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C. D. Fassnacht

Publications and source records attributed to C. D. Fassnacht.

At least 19 recordsLinked to original sources

TDCOSMO. XXVII. JWST-based Lens Models and H$_0$ Measurement of WFI2033, HE0435, and PG1115

Time-delay cosmography offers a one-step, distance-ladder-independent route to the Hubble-Lemaitre constant, H_0. We present new cosmography-grade lens models of three quadruply imaged quasars based on JWST-NIRCam/F115W imaging (WFI2033-4723, HE0435-1223, PG1115+080). We use the STARRED modeling technique, introduced in our previous analysis of WFI2033-4723, to reconstruct the complex JWST-NIRCam Point Spread Function at high fidelity. We combine NIRCam-based lens models with improved external convergence estimates, published time delays, and aperture-integrated stellar velocity dispersions from JWST NIRSpec to infer H_0. The analysis was carried out blindly for HE0435-1223 and PG1115+080, while it was not blind for WFI2033-4723, as we build upon the previous published model. For comparison with previous HST-based work, we limit our analysis to the case of no internal mass-sheet degeneracy ($λ_{\rm int}=1$). We quantify the impact of improved imaging, single-aperture kinematics, and environment measurements on central values and uncertainties. Within flat $Λ$CDM, assuming a uniform prior on $Ω_{\rm m}$, we find H_0 = 71.8$_{-7.0}^{+9.2}$ $λ_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for PG1115+080, 74.2$_{-4.2}^{+4.2}$ $λ_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for HE0435-1223, and 73.4$_{-4.4}^{+3.4}$ $λ_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$ for WFI2033-4723. Combining the three lenses yields H_0 = 73.5$_{-2.8}^{+2.7}$ $λ_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$, consistent with HST-based results (73.6$_{-2.6}^{+2.6}$ $λ_{\rm int}$ km s$^{-1}$ Mpc$^{-1}$), but with reduced scatter between the three systems. These models will be incorporated in the TDCOSMO-2026 milestone paper with free $λ_{\rm int}$ in a hierarchical fashion. We close by outlining how 16 forthcoming JWST NIRCam targets will further tighten uncertainties toward percent-level precision on H_0.

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A possible challenge for Cold and Warm Dark Matter

Measuring the density profile and mass concentration of dark-matter haloes is a key test of the standard cold dark matter paradigm. Such objects are dark and thus challenging to characterise, but they can be studied via gravitational lensing. Recently, a million-solar-mass object was discovered superposed on an extended and extremely thin gravitational arc. Here we report on extensive tests of various assumptions for the mass density profile and redshift of this object. We find models that best describe the data have two components: an unresolved point-mass of radius $\leq10$ pc centred on an extended mass distribution with an almost constant surface density out to a truncation radius of 139 pc. These properties do not resemble any known astronomical object. However, if the object is dark matter-dominated, its structure is incompatible with cold dark matter models, but may be compatible with a self-interacting dark matter halo where the central region has collapsed to form a black hole. This detection could thus carry substantial implications for our current understanding of dark matter.

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A million-solar-mass object detected at cosmological distance using gravitational imaging

Structure on sub-galactic scales provides important tests of galaxy formation models and the nature of dark matter. However, such objects are typically too faint to provide robust mass constraints. Here, we report the discovery of an extremely low-mass object detected via its gravitational perturbation to a thin lensed arc observed with milli-arcsecond-resolution very long baseline interferometry (VLBI). The object was identified using a non-parametric gravitational imaging technique and confirmed using independent parametric modelling. It contains a mass of $m_{\rm 80}=(1.13 \pm 0.04)\times 10^6{M_\odot}$ within a projected radius of 80 parsecs at an assumed redshift of 0.881. This detection is extremely robust and precise, with a statistical significance of 26$σ$, a 3.3 per cent fractional uncertainty on $m_{\rm 80}$, and an astrometric uncertainty of 194 $μ$as. This is the lowest-mass object known to us, by two orders of magnitude, to be detected at a cosmological distance by its gravitational effect. This work demonstrates the observational feasibility of using gravitational imaging to probe the million-solar-mass regime far beyond our local Universe.

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Complex angular structure of three elliptical galaxies from high-resolution ALMA observations of strong gravitational lenses

The large-scale mass distributions of galaxy-scale strong lenses have long been assumed to be well-described by a singular ellipsoidal power-law density profile with external shear. However, the inflexibility of this model could lead to systematic errors in astrophysical parameters inferred with gravitational lensing observables. Here, we present observations with the Atacama Large (sub-)Millimetre Array (ALMA) of three strongly lensed dusty star-forming galaxies at $\simeq30$ mas angular resolution and investigate the sensitivity of these data to angular structure in the lensing galaxies. We jointly infer the lensing mass distribution and the full surface brightness of the lensed sources with multipole expansions of the power-law density profile up to fourth order using a technique developed for interferometric data. All three data sets strongly favour third and fourth-order multipole amplitudes of $\approx1$ percent of the convergence. While the infrared stellar isophotes and isodensity shapes agree for one lens system, for the other two the isophotes disagree to varying extents, suggesting contributions to the angular structure from dark matter intrinsic or extrinsic to the lensing galaxy.

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JWST lensed quasar dark matter survey I: Description and First Results

The flux ratios of gravitationally lensed quasars provide a powerful probe of the nature of dark matter. Importantly, these ratios are sensitive to small-scale structure, irrespective of the presence of baryons. This sensitivity may allow us to study the halo mass function even below the scales where galaxies form observable stars. For accurate measurements, it is essential that the quasar's light is emitted from a physical region of the quasar with an angular scale of milli-arcseconds or larger; this minimizes microlensing effects by stars within the deflector. The warm dust region of quasars fits this criterion, as it has parsec-size physical scales and dominates the spectral energy distribution of quasars at wavelengths greater than 10$μ$m. The JWST Mid-Infrared Instrument (MIRI) is adept at detecting redshifted light in this wavelength range, offering both the spatial resolution and sensitivity required for accurate gravitational lensing flux ratio measurements. Here, we introduce our survey designed to measure the warm dust flux ratios of 31 lensed quasars. We discuss the flux-ratio measurement technique and present results for the first target, DES J0405-3308. We find that we can measure the quasar warm dust flux ratios with 3% precision. Our simulations suggest that this precision makes it feasible to detect the presence of 10$^7$ M$_\odot$ dark matter halos at cosmological distances. Such halos are expected to be completely dark in Cold Dark Matter models.

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Strong gravitational lensing as a probe of dark matter

Dark matter structures within strong gravitational lens galaxies and along their line of sight leave a gravitational imprint on the multiple images of lensed sources. Strong gravitational lensing provides, therefore, a key test of different dark matter models in a way that is independent of the baryonic content of matter structures on subgalactic scales. In this chapter, we describe how galaxy-scale strong gravitational lensing observations are sensitive to the physical nature of dark matter. We provide a historical perspective of the field, and review its current status. We discuss the challenges and advances in terms of data, treatment of systematic errors and theoretical predictions, that will enable one to deliver a stringent and robust test of different dark matter models in the near future. With the advent of the next generation of sky surveys, the number of known strong gravitational lens systems is expected to increase by several orders of magnitude. Coupled with high-resolution follow-up observations, these data will provide a key opportunity to constrain the properties of dark matter with strong gravitational lensing.

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TDCOSMO. XI. New lensing galaxy redshift and velocity dispersion measurements from Keck spectroscopy of eight lensed quasar systems

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.

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Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses. II.Observational constraints on the sub-galactic matter power spectrum

Stringent observational constraints on the sub-galactic matter power spectrum would allow one to distinguish between the concordance $Λ$CDM and the various alternative dark-matter models that predict significantly different properties of mass structure in galactic haloes. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to probe the sub-galactic mass structure in lens galaxies beyond the Local Group. Here, we demonstrate the first application of a novel methodology to observationally constrain the sub-galactic matter power spectrum in the inner regions of massive elliptical lens galaxies on 1-10 kpc scales from the power spectrum of surface-brightness anomalies in highly magnified galaxy-scale Einstein rings and gravitational arcs. The pilot application of our approach to Hubble Space Telescope (HST/WFC3/F390W) observations of the SLACS lens system SDSS J0252+0039 allows us to place the following observational constraints (at the 99 per cent confidence level) on the dimensionless convergence power spectrum $Δ^{2}_{δκ}$ and the standard deviation in the aperture mass $σ_{\rm AM}$: $Δ^{2}_{δκ}<1$ ($σ_{\rm AM}< 0.8 \times 10^8 M_\odot$) on 0.5-kpc scale, $Δ^{2}_{δκ}<0.1$ ($σ_{\rm AM}< 1 \times 10^8 M_\odot$) on 1-kpc scale and $Δ^{2}_{δκ}<0.01$ ($σ_{\rm AM}< 3 \times 10^8 M_\odot$) on 3-kpc scale. These first upper-limit constraints still considerably exceed the estimated effect of CDM subhaloes. However, future analysis of a larger sample of galaxy-galaxy strong lens systems can substantially narrow down these limits and possibly rule out dark-matter models that predict a significantly higher level of density fluctuations on the critical sub-galactic scales.

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Probing sub-galactic mass structure with the power spectrum of surface-brightness anomalies in high-resolution observations of galaxy-galaxy strong gravitational lenses. I. Power-spectrum measurement and feasibility study

While the direct detection of the dark-matter particle remains very challenging, the nature of dark matter could be possibly constrained by comparing the observed abundance and properties of small-scale sub-galactic mass structures with predictions from the phenomenological dark-matter models, such as cold, warm or hot dark matter. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to search for tiny surface-brightness anomalies in the extended lensed images (i.e. Einstein rings or gravitational arcs), induced by possible small-scale mass structures in the foreground lens galaxy. In this paper, the first in a series, we introduce and test a methodology to measure the power spectrum of such surface-brightness anomalies from high-resolution Hubble Space Telescope (HST) imaging. In particular, we focus on the observational aspects of this statistical approach, such as the most suitable observational strategy and sample selection, the choice of modelling techniques and the noise correction. We test the feasibility of the power-spectrum measurement by applying it to a sample of galaxy-galaxy strong gravitational lens systems from the Sloan Lens ACS Survey, with the most extended, bright, high-signal-to-noise-ratio lensed images, observed in the rest frame ultraviolet. In the companion paper, we present the methodology to relate the measured power spectrum to the statistical properties of the underlying small-scale mass structures in the lens galaxy and infer the first observational constraints on the sub-galactic matter power spectrum in a massive elliptical (lens) galaxy.

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STRIDES: Automated uniform models for 30 quadruply imaged quasars

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.

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Time Delay Lens Modelling Challenge

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.

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An Optical Observational Cluster Mass Function at $z\sim1$ with the ORELSE Survey

We present a new mass function of galaxy clusters and groups using optical/near-infrared wavelength spectroscopic and photometric data from the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) survey. At $z\sim1$, cluster mass function studies are rare regardless of wavelength and have never been attempted from an optical/near-infrared perspective. This work serves as a proof of concept that $z\sim1$ cluster mass functions are achievable without supplemental X-ray or Sunyaev-Zel'dovich (SZ) data. Measurements of the cluster mass function provide important contraints on cosmological parameters and are complementary to other probes. With ORELSE, a new cluster finding technique based on Voronoi tessellation Monte-Carlo (VMC) mapping, and rigorous purity and completeness testing, we have obtained $\sim$240 galaxy overdensity candidates in the redshift range $0.55<z<1.37$ at a mass range of $13.6<\log(M/M_{\odot})<14.8$. This mass range is comparable to existing optical cluster mass function studies for the local universe. Our candidate numbers vary based on the choice of multiple input parameters related to detection and characterization in our cluster finding algorithm, which we incorporated into the mass function analysis through a Monte-Carlo scheme. We find cosmological constraints on the matter density of $Ω_{m} = 0.250^{+0.104}_{-0.099}$ and on the amplitude of fluctuations of $σ_{8} = 1.150^{+0.260}_{-0.163}$. While our $Ω_{m}$ value is close to concordance, our $σ_{8}$ value is $\sim2σ$ higher because of the inflated observed number densities compared to theoretical mass function models owing to how our survey targeted overdense regions. With Euclid and several other large, unbiased optical surveys on the horizon, VMC mapping will enable optical/NIR cluster cosmology at redshifts much higher than what has been possible before.

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TDCOSMO IV: Hierarchical time-delay cosmography -- joint inference of the Hubble constant and galaxy density profiles

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.

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TDCOSMO II: 6 new time delays in lensed quasars from high-cadence monitoring at the MPIA 2.2m telescope

We present six new time-delay measurements obtained from $R_c$-band monitoring data acquired at the Max Planck Institute for Astrophysics (MPIA) 2.2 m telescope at La Silla observatory between October 2016 and February 2020. The lensed quasars HE 0047-1756, WG 0214-2105, DES 0407-5006, 2M 1134-2103, PSJ 1606-2333 and DES 2325-5229 were observed almost daily at high signal-to-noise ratio to obtain high-quality light curves where we can record fast and small-amplitude variations of the quasars. We measured time delays between all pairs of multiple images with only one or two seasons of monitoring with the exception of the time delays relative to image D of PSJ 1606-2333. The most precise estimate was obtained for the delay between image A and image B of DES 0407-5006, where $τ_{AB} = -128.4^{+3.5}_{-3.8}$ d (2.8% precision) including systematics due to extrinsic variability in the light curves. For HE 0047-1756, we combined our high-cadence data with measurements from decade-long light curves from previous COSMOGRAIL campaigns, and reach a precision of 0.9 d on the final measurement. The present work demonstrates the feasibility of measuring time delays in lensed quasars in only one or two seasons, provided high signal-to-noise ratio data are obtained at a cadence close to daily.

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Is every strong lens model unhappy in its own way? Uniform modelling of a sample of 13 quadruply+ imaged quasars

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.

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TDCOSMO. I. An exploration of systematic uncertainties in the inference of $H_0$ from time-delay cosmography

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.

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H0LiCOW XI. A weak lensing measurement of the external convergence in the field of the lensed quasar B1608+656 using HST and Subaru deep imaging

We investigate the environment and line of sight of the H0LiCOW lens B1608+656 using Subaru Suprime-Cam and the Hubble Space Telescope (HST) to perform a weak lensing analysis. We compare three different methods to reconstruct the mass map of the field, i.e. the standard Kaiser-Squires inversion coupled with inpainting and Gaussian or wavelet filtering, and $\tt{Glimpse}$ a method based on sparse regularization of the shear field. We find no substantial difference between the 2D mass reconstructions, but we find that the ground-based data is less sensitive to small-scale structures than the space-based observations. Marginalising over the results obtained with all the reconstruction techniques applied to the two available HST filters F606W and F814W, we estimate the external convergence, $κ_{\rm ext}$ at the position of B1608+656 is $κ_{\rm ext} = 0.11^{+0.06}_{-0.04}$, where the error bars corresponds respectively to the 16th and 84th quartiles. This result is compatible with previous estimates using the number-counts technique, suggesting that B1608+656 resides in an over-dense line of sight, but with a completely different technique. Using our mass reconstructions, we also compare the convergence at the position of several groups of galaxies in the field of B1608+656 with the mass measurements using various analytical mass profiles, and find that the weak lensing results favor truncated halo models.

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SHARP -- VI. Evidence for CO (1-0) molecular gas extended on kpc-scales in AGN star forming galaxies at high redshift

We present a study of the stellar host galaxy, CO (1$-$0) molecular gas distribution and AGN emission on 50 to 500 pc-scales of the gravitationally lensed dust-obscured AGN MG J0751+2716 and JVAS B1938+666 at redshifts 3.200 and 2.059, respectively. By correcting for the lensing distortion using a grid-based lens modelling technique, we spatially locate the different emitting regions in the source plane for the first time. Both AGN host galaxies have 300 to 500 pc-scale size and surface brightness consistent with a bulge/pseudo-bulge, and 2 kpc-scale AGN radio jets that are embedded in extended molecular gas reservoirs that are 5 to 20 kpc in size. The CO (1$-$0) velocity fields show structures possibly associated with discs (elongated velocity gradients) and interacting objects (off-axis velocity components). There is evidence for a decrement in the CO (1$-$0) surface brightness at the location of the host galaxy, which may indicate radiative feedback from the AGN, or offset star formation.We find CO-H$_2$ conversion factors of around $α_{\rm CO} = 1.5\pm0.5$ (K km s$^{-1}$ pc$^2$)$^{-1}$, molecular gas masses of $> 3\times10^{10}$ M$_{\odot}$, dynamical masses of $\sim 10^{11}$ M$_{\odot}$ and gas fractions of around 60 per cent. The intrinsic CO line luminosities are comparable to those of unobscured AGN and dusty star-forming galaxies at similar redshifts, but the infrared luminosities are lower, suggesting that the targets are less efficient at forming stars. Therefore, they may belong to the AGN feedback phase predicted by galaxy formation models, because they are not efficiently forming stars considering their large amount of molecular gas.

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