, about 80 lensed QSOs and 10 lensed SNe will have maximum image separations larger than 10 arcsec, which roughly correspond to cluster-scale strong lensing. We find that adopting the Chabrier stellar IMF instead of the fiducial Salpeter IMF reduces the predicted number of strong lenses approximately by half, while the distributions of lens and source redshifts and image separations are not significantly changed. In addition to mock catalogs of multiple-image lens systems, we create mock catalogs of highly magnified systems, including both multiple-image and single-image systems. We find that such highly magnified systems are typically produced by massive galaxies, but non-negligible fraction of them are located in the outskirt of galaxy groups and clusters. Furthermore, we compare subsamples of our mock catalogs with lensed QSO samples constructed from the SDSS and Gaia to find that our mock catalogs with the fiducial Salpeter IMF reproduce the observation quite well. In contrast, our mock catalogs with the Chabrier IMF predict a significantly smaller number of lensed QSOs compared with observations, which adds evidence that the stellar IMF of massive galaxies is Salpeter-like. Our python code SL-Hammocks as well as the mock catalogs are made available online. (abridged)

astro-ph.CO↗

arXiv2025

TDCOSMO XVII. New time delays in 22 lensed quasars from optical monitoring with the ESO-VST 2.6m and MPG 2.2m telescopes

We present new time delays, the main ingredient of time delay cosmography, for 22 lensed quasars resulting from high-cadence r-band monitoring on the 2.6 m ESO VLT Survey Telescope and Max-Planck-Gesellschaft 2.2 m telescope. Each lensed quasar was typically monitored for one to four seasons, often shared between the two telescopes to mitigate the interruptions forced by the COVID-19 pandemic. The sample of targets consists of 19 quadruply and 3 doubly imaged quasars, which received a total of 1 918 hours of on-sky time split into 21 581 wide-field frames, each 320 seconds long. In a given field, the 5-σ depth of the combined exposures typically reaches the 27th magnitude, while that of single visits is 24.5 mag - similar to the expected depth of the upcoming Vera-Rubin LSST. The fluxes of the different lensed images of the targets were reliably de-blended, providing not only light curves with photometric precision down to the photon noise limit, but also high-resolution models of the targets whose features and astrometry were systematically confirmed in Hubble Space Telescope imaging. This was made possible thanks to a new photometric pipeline, lightcurver, and the forward modelling method STARRED. Finally, the time delays between pairs of curves and their uncertainties were estimated, taking into account the degeneracy due to microlensing, and for the first time the full covariance matrices of the delay pairs are provided. Of note, this survey, with 13 square degrees, has applications beyond that of time delays, such as the study of the structure function of the multiple high-redshift quasars present in the footprint at a new high in terms of both depth and frequency. The reduced images will be available through the European Southern Observatory Science Portal.

astro-ph.CO↗

arXiv2025

Correcting for Selection Biases in the Determination of the Hubble Constant from Time-Delay Cosmography

The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred $H_0$. The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred $H_0$ by 8$\%$. Here, we test the assumption that the density profiles of galaxy-galaxy and galaxy-quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy-galaxy and galaxy-quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy-galaxy lenses have systematically higher mass-sheet components than galaxy-quasar lenses. For individual systems, $λ_\mathrm{int}$ correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO methodology, we find that $H_0$ is lowered by a further $\sim$3\%. Using the velocity dispersions from \citet{slacs9} and our fiducial model for selection biases, we infer $H_0 = 66\pm4 \ \mathrm{(stat)} \pm 1 \ \mathrm{(model \ sys)} \pm 2 \ \mathrm{(measurement \ sys)} \ \mathrm{km} \ \mathrm{s}^{-1} \ \mathrm{Mpc}^{-1}$ for the TDCOSMO plus SLACS dataset. The first residual systematic error is due to plausible alternative choices in modeling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.

astro-ph.CO↗

arXiv2024

Image deconvolution and PSF reconstruction with STARRED: a wavelet-based two-channel method optimized for light-curve extraction

We present STARRED, a Point Spread Function (PSF) reconstruction, two-channel deconvolution, and light curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, STARRED performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a deep sharp frame combining all data, and the photometry of all point sources in the field of view as a function of time. Of note, STARRED also provides exquisite PSF models for each data frame. We showcase three applications of STARRED in the context of the imminent LSST survey and of JWST imaging: i) the extraction of supernovae light curves and the scene representation of their host galaxy, ii) the extraction of lensed quasar light curves for time-delay cosmography, and iii) the measurement of the spectral energy distribution of globular clusters in the "Sparkler", a galaxy at redshift z=1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. STARRED is implemented in JAX, leveraging automatic differentiation and GPU acceleration. This enables rapid processing of large time-domain datasets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.

astro-ph.IM↗

arXiv2024

TDCOSMO. XVI. Measurement of the Hubble Constant from the Lensed Quasar WGD$\,$2038$-$4008

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 $D_{Δt} = 1.68^{+0.40}_{-0.38}$ 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 $Λ$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.

astro-ph.CO↗

arXiv2024

A Bayesian Approach to Strong Lens Finding in the Era of Wide-area Surveys

The arrival of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), Euclid-Wide and Roman wide area sensitive surveys will herald a new era in strong lens science in which the number of strong lenses known is expected to rise from $\mathcal{O}(10^3)$ to $\mathcal{O}(10^5)$. However, current lens-finding methods still require time-consuming follow-up visual inspection by strong-lens experts to remove false positives which is only set to increase with these surveys. In this work we demonstrate a range of methods to produce calibrated probabilities to help determine the veracity of any given lens candidate. To do this we use the classifications from citizen science and multiple neural networks for galaxies selected from the Hyper Suprime-Cam (HSC) survey. Our methodology is not restricted to particular classifier types and could be applied to any strong lens classifier which produces quantitative scores. Using these calibrated probabilities, we generate an ensemble classifier, combining citizen science and neural network lens finders. We find such an ensemble can provide improved classification over the individual classifiers. We find a false positive rate of $10^{-3}$ can be achieved with a completeness of $46\%$, compared to $34\%$ for the best individual classifier. Given the large number of galaxy-galaxy strong lenses anticipated in LSST, such improvement would still produce significant numbers of false positives, in which case using calibrated probabilities will be essential for population analysis of large populations of lenses.

astro-ph.GA↗

arXiv2023

On the detectability of strong lensing in near-infrared surveys

We present new lensing frequency estimates for existing and forthcoming deep near-infrared surveys, including those from JWST and VISTA. The estimates are based on the JAdes extraGalactic Ultradeep Artificial Realisations (JAGUAR) galaxy catalogue accounting for the full photometry and morphologies for each galaxy. Due to the limited area of the JAGUAR simulations, they are less suited to wide-area surveys, however we also present extrapolations to the surveys carried out by Euclid and the Nancy Grace Roman Space Telescope. The methodology does not make assumptions on the nature of the lens itself and probes a wide range of lens masses. The lenses and sources are selected from the same catalogue and extend the analysis from the visible bands into the near-infrared. After generating realistic simulated lensed sources and selecting those that are detectable with SNR>20, we verify the lensing frequency expectations against published lens samples selected in the visible, finding them to be broadly consistent. We find that JWST could yield ~ 65 lensed systems in COSMOS-Web, of which ~ 25 per cent have source redshifts >4. Deeper, narrower programs (e.g. JADES-Medium) will probe more typical source galaxies (in flux and mass) but will find fewer systems (~ 25). Of the surveys we investigate, we find 55-80 per cent have detectable multiple imaging. Forthcoming NIR surveys will likely reveal new and diverse strong lens systems including lensed sources that are at higher redshift (JWST) and dustier, more massive and older (Euclid NISP) than those typically detected in the corresponding visible surveys.

astro-ph.GA↗

arXiv2023

From Images to Dark Matter: End-To-End Inference of Substructure From Hundreds of Strong Gravitational Lenses

Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos ($<10^{10} M_\odot$) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large datasets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST's COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated datasets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys.

astro-ph.CO↗

arXiv2022

GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the Sérsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.

astro-ph.CO↗

arXiv2022

Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks

We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ($κ$) from photometric measurements of galaxies along a given line of sight. The method is of particular interest in strong gravitational time delay cosmography (TDC), where characterizing the "external convergence" ($κ_{\rm ext}$) from the lens environment and line of sight is necessary for precise inference of the Hubble constant ($H_0$). Starting from a large-scale simulation with a $κ$ resolution of $\sim$1$'$, we introduce fluctuations on galaxy-galaxy lensing scales of $\sim$1$''$ and extract random sightlines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1,000 sightlines, the BGNN infers the individual $κ$ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of $κ$ precisely and without bias, resulting in a contribution to the $H_0$ error budget well under 1\%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sightline, extracts more $κ$ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the $κ_{\rm ext}$ characterization for precision TDC. The implementation of our pipeline is available as a public Python package, Node to Joy.

astro-ph.CO↗

arXiv2021

The LSST Dark Energy Science Collaboration (DESC) Science Requirements Document

The Large Synoptic Survey Telescope (LSST) Dark Energy Science Collaboration (DESC) will use five cosmological probes: galaxy clusters, large scale structure, supernovae, strong lensing, and weak lensing. This Science Requirements Document (SRD) quantifies the expected dark energy constraining power of these probes individually and together, with conservative assumptions about analysis methodology and follow-up observational resources based on our current understanding and the expected evolution within the field in the coming years. We then define requirements on analysis pipelines that will enable us to achieve our goal of carrying out a dark energy analysis consistent with the Dark Energy Task Force definition of a Stage IV dark energy experiment. This is achieved through a forecasting process that incorporates the flowdown to detailed requirements on multiple sources of systematic uncertainty. Future versions of this document will include evolution in our software capabilities and analysis plans along with updates to the LSST survey strategy.

astro-ph.CO↗

arXiv2021

Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). VI. Crowdsourced lens finding with Space Warps

Strong lenses are extremely useful probes of the distribution of matter on galaxy and cluster scales at cosmological distances, but are rare and difficult to find. The number of currently known lenses is on the order of 1,000. We wish to use crowdsourcing to carry out a lens search targeting massive galaxies selected from over 442 square degrees of photometric data from the Hyper Suprime-Cam (HSC) survey. We selected a sample of $\sim300,000$ galaxies with photometric redshifts in the range $0.2 < z_{phot} < 1.2$ and photometrically inferred stellar masses $\log{M_*} > 11.2$. We crowdsourced lens finding on this sample of galaxies on the Zooniverse platform, as part of the Space Warps project. The sample was complemented by a large set of simulated lenses and visually selected non-lenses, for training purposes. Nearly 6,000 citizen volunteers participated in the experiment. In parallel, we used YattaLens, an automated lens finding algorithm, to look for lenses in the same sample of galaxies. Based on a statistical analysis of classification data from the volunteers, we selected a sample of the most promising $\sim1,500$ candidates which we then visually inspected: half of them turned out to be possible (grade C) lenses or better. Including lenses found by YattaLens or serendipitously noticed in the discussion section of the Space Warps website, we were able to find 14 definite lenses, 129 probable lenses and 581 possible lenses. YattaLens found half the number of lenses discovered via crowdsourcing. Crowdsourcing is able to produce samples of lens candidates with high completeness and purity, compared to currently available automated algorithms. A hybrid approach, in which the visual inspection of samples of lens candidates pre-selected by discovery algorithms and/or coupled to machine learning is crowdsourced, will be a viable option for lens finding in the 2020s.

astro-ph.IM↗

arXiv2021

Inferring Black Hole Properties from Astronomical Multivariate Time Series with Bayesian Attentive Neural Processes

Among the most extreme objects in the Universe, active galactic nuclei (AGN) are luminous centers of galaxies where a black hole feeds on surrounding matter. The variability patterns of the light emitted by an AGN contain information about the physical properties of the underlying black hole. Upcoming telescopes will observe over 100 million AGN in multiple broadband wavelengths, yielding a large sample of multivariate time series with long gaps and irregular sampling. We present a method that reconstructs the AGN time series and simultaneously infers the posterior probability density distribution (PDF) over the physical quantities of the black hole, including its mass and luminosity. We apply this method to a simulated dataset of 11,000 AGN and report precision and accuracy of 0.4 dex and 0.3 dex in the inferred black hole mass. This work is the first to address probabilistic time series reconstruction and parameter inference for AGN in an end-to-end fashion.

astro-ph.IM↗

arXiv2021

Large-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time-delay gravitational lenses for Hubble constant ($H_0$) determination. Our BNN was trained on synthetic HST-quality images of strongly lensed active galactic nuclei (AGN) with lens galaxy light included. The BNN can accurately characterize the posterior PDFs of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into ensemble $H_0$ inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of $9.3$\% per lens in the inferred $H_0$. A simple combination of 200 test-set lenses results in a precision of 0.5 $\textrm{km s}^{-1} \textrm{ Mpc}^{-1}$ ($0.7\%$), with no detectable bias in this $H_0$ recovery test. The computation time for the entire pipeline -- including the training set generation, BNN training, and $H_0$ inference -- translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for $H_0$ inference.

astro-ph.IM↗

arXiv2021

Hierarchical Inference With Bayesian Neural Networks: An Application to Strong Gravitational Lensing

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our Universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope (HST) quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (i.e., statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training set's interim prior. Simultaneously, given a sufficiently broad training set, we can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys.

astro-ph.CO↗

arXiv2020

Time Delay Lens Modeling Challenge: I. Experimental Design

Strong gravitational lenses with measured time delay are a powerful tool to measure cosmological parameters, especially the Hubble constant ($H_0$). Recent studies show that by combining just three multiply-imaged AGN systems, one can determine $H_0$ to 2.4% precision. Furthermore, the number of time-delay lens systems is growing rapidly, enabling the determination of $H_0$ to 1% precision in the near future. However, as the precision increases it is important to ensure that systematic errors and biases remain subdominant. For this purpose, challenges with simulated datasets are a key component in this process. Following the experience of the past challenge on time delay, where it was shown that time delays can indeed be measured precisely and accurately at the sub-percent level, we now present the "Time Delay Lens Modeling Challenge" (TDLMC). The goal of this challenge is to assess the present capabilities of lens modeling codes and assumptions and test the level of accuracy of inferred cosmological parameters given realistic mock datasets. We invite scientists to model a set of simulated HST observations of 50 mock lens systems. The systems are organized in rungs, with the complexity and realism increasing going up the ladder. The goal of the challenge is to infer $H_0$ for each rung, given the HST images, the time delay, and stellar velocity dispersion of the deflector for a fixed background cosmology. The TDLMC challenge starts with the mock data release on 2018 January 8th. The deadline for blind submission is different for each rung. The deadline for Rung 0-1 is 2018 September 8; the deadline for Rung 2 is 2019 April 8 and the one for Rung 3 is 2019 September 8. This first paper gives an overview of the challenge including the data design, and a set of metrics to quantify the modeling performance and challenge details.

astro-ph.CO↗

arXiv2019

H0LiCOW XII. Lens mass model of WFI2033-4723 and blind measurement of its time-delay distance and $H_0$

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 $Λ$CDM cosmology with a uniform prior on $Ω_\mathrm{m}$ 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).

astro-ph.CO↗