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NASA NTRS2003

Enhancing and Archiving the APS Catalog of the POSS I

We have worked on two different projects: 1) Archiving the APS Catalog of the POSS I for distribution to NASA's NED at IPAC, SIMBAD in France, and individual astronomers and 2) The automated morphological classification of galaxies. We have completed archiving the Catalog into easily readable binary files. The database together with the software to read it has been distributed on DVD's to the national and international data centers and to individual astronomers. The archived Catalog contains more than 89 million objects in 632 fields in the first epoch Palomar Observatory Sky Survey. Additional image parameters not available in the original on-line version are also included in the archived version. The archived Catalog is also available and can be queried at the APS web site (URL: http://aps.umn.edu) which has been improved with a much faster and more efficient querying system. The Catalog can be downloaded as binary datafiles with the source code for reading it. It is also being integrated into the SkyQuery system which includes the Sloan Digital Sky Survey, 2MASS, and the FIRST radio sky survey. We experimented with different classification algorithms to automate the morphological classification of galaxies. This is an especially difficult problem because there are not only a large number of attributes or parameters and measurement uncertainties, but also the added complication of human disagreement about the adopted types. To solve this problem we used 837 galaxy images from nine POSS I fields at the North Galactic Pole classified by two independent astronomers for which they agree on the morphological types. The initial goal was to separate the galaxies into the three broad classes relevant to issues of large scale structure and galaxy formation and evolution: early (ellipticals and lenticulars), spirals, and late (irregulars) with an accuracy or success rate that rivals the best astronomer classifiers. We also needed to identify a set of parameters derived from the digitized images that separate the galaxies by type. The human eye can easily recognize complicated patterns in images such as spiral arms which can be spotty, blotchy affairs that are difficult for automated techniques. A galaxy image can potentially be described by hundreds of parameters, all of which may have some relation to the morphological type. In the set of initial experiments we used 624 such parameters, in two colors, blue and red. These parameters include the surface brightness and color measured at different radii, ratios of these parameters at different radii, concentration indices, Fourier transforms and wavelet decomposition coefficients. We experimented with three different classes of classification algorithms; decision trees, k-nearest neighbors, and support vector machines (SVM). A range of experiments were conducted and we eventually narrowed the parameters to 23 selected parameters. SVM consistently outperformed the other algorithms with both sets of features. By combining the results from the different algorithms in a weighted scheme we achieved an overall classification success of 86%.

Humphreys, Roberta M.↗

NASA NTRS1992

Tektite-bearing, deep-water clastic unit at the Cretaceous-Tertiary boundary in northeastern Mexico

The hypothesis of Cretaceous-Tertiary (K-T) boundary impact on Yucatan, Mexico, predicts that nearby sites should show evidence of proximal impact ejecta and disturbance by giant waves. An outcrop along the Arroyo el Mimbral in northeastern Mexico contains a layered clastic unit up to 3 m thick that interrupts a biostratigraphically complete pelagic-marl sequence deposited at more than 400 m water depth. The marls were found to be unsuitable for determining magnetostratigraphy, but foraminiferal biostratigraphy places the clastic unit precisely at the K-T boundary. We interpret this clastic unit as the deposit of a megawave or tsunami produced by an extraterrestrial impact. The clastic unit comprises three main subunits. (1) The basal "spherule bed" contains glass in the form of tektites and microtektites, glass spherules replaced by chlorite-smectite and calcite, and quartz grains showing probable shock features. This bed is interpreted as a channelized deposit of proximal ejecta. (2) A set of lenticular, massive, graded "laminated beds" contains intraclasts and abundant plant debris, and may be the result of megawave backwash that carried coarse debris from shallow parts of the continental margin into deeper water. (3) At the top, several thin "ripple beds" composed of fine sand are separated by clay drapes; they are interpreted as deposits of oscillating currents, perhaps a seiche. An iridium anomaly (921 +/- 23 pg/g) is observed at the top of the ripple beds. Our observations at the Mimbral locality support the hypothesis of a K-T impact on nearby Yucatan.

NASA Discipline Number 52-40↗

NASA NTRS2004

Shaping off-axis metallic membrane reflectors using optimal boundary shapes and inelastic strains

This paper will describe a novel concept for constructing off-axis membrane reflector surfaces. Membrane reflectors have been extensively studied, including investigations into inflated lenticular architectures, shaping by spin casting, shaping using electrostatic forces, and shaping by evacuating behind a membrane surface stretched between circular or annular-shaped supports.

membrane↗

NASA NTRS1999

Reduced-thickness backlighter for autostereoscopic display and display using the backlighter

A reduced-thickness backlighter for an autostereoscopic display is disclosed having a lightguide and at least one light source parallel to an edge of the lightguide so as to be substantially coplanar with the lightguide. The lightguide is provided with a first surface which has a plurality of reflective linear regions, such as elongated grooves or glossy lines, parallel to the illuminated edge of the lightguide. Preferably the lightguide further has a second surface which has a plurality of lenticular lenses for reimaging the reflected light from the linear regions into a series of thin vertical lines outside the guide. Because of the reduced thickness of the backlighter system, autostereoscopic viewing is enabled in applications requiring thin backlighter systems. In addition to taking up less space, the reduced-thickness backlighter uses less lamps and less power. For accommodating 2-D applications, a 2-D diffuser plate or a 2-D lightguide parallel to the 3-D backlighter is disclosed for switching back and forth between 3-D viewing and 2-D viewing.

Eichenlaub, Jesse B↗

NASA NTRS2014

Microstructure and Oxidation of a MAX Phase/Superalloy Hybrid Interface

Corrosion resistant, strain tolerant MAX phase coatings are of interest for turbine applications. Thin Cr2AlC MAX phase wafers were vacuum diffusion bonded to an advanced turbine disk alloy, LSHR, at 1100 C. The interface, examined by optical and scanning electron microscopy, revealed a primary diffusion zone consisting of ~ 10 micrometers of beta-Ni(Co)Al, decorated with various NiCoCrAl, MC and M3B2 precipitates. On the Cr2AlC side, an additional ~40 micrometers Al-depletion zone of Cr7C3 formed in an interconnected network with the beta-Ni(Co)Al. Oxidation of an exposed edge at 800 C for 100 h produced a fine-grained lenticular alumina scale over Cr2AlC and beta-Ni(Co)Al, with coarser chromia granules over the Cr7C3 regions. Subsequent growth of the diffusion layers was only ~ 5 micrometers in total. A residual stress of ~ 500 MPa was estimated for the MAX phase layer, but no interfacial damage was observed. Subsequent tests for 1000 h reveal similar results.

heat resistant alloys↗

NASA NTRSDate not supplied

Simulation of Deployable Composite Structures Based On Mechanics of Structure Genome

In this paper, a simulation method for analyzing deployable composite structures is presented. With a proper material model, effective plate/shell properties of the composites is obtained based on Mechanics of Structure Genome (MSG), and then implemented into a user subroutine UGENS for global structure simulation in ABAQUS. Column bending test (CBT) and composite boom and hub structure are studied for demonstration. A viscoelastic material model with direct integration implementation is adopted in this paper. CBT simulation shows good agreement with experiments during relaxation, while errors are observed when comparing residual deformation. This simulation can be potentially used as a calibration tool for material properties. After CBT simulation, a demonstrative model with a lenticular boom and the hub is created in ABAQUS. Complete process of flattening, coiling, stowage, deploying and recovery is simulated with the viscoelastic material model. Residual deformation of the boom is analyzed.

Multi-scale modeling↗

NASA NTRSDate not supplied

Thermoviscoelastic modelling of high strain thin-ply composites by means of multiscale plate and beam model

High strain thin-ply (HS-TPC) technology is being increasingly adopted for high-performanceaerospace applications. Albeit many of these structures such as deployable booms can bemodeled as one-dimensional beam problems, there is a lack of themoviscoelastic beam mod-els to efficiently and accurately simulate HS-TPC. This work will use mechanics of struc-ture genome (MSG) to construct linear thermoviscoelastic beam models that can homogenizethree-dimensional heterogeneous materials made of constituents with time- and temperature-dependent behavior. The formulation derives the transient strain energy based on integralformulation for thermorheologically simple materials subject to finite temperature changeswith the restriction that the strain is small. A lenticular boom is used as a numerical exampleto verify the MSG-based linear thermoviscoelastic beam model against MSG-based shell/platemodel, which has already been validated against experimental data provided by NASA, anddirect numerical simulations performed in a finite element commercial package.

Orzuri Rique Garaizar↗

NASA NTRSDate not supplied

Advanced Composite Solar Sail System (ACS3) Mission Update

The Advanced Composite Solar Sail System (ACS3) will be the first practical solar sail for the National Aeronautics and Space Administration. [1] ACS3 will also be the first spaceflight demonstration of NASA compact deployable composite boom technology.[2] The primary mission objective of ACS3 will be to deploy and characterize an 80-m2 composite boom structure solar sail technology in low Earth orbit. Extended mission goals will be to demonstrate controlled solar sailing flight via a series of orbit raising and lowering maneuvers. Target mission orbit is a 1000 km x 1000 km midnight-noon sun-synchronous orbit. Launch of ACS3 is scheduled for July 2023 with sail deployment in September 2023. Mission duration is expected to be six to nine months. The ACS3 solar sail vehicle is a 12U Cubesat consisting of a bus module, containing flight and solar sail control avionics, and a solar sail module, containing the composite booms and metallized polymer solar sail membranes of the solar sail structure stowed within a boom deployer mechanism. A four-camera instrument suite for 360-degree imaging of the ACS3 solar sail during and after deployment is also housed within the bus module. The ACS3 80-m2 solar sail design is a sub-scale version of an intermediate-size 500-m2 solar sail using NASA deployable composite boom technology. The sail consists of four metallized 2-m thick polyethylene naphthalate (PEN) 20-m2 triangular quadrants supported by four 7-m long lenticular cross-section composite booms. Booms are flattened and co-coiled for stowage within a tape-spool driven deployer mechanism. Total mass of the ACS3 space vehicle including solar sail is 16 kg. An overview of the ACS3 mission and mission systems will be provided in this presentation. This overview will include descriptions of the solar sail structures and materials technology used with ACS3, and discussion of the scalability and extensibility of the ACS3 solar sail to future larger-scale solar sailing mission requirements. An update on progress towards the launch of ACS3 in July 2023 will also be provided. References [1] https://www.nasa.gov/directorates/spacetech/small_spacecraft/ACS3 [2] https://www.nasa.gov/directorates/spacetech/game_changing_development/projects/dcb

Solar sail↗

DOE OSTI2024

Strong Lensing by Galaxies

Strong gravitational lensing at the galaxy scale is a valuable tool for various applications in astrophysics and cosmology. Some of 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.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Identification and properties of isolated field elliptical galaxies from CFHTLS-W1

We present a catalogue of isolated field elliptical (IfE) galaxies drawn from the W1 field of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). 228 IfEs were identified from a flux-limited (r < 21.8) galaxy catalogue which corresponds to a density of 3 IfE/sq.deg. For comparison we consider a sample of elliptical galaxies living in dense environments, based on identification of the brightest cluster galaxies (BGCs) in the same survey. Using the same dataset for the comparison sample ensures a uniform selection, including in the redshift range as IfEs (i.e. 0.1 < z <0.9). A comparison of elliptical galaxies in different environments reveals that IfEs and BCGs have similar behaviours in their colours, star formation activities, and scaling relations of mass–size and size–luminosity. IfEs and BCGs have similar slopes in the scaling relations with respect to cluster ellipticals within the $ -24 \leq M_{r} \leq -22 $ magnitude and $10.2 < \textrm{log}(M_{*}/ \textrm M_\odot)\leq12.0 $ mass ranges. Three IfEs identified in this study can be associated with fossil groups found in the same survey area which gives clues for future studies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Star formation in outer rings of S0 galaxies: IV. NGC 254: A double-ringed S0 with gas counter-rotation

Although S0 galaxies are usually considered “red and dead”, they often demonstrate star formation organized into ring structures. We aim to clarify the nature of this phenomenon and how it differs from star formation in spiral galaxies. We investigated the nearby, moderate-luminosity S0 galaxy NGC 254 using long-slit spectroscopy taken with the South African Large Telescope and publicly available imaging data. Applying a full spectral fitting, we analyzed gaseous and stellar kinematics as well as ionized gas excitation and metallicity and stellar population properties resolved by radius. An advanced approach of simultaneously fitting spectra and photometric data allowed us to quantify the fraction of hidden counter-rotating stars in this galaxy. We find that the ionized gas is counter-rotating with respect to the stars throughout NGC 254 disk, indicating an external origin of the gas. We argue the gas-rich galaxy merger from retrograde orbit as a main source of counter-rotating material. The star formation fed by this counter-rotating gas occurs within two rings: an outer ring at R = 55' - 70" and an inner ring at R = 18". The star formation rate is weak, 0.02 solar mass per year in total, and the gas metallicity is slightly subsolar. We estimated that the accretion of the gas occurred about 1 Gyr ago, and about 1% of all stars have formed in situ from counter-rotating gas.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies (log M*/M ⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u - g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, L r, 10 , and the light-weighted surface brightness slope, Γ 10 . Results. We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with L r,10 and anti-correlates with Γ 10 . At fixed redshift, L r, 10 and Γ 10 , the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

TDCOSMO. IX. Systematic comparison between lens modelling software programs: time delay prediction for WGD 2038-4008

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 1.2σ, implying that once the time delay is measured the inferred Hubble constant will also be mutually consistent. However, there is a ~4σ 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 ~0.6σ<, indicating that potential systematics stemming from source reconstruction algorithms and investigator choices are well under control. We recommend that future studies supersample the PSF as needed and marginalize over multiple algorithms or realizations for the PSF reconstruction to mitigate the systematics associated with the PSF. A future study will measure the time delays of the system WGD 2038-4008 and infer the Hubble constant based on our mass models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

TDCOSMO VIII. A key test of systematics in the hierarchical method of time-delay cosmography

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H$ 0 . A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the $H$ 0 bias associated with model choice to find $H$ 0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower $z$, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of $H$ 0 which is both more precise (σ ~ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of $H$ 0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

TDCOSMO. X. Automated modeling of nine strongly lensed quasars and comparison between lens-modeling software

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

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Deep optical imaging of star-forming blue early-type galaxies: Color map structures and faint features indicative of recent mergers

Blue early-type galaxies with galaxy-scale ongoing star formation are interesting targets in order to understand the stellar mass buildup in elliptical and S0 galaxies in the local Universe. We study the star-forming population of blue early-type galaxies to understand the origin of star formation in these otherwise red and dead stellar systems. The legacy survey imaging data taken with the dark energy camera in the g, r, and z bands for 55 star-forming blue early-type galaxies were examined, and g – r color maps were created. We identified low surface brightness features near 37 galaxies, faint-level interaction signatures near 15 galaxies, and structures indicative of recent merger activity in the optical color maps of all 55 galaxies. These features are not visible in the shallow Sloan Digital Sky Survey imaging data in which these galaxies were originally identified. Low surface brightness features found around galaxies could be remnants of recent merger events. The star-forming population of blue early-type galaxies could be post-merger systems that are expected to be the pathway for the formation of elliptical galaxies. We hypothesize that the star-forming population of blue early-type galaxies is a stage in the evolution of early-type galaxies. The merger features will eventually disappear, fuel for star formation will cease, and the galaxy will move to the passive population of normal early-type galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Decoding NGC 7252 as a blue elliptical galaxy

Elliptical galaxies with blue optical colours and significant star formation are hypothesised to be major merger remnants of gas-rich spiral galaxies or normal elliptical galaxies with a sudden burst of star formation. We present here a scenario in which blue elliptical galaxies identified in shallow imaging surveys may fail to recover faint features that are indicative of past merger activity using a nearby major merger remnant. Based on deep optical imaging data of the post-merger galaxy, NGC 7252, we demonstrate that the galaxy can appear as an elliptical galaxy if it is observed at higher redshifts. The main body and the low surface brightness merger features found at the outskirts of the galaxy are blue in the optical g – r colour map. We argue that the higher-redshift blue elliptical galaxies discovered in surveys as shallow as the SDSS or DECaLS may be advanced mergers whose defining tidal features fall below the detection limits of the surveys. This should be taken into consideration during the morphological classification of these systems in future and ongoing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

TDCOSMO. XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

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.

79 ASTRONOMY AND ASTROPHYSICS↗