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The Hubble Frontier Fields data, along with multiple data sets obtained by other telescopes, have provided some of the most extensive constraints on cluster lenses to date. Multiple lens modelling teams analyzed the fields and made public a number of deliverables. By comparing these results, we can then undertake a unique and vital test of the state of cluster lens modelling. Specifically, we see how well the different teams can reproduce similar magnifications and mass profiles. We find that the circularly averaged mass profiles of the fields are remarkably constrained (scatter |$\lt 5{{\ \rm per\ cent}}$|⁠) at distances of 1 arcmin from the cluster core, yet magnifications can vary significantly. Averaged across the six fields, we find a bias of −6 per  cent (−17 per cent) and a scatter of ∼40 per cent (∼65 per cent) at a modest magnification of 3 (10). Statistical errors reported by individual teams are often significantly smaller than the differences among all the teams, indicating the importance of continued systematics studies in cluster lensing. [ABSTRACT FROM AUTHOR]

Cluster lensing has become an important tool in the search for high-redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to determine the magnification of the images. These models are traditionally 2D, focusing on the mass within the cluster and either ignoring or approximating any contribution from line-of-sight galaxies. In this paper, we present the first full set of 3D mass models of the six Hubble Frontier Fields and use them to test for systematic biases in magnifications due to using the traditional 2D approach. We find that omitting foreground or background galaxies causes image position offsets between 0.1 and 0.4 arcsec, a non-negligible fraction of the typical 0.3–0.7 arcsec residuals of current state-of-the-art models. We also find that median image magnifications can shift by up to 6 per cent, though it is dependent on the field. This can be alleviated in some cases by approximating the mass in the lensing plane, but a 5 per cent magnification bias still exists in other cases; image position offsets are also improved, but are still present at 0.10 arcsec. [ABSTRACT FROM AUTHOR]

Gravitational lens modelling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularization, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularization schemes that minimize derivatives of the source (using two finite difference methods) and introduce a scheme that minimizes deviations from an analytic source profile. Careful choice of gridding and regularization can reduce ‘discreteness noise’ in the χ2 surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realizations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different ‘observations’ can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few per cent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves. [ABSTRACT FROM PUBLISHER]

In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e. including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors. [ABSTRACT FROM PUBLISHER]

We report Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the dust continuum and [C ii ] emission of the host galaxy of J0439+1634, a gravitationally lensed quasar at z = 6.5. Gravitational lensing boosts the source-plane resolution to ∼0.″15 (∼0.8 kpc). The lensing model derived from the ALMA data is consistent with the fiducial model in Fan et al. based on HST imaging. The host galaxy of J0439+1634 can be well-fitted by a Sérsic profile consistent with an exponential disk, both in the far-infrared (FIR) continuum and the [C ii ] emission. The overall magnification is 4.53 ± 0.05 for the continuum and 3.44 ± 0.05 for the [C ii ] line. The host galaxy of J0439+1634 is a compact ultraluminous infrared galaxy, with a total star formation rate (SFR) of 1.56 × 103M⊙ yr−1 after correcting for lensing and an effective radius of 0.74 kpc. The resolved regions in J0439+1634 follow the "[C ii ] deficit," where the [C ii ]-to-FIR ratio decreases with FIR surface brightness. The reconstructed velocity field of J0439+1634 appears to be rotation-like. The maximum line-of-sight rotation velocity is 130 km s−1 at a radius of 2 kpc. However, our data cannot be fit by an axisymmetric thin rotating disk, and the inclination of the rotation axis, i, remains unconstrained. We estimate the dynamical mass of the host galaxy to be. J0439+1634 is likely to have a high gas-mass fraction and an oversized SMBH compared to local relations. The SFR of J0439+1634 reaches the maximum possible values, and the SFR surface density is close to the highest value seen in any star-forming galaxy currently known in the universe. [ABSTRACT FROM AUTHOR]

In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this small-scale structure. Much of the attention has been given to detecting individual dark matter subhaloes through lens modelling, but recent work has suggested that the full population of subhaloes could be probed using a power spectrum analysis. In this paper, we quantify the power spectrum of small-scale structure in simulated galaxies, with the goal of understanding theoretical predictions and setting the stage for using measurements of the power spectrum to test dark matter models. We use a sample of simulated galaxies generated from the galacticus semi-analytic model to determine the power spectrum distribution first in the CDM paradigm and then in a warm dark matter scenario. We find that a measurement of the slope and amplitude of the power spectrum on galaxy strong lensing scales (k ∼ 1 kpc−1) could be used to distinguish between CDM and alternate dark matter models, especially if the most massive subhaloes can be directly detected via gravitational imaging. [ABSTRACT FROM AUTHOR]

The free streaming length of dark matter particles determines the abundance of structure on sub-galactic scales. We present a statistical technique, amendable to any parametrization of subhalo density profile and mass function, to probe dark matter on these scales with quadrupole image lenses. We consider a warm dark matter particle with a mass function characterized by a normalization and free streaming scale m hm. We forecast bounds on dark matter warmth for 120–180 lenses, attainable with future surveys, at typical lens (source) redshifts of 0.5 (1.5) in early-type galaxies with velocity dispersions of  220–270 km s-1. We demonstrate that limits on m hm deteriorate rapidly with increasing uncertainty in image fluxes, underscoring the importance of precise measurements and accurate lens models. For our forecasts, we assume the deflectors in the lens sample do not exhibit complex morphologies, so we neglect systematic errors in their modelling. Omitting the additional signal from line-of-sight haloes, our constraints underestimate the true power of the method. Assuming cold dark matter, for a low normalization, corresponding to the destruction of all subhaloes within the host scale radius, we forecast 2σ bounds on m hm (thermal relic mass) of 107.5 (5.0), 108 (3.6), and |$10^{8.5} \ (2.7) \ {\rm M}_{\odot } \left(\rm {keV}\right)$| for flux errors of |$2{{\ \rm per\ cent}}$|⁠, |$4{{\ \rm per\ cent}}$|⁠, and |$8{{\ \rm per\ cent}}$|⁠. With a higher normalization, these constraints improve to 107.2 (6.6), 107.5 (5.3), and |$10^{7.8} \ (4.3) \ {\rm M}_{\odot } \left(\rm {keV}\right)$| with 120 systems. We are also able to measure the normalization of the mass function, which has implications for baryonic feedback models and tidal stripping. [ABSTRACT FROM AUTHOR]