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    We investigate the mass structure of a strong gravitational lens galaxy at z = 0.350, taking advantage of the milliarcsecond (mas) angular resolution of very long baseline interferometric (VLBI) observations. In the first analysis of its kind at this resolution, we jointly infer the lens model parameters and pixellated radio source surface brightness. We consider several lens models of increasing complexity, starting from an elliptical power-law density profile. We extend this model to include angular multipole structures, a separate stellar mass component, additional nearby field galaxies, and/or a generic external potential. We compare these models using their relative Bayesian log-evidence (Bayes factor). We find strong evidence for angular structure in the lens; our best model is comprised of a power-law profile plus multipole perturbations and external potential, with a Bayes factor of +14984 relative to the elliptical power-law model. It is noteworthy that the elliptical power-law mass distribution is a remarkably good fit on its own, with additional model complexity correcting the deflection angles only at the ∼5 mas level. We also consider the effects of added complexity in the lens model on time-delay cosmography and flux-ratio analyses. We find that an overly simplistic power-law ellipsoid lens model can biasmore »the measurement of H0 by ∼3 per cent and mimic flux ratio anomalies of ∼8 per cent. Our results demonstrate the power of high-resolution VLBI observations to provide strong constraints on the inner density profiles of lens galaxies.

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  2. Free, publicly-accessible full text available August 1, 2023

    Strongly lensed quasars can provide measurements of the Hubble constant (H0) independent of any other methods. One of the key ingredients is exquisite high-resolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptive-optics (AO) imaging from ground-based telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three time-delay lenses with AO imaging (RX J1131−1231, HE 0435−1223, and PG 1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck telescope, obtained as part of the Strong lensing at High Angular Resolution Program (SHARP) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat Λ cold dark matter (ΛCDM) model with fixed Ωm = 0.3, we show that by marginalizing over two different kinds of mass models (power-law and composite models) and their transformed mass profiles via a mass-sheet transformation, we obtain $\Delta t_{\rm BA}=6.89\substack{+0.8\\-0.7}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, $\Delta t_{\rm CA}=10.7\substack{+1.6\\-1.2}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, and $\Delta t_{\rm DA}=7.70\substack{+1.0\\-0.9}\, h^{-1}\hat{\sigma }_{v}^{2}$ d, where $h=H_{0}/100\,\rm km\, s^{-1}\, Mpc^{-1}$ is the dimensionless Hubble constant and $\hat{\sigma }_{v}=\sigma ^{\rm ob}_{v}/(280\,\rm km\, s^{-1})$ is the scaled dimensionless velocity dispersion. Future measurements of timemore »delays with 10 per cent uncertainty and velocity dispersion with 5 per cent uncertainty would yield a H0 constraint of ∼15 per cent precision.

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  4. ABSTRACT The presence of an invisible substructure has previously been detected in the gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed images. Using flexible models for the main halo and the subhalo perturbation, we demonstrate that the subhalo has an extraordinarily high central density and steep density slope. We robustly infer the subhalo’s projected mass within 1 kpc to be ∼2–3.7 × 109 M⊙ at >95 per cent CL for all our lens models, while the average log-slope of the subhalo’s projected density profile over the radial range 0.75–1.25 kpc is constrained to be steeper than isothermal (γ2D ≲ −1). By modeling the subhalo light, we infer a conservative upper bound on its luminosity LV < 1.2 × 108L⊙ at 95 per cent CL that shows that the perturber is dark matter dominated. We analyse lensing galaxy analogues in the Illustris TNG100-1 simulation over many lines of sight, and find hundreds of subhalos that achieve a mass within 1 kpc ≳ 2 × 109M⊙. However, less than 1 per cent of the mock observations yield a log-slope steep enough to be consistent with our lensing models, and they all have stellar masses exceeding that allowed by observations by an order of magnitude or more. We conclude that the presence of such a darkmore »highly concentrated subhalo is unexpected in a Lambda cold dark matter universe. While it remains to be determined whether this tension can be reduced by adding more complexity to the primary lens model, it is not significantly alleviated if the perturber is assumed to be a LOS structure, rather than a subhalo.« less

    This paper aims to quantify how the lowest halo mass that can be detected with galaxy-galaxy strong gravitational lensing depends on the quality of the observations and the characteristics of the observed lens systems. Using simulated data, we measure the lowest detectable NFW mass at each location of the lens plane, in the form of detailed sensitivity maps. In summary, we find that: (i) the lowest detectable mass Mlow decreases linearly as the signal-to-noise ratio (SNR) increases and the sensitive area is larger when we decrease the noise; (ii) a moderate increase in angular resolution (0.07″ versus 0.09″) and pixel scale (0.01″ versus 0.04″) improves the sensitivity by on average 0.25 dex in halo mass, with more significant improvement around the most sensitive regions; (iii) the sensitivity to low-mass objects is largest for bright and complex lensed galaxies located inside the caustic curves and lensed into larger Einstein rings (i.e rE ≥ 1.0″). We find that for the sensitive mock images considered in this work, the minimum mass that we can detect at the redshift of the lens lies between 1.5 × 108 and $3\times 10^{9}\, \mathrm{M}_{\odot }$. We derive analytic relations between Mlow, the SNR and resolution and discuss themore »impact of the lensing configuration and source structure. Our results start to fill the gap between approximate predictions and real data and demonstrate the challenging nature of calculating precise forecasts for gravitational imaging. In light of our findings, we discuss possible strategies for designing strong lensing surveys and the prospects for HST, Keck, ALMA, Euclid and other future observations.

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  6. ABSTRACT We derive joint constraints on the warm dark matter (WDM) half-mode scale by combining the analyses of a selection of astrophysical probes: strong gravitational lensing with extended sources, the Ly α forest, and the number of luminous satellites in the Milky Way. We derive an upper limit of λhm = 0.089 Mpc h−1 at the 95 per cent confidence level, which we show to be stable for a broad range of prior choices. Assuming a Planck cosmology and that WDM particles are thermal relics, this corresponds to an upper limit on the half-mode mass of Mhm < 3 × 107 M⊙ h−1, and a lower limit on the particle mass of mth > 6.048 keV, both at the 95 per cent confidence level. We find that models with λhm > 0.223 Mpc h−1 (corresponding to mth > 2.552 keV and Mhm < 4.8 × 108 M⊙ h−1) are ruled out with respect to the maximum likelihood model by a factor ≤1/20. For lepton asymmetries L6 > 10, we rule out the 7.1 keV sterile neutrino dark matter model, which presents a possible explanation to the unidentified 3.55 keV line in the Milky Way and clusters of galaxies. The inferred 95 percentiles suggest that we further rule out the ETHOS-4 model of self-interacting DM. Our results highlight themore »importance of extending the current constraints to lower half-mode scales. We address important sources of systematic errors and provide prospects for how the constraints of these probes can be improved upon in the future.« less
  7. ABSTRACT We present the measurement of the Hubble constant, H0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H0. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rm km\, s^{-1}\, Mpc^{-1}$ for PG 1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$ for HE 0435−1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$ for RXJ 1131−1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\, s^{-1}\, Mpc^{-1}$. The joint result of the AO + HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rm km\, s^{-1}\, Mpc^{-1}$. All of these results assume a flat Λ cold dark matter cosmology with a uniform priormore »on Ωm in [0.05, 0.5] and H0 in [0, 150] $\rm km\, s^{-1}\, Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H0. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper.« less