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In a strong gravitational lensing system, the distorted light from a source is analysed to infer the properties of the lens. However, light emitted by the lens itself can contaminate the image of the source, introducing systematic errors in the analysis. We present a simple and efficient lens light model based on the well-tested multi-Gaussian expansion (MGE) method for representing galaxy surface brightness profiles, which we combine with a semi-linear inversion scheme for pixelized source modelling. Testing it against realistic mock lensing images, we show that our scheme can fit the lensed images to the noise level, with relative differences between the true input and best-fitting lens light model remaining below 5 per cent. We apply the MGE lens light model to 38 lenses from the HST SLACS sample. We find that the new scheme provides a good fit for the majority of the sample with only 3 exceptions – these show clear asymmetric residuals in the lens light. We examine the radial dependence of the ellipticity and position angles and confirm that it is common for a typical lens galaxy to exhibit twisting non-elliptical isophotes and boxy / disky isophotes. Our MGE lens light model will be a valuable tool for understanding the hidden complexity of the lens mass distribution. [ABSTRACT FROM AUTHOR]

Aims. We provide an in-depth analysis of the COSMOS-Web ring, an Einstein ring at z ≈ 2 that we serendipitously discovered during the data reduction of the COSMOS-Web survey and that could be the most distant lens discovered to date. Methods. We extracted the visible and near-infrared photometry of the source and the lens from more than 25 bands. We combined these observations with far-infrared detections to study the dusty nature of the source and we derived the photometric redshifts and physical properties of both the lens and the source with three different spectral energy distribution (SED) fitting codes. Using JWST/NIRCam images, we also produced two lens models to (i) recover the total mass of the lens, (ii) derive the magnification of the system, (iii) reconstruct the morphology of the lensed source, and (iv) measure the slope of the total mass density profile of the lens. Results. We find the lens to be a very massive elliptical galaxy at z = 2.02 ± 0.02 with a total mass within the Einstein radius of Mtot(<θEin = (3.66 ± 0.36) × 1011M⊙ and a total stellar mass of M⋆ = 1.37−0.11+0.14 × 1011 M⊙. We also estimate it to be compact and quiescent with a specific star formation rate below 10−13 yr. Compared to stellar-to-halo mass relations from the literature, we find that the total mass of the lens within the Einstein radius is consistent with the presence of a dark matter (DM) halo of total mass Mh = 1.09−0.57+1.46 × 1013 M⊙. In addition, the background source is a M⋆ = (1.26 ± 0.17) × 1010M⊙ star-forming galaxy (SFR ≈ (78 ± 15) M⊙ yr) at z = 5.48 ± 0.06. The morphology reconstructed in the source plane shows two clear components with different colors. Dust attenuation values from SED fitting and nearby detections in the far infrared also suggest that the background source could be at least partially dust-obscured. Conclusions. We find the lens at z ≈ 2. Its total, stellar, and DM halo masses are consistent within the Einstein ring, so we do not need any unexpected changes in our description of the lens such as changing its initial mass function or including a non-negligible gas contribution. The most likely solution for the lensed source is at z ≈ 5.5. Its reconstructed morphology is complex and highly wavelength dependent, possibly because it is a merger or a main sequence galaxy with a heterogeneous dust distribution. [ABSTRACT FROM AUTHOR]

The distribution of mass in galaxy-scale strong gravitational lenses is often modelled as an elliptical power-law plus 'external shear', which notionally accounts for neighbouring galaxies and cosmic shear along our line of sight. A small amount of external shear could come from these sources, but we show that the vast majority does not. Except in a handful of rare systems, the best-fitting values do not correlate with independent measurements of line-of-sight shear: from weak lensing in 45 Hubble Space Telescope images, or in 50 mock images of lenses with complex distributions of mass. Instead, the best-fit external shear is aligned with the major or minor axis of 88 per cent of lens galaxies; and the amplitude of the external shear increases if that galaxy is discy. We conclude that 'external shear' attached to a power-law model is not physically meaningful, but a fudge to compensate for lack of model complexity. Since it biases other model parameters that are interpreted as physically meaningful in several science analyses (e.g. measuring galaxy evolution, dark matter physics or cosmological parameters), we recommend that future studies of galaxy-scale strong lensing should employ more flexible mass models. [ABSTRACT FROM AUTHOR]

The cold dark matter (DM) model predicts that every galaxy contains thousands of DM subhaloes; almost all other DM models include a physical process that smooths away the subhaloes. The subhaloes are invisible, but could be detected via strong gravitational lensing, if they lie on the line of sight to a multiply imaged background source, and perturb its apparent shape. We present a predominantly automated strong lens analysis framework, and scan for DM subhaloes in Hubble Space Telescope imaging of 54 strong lenses. We identify five DM subhalo candidates, including two especially compelling candidates (one previously known in SLACS0946 + 1006) where a subhalo is favoured after all of our tests for systematics. We find that the detectability of subhaloes depends upon the assumed parametric form for the lens galaxy's mass distribution, especially its degree of azimuthal freedom. Using separate components for DM and stellar mass reveals two DM subhalo candidates and removes four false positives compared to the single power-law mass model that is common in the literature. We identify 45 lenses without substructures, the number of which is key to statistical tests able to rule out models of, for example, warm or self-interacting DM. Our full analysis results are available at https://github.com/Jammy2211/autolens_subhalo. [ABSTRACT FROM AUTHOR]

We report the ALMA Band 7 observations of 86 Herschel sources that likely contain gravitationally lensed galaxies. These sources are selected with relatively faint 500 μ m flux densities between 15 and 85 mJy in an effort to characterize the effect of lensing across the entire million-source Herschel catalogue. These lensed candidates were identified by their close proximity to bright galaxies in the near-infrared VISTA Kilo-Degree Infrared Galaxy survey. Our high-resolution observations (0.15 arcsec) confirm 47 per cent of the initial candidates as gravitational lenses, while lensing cannot be excluded across the remaining sample. We find average lensing masses (log  M /M⊙ = 12.9 ± 0.5) in line with previous experiments, although direct observations might struggle to identify the most massive foreground lenses across the remaining 53 per cent of the sample, particularly for lenses with larger Einstein radii. Our observations confirm previous indications that more lenses exist at low flux densities than expected from strong galaxy–galaxy lensing models alone, where the excess is likely due to additional contributions of cluster lenses and weak lensing. If we apply our method across the total 660 square degree H-ATLAS field, it would allow us to robustly identify 3000 gravitational lenses across the 660 square degree Herschel ATLAS fields. [ABSTRACT FROM AUTHOR]

We present 101- and 151-GHz ALMA continuum images for 85 fields selected from Herschel observations that have 500-μm flux densities >80 mJy and 250–500-μm colours consistent with z > 2, most of which are expected to be gravitationally lensed or hyperluminous infrared galaxies. Approximately half of the Herschel 500-μm sources were resolved into multiple ALMA sources, but 11 of the 15 brightest 500-μm Herschel sources correspond to individual ALMA sources. For the 37 fields containing either a single source with a spectroscopic redshift or two sources with the same spectroscopic redshift, we examined the colour temperatures and dust emissivity indices. The colour temperatures only vary weakly with redshift and are statistically consistent with no redshift-dependent temperature variations, which generally corresponds to results from other samples selected in far-infrared, submillimetre, or millimetre bands but not to results from samples selected in optical or near-infrared bands. The dust emissivity indices, with very few exceptions, are largely consistent with a value of 2. We also compared spectroscopic redshifts to photometric redshifts based on spectral energy distribution templates designed for infrared-bright high-redshift galaxies. While the templates systematically underestimate the redshifts by ∼15 per cent, the inclusion of ALMA data decreases the scatter in the predicted redshifts by a factor of ∼2, illustrating the potential usefulness of these millimetre data for estimating photometric redshifts. [ABSTRACT FROM AUTHOR]

Supermassive black holes (SMBHs) are a key catalyst of galaxy formation and evolution, leading to an observed correlation between SMBH mass M BH and host galaxy velocity dispersion σe. Outside the local Universe, measurements of M BH are usually only possible for SMBHs in an active state: limiting sample size and introducing selection biases. Gravitational lensing makes it possible to measure the mass of non-active SMBHs. We present models of the |$z$|  = 0.169 galaxy-scale strong lens Abell 1201. A cD galaxy in a galaxy cluster, it has sufficient 'external shear' that a magnified image of a |$z$|  = 0.451 background galaxy is projected just ∼1 kpc from the galaxy centre. Using multiband Hubble Space Telescope imaging and the lens modelling software PYAUTOLENS , we reconstruct the distribution of mass along this line of sight. Bayesian model comparison favours a point mass with M BH = 3.27 ± 2.12 × 1010 M⊙ (3σ confidence limit); an ultramassive black hole. One model gives a comparable Bayesian evidence without an SMBH; however, we argue this model is nonphysical given its base assumptions. This model still provides an upper limit of M BH ≤ 5.3 × 1010 M⊙, because an SMBH above this mass deforms the lensed image ∼1 kpc from Abell 1201's centre. This builds on previous work using central images to place upper limits on M BH, but is the first to also place a lower limit and without a central image being observed. The success of this method suggests that surveys during the next decade could measure thousands more SMBH masses, and any redshift evolution of the M BH−σe relation. Results are available at https://github.com/Jammy2211/autolens_abell_1201. [ABSTRACT FROM AUTHOR]

Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of ∼109 M⊙ and below to be detected. We test commonly used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a ∼1013 M⊙ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the baryon dominated region. To remove particle noise, we represent the projected galaxy mass distribution by a series of Gaussian profiles which precisely capture the features of the projected galaxy. We first model the lens mass as a (broken) power-law density profile and then search for small haloes. Of the two projections, one has a regular elliptical shape, while the other has distinct deviations from an elliptical shape. For the former, the broken power-law model gives no false positives and correctly recovers the mass of the superposed small halo; however, for the latter we find false positives and the inferred halo mass is overestimated by ∼4–5 times. We then use a more complex model in which the lens mass is decomposed into stellar and dark matter components. In this case, we show that we can capture the simulated galaxy's complex projected structures and correctly infer the input small halo. [ABSTRACT FROM AUTHOR]

We rederive the number density of intervening line-of-sight haloes relative to lens subhaloes in galaxy-galaxy strong lensing observations, where these perturbers can generate detectable image fluctuations. Previous studies have calculated the detection limit of a line-of-sight small-mass dark halo by comparing the lensing deflection angles it would cause, to those caused by a subhalo within the lens. However, this overly simplifies the difference in observational consequences between a subhalo and a line-of-sight halo. Furthermore, it does not take into account degeneracies between an extra subhalo and the uncertain properties of the main lens. More in keeping with analyses of real-world observations, we regard a line-of-sight halo as detectable only if adding it to a smooth model generates a statistically significant improvement in the reconstructed image. We find that the number density of detectable line-of-sight perturbers has been overestimated by as much as a factor of two in the previous literature. For typical lensing geometries and configurations, very deep imaging is sensitive to twice as many line-of-sight perturbers as subhaloes, but moderate depth imaging is sensitive to only slightly more line-of-sight perturbers than subhaloes. [ABSTRACT FROM AUTHOR]

We present modelling of ∼0.1 arcsec resolution Atacama Large Millimetre/submillimetre Array imaging of seven strong gravitationally lensed galaxies detected by the Herschel Space Observatory. Four of these systems are galaxy–galaxy strong lenses, with the remaining three being group-scale lenses. Through careful modelling of visibilities, we infer the mass profiles of the lensing galaxies and by determining the magnification factors, we investigate the intrinsic properties and morphologies of the lensed submillimetre sources. We find that these submillimetre sources all have ratios of star formation rate to dust mass that are consistent with, or in excess of, the mean ratio for high-redshift submillimetre galaxies and low redshift ultra-luminous infrared galaxies. Reconstructions of the background sources reveal that the majority of our sample display disturbed morphologies. The majority of our lens models have mass density slopes close to isothermal, but some systems show significant differences. [ABSTRACT FROM AUTHOR]

A fundamental prediction of the cold dark matter (CDM) model of structure formation is the existence of a vast population of dark matter haloes extending to subsolar masses. By contrast, other dark matter models, such as a warm thermal relic (WDM), predict a cutoff in the mass function at a mass which, for popular models, lies approximately between 107 and |$10^{10}\, {\rm M}_\odot$|⁠. We use mock observations to demonstrate the viability of a forward modelling approach to extract information about low-mass dark haloes lying along the line of sight to galaxy–galaxy strong lenses. This can be used to constrain the mass of a thermal relic dark matter particle, m DM. With 50 strong lenses at Hubble Space Telescope resolution and a maximum pixel signal-to-noise ratio of ∼50, the expected median 2σ constraint for a CDM-like model (with a halo mass cutoff at |$10^{7}\, {\rm M}_\odot$|⁠) is |$m_\mathrm{DM} \gt 4.10 \, \mathrm{keV}$| (50 per cent chance of constraining m DM to be better than 4.10 keV). If, however, the dark matter is a warm particle of |$m_\mathrm{DM}=2.2 \, \mathrm{keV}$|⁠ , our 'approximate Bayesian computation' method would result in a median estimate of m DM between 1.43 and 3.21 keV. Our method can be extended to the large samples of strong lenses that will be observed by future telescopes and could potentially rule out the standard CDM model of cosmogony. To aid future survey design, we quantify how these constraints will depend on data quality (spatial resolution and integration time) as well as on the lensing geometry (source and lens redshifts). [ABSTRACT FROM AUTHOR]

A defining prediction of the cold dark matter cosmological model is the existence of a very large population of low-mass haloes. This population is absent in models in which the dark matter particle is warm (WDM). These alternatives can, in principle, be distinguished observationally because haloes along the line of sight can perturb galaxy–galaxy strong gravitational lenses. Furthermore, the WDM particle mass could be deduced because the cut-off in their halo mass function depends on the mass of the particle. We systematically explore the detectability of low-mass haloes in WDM models by simulating and fitting mock lensed images. Contrary to previous studies, we find that haloes are harder to detect when they are either behind or in front of the lens. Furthermore, we find that the perturbing effect of haloes increases with their concentration: Detectable haloes are systematically high-concentration haloes, and accounting for the scatter in the mass–concentration relation boosts the expected number of detections by as much as an order of magnitude. Haloes have lower concentration for lower particle masses and this further suppresses the number of detectable haloes beyond the reduction arising from the lower halo abundances alone. Taking these effects into account can make lensing constraints on the value of the mass function cut-off at least an order of magnitude more stringent than previously appreciated. [ABSTRACT FROM AUTHOR]

Verifying that sub-mm galaxies are gravitationally lensed requires time-expensive observations with oversubscribed high-resolution observatories. Here, we aim to strengthen the evidence of gravitational lensing within the Herschel Bright Sources (HerBS) by cross-comparing their positions to optical (SDSS) and near-infrared (VIKING) surveys, in order to search for the foreground lensing galaxy candidates. Resolved observations of the brightest HerBS sources have already shown that most are lensed, and a galaxy evolution model predicts that ∼76 per cent of the total HerBS sources are lensed, although with the SDSS survey we are only able to identify the likely foreground lenses for 25 per cent of the sources. With the near-infrared VIKING survey, however, we are able to identify the likely foreground lenses for 57 per cent of the sources, and we estimate that 82 per cent of the HerBS sources have lenses on the VIKING images even if we cannot identify the lens in every case. We find that the angular offsets between lens and Herschel source are larger than that expected if the lensing is done by individual galaxies. We also find that the fraction of HerBS sources that are lensed falls with decreasing 500-micron flux density, which is expected from the galaxy evolution model. Finally, we apply our statistical VIKING cross-identification to the entire Herschel -ATLAS catalogue, where we also find that the number of lensed sources falls with decreasing 500-micron flux density. [ABSTRACT FROM AUTHOR]

With the advent of wide-area submillimetre surveys, a large number of high-redshift gravitationally lensed dusty star-forming galaxies have been revealed. Because of the simplicity of the selection criteria for candidate lensed sources in such surveys, identified as those with S500 µm > 100 mJy, uncertainties associated with the modelling of the selection function are expunged. The combination of these attributes makes submillimetre surveys ideal for the study of strong lens statistics. We carried out a pilot study of the lensing statistics of submillimetreselected sources by making observations with the Atacama Large Millimeter Array (ALMA) of a sample of strongly lensed sources selected from surveys carried out with the Herschel Space Observatory. We attempted to reproduce the distribution of image separations for the lensed sources using a halo mass function taken from a numerical simulation that contains both dark matter and baryons. We used three different density distributions, one based on analytical fits to the haloes formed in the EAGLE simulation and two density distributions [Singular Isothermal Sphere (SIS) and SISSA] that have been used before in lensing studies. We found that we could reproduce the observed distribution with all three density distributions, as long as we imposed an upper mass transition of ~1013M⊙ for the SIS and SISSA models, above which we assumed that the density distribution could be represented by a Navarro-Frenk-White profile. We show that we would need a sample of ~500 lensed sources to distinguish between the density distributions, which is practical given the predicted number of lensed sources in the Herschel surveys. [ABSTRACT FROM AUTHOR]