Lens Mass Model Research Articles

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

HOLISMOKES - XII. Time-delay measurements of strongly lensed Type Ia supernovae using a long short-term memory network

Strongly lensed Type Ia supernovae (LSNe Ia) are a promising probe with which to measure the Hubble constant ($H_0$) directly. To use LSNe Ia for cosmography, a time-delay measurement between multiple images, a lens-mass model, and a mass reconstruction along the line of sight are required. In this work, we present the machine-learning network which is a combination of a long short-term memory network (LSTM) and a fully connected neural network (FCNN). The is designed to measure time delays on a sample of LSNe Ia spanning a broad range of properties, which we expect to find with the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) and for which follow-up observations are planned. With follow-up observations in the $i$ band (cadence of one to three days with a single-epoch $5 depth of 24.5 mag), we reach a bias-free delay measurement with a precision of around 0.7 days over a large sample of LSNe Ia. The is far more general than previous machine-learning approaches such as the random forest (RF) one, whereby an RF has to be trained for each observational pattern separately, and yet the outperforms the RF by a factor of roughly three. Therefore, the is a very promising approach to achieve robust time delays in LSNe Ia, which is important for a precise and accurate constraint on $H_0$.

Breaking the mass-sheet degeneracy in strong lensing mass modelling with weak lensing observations

ABSTRACT The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring $H_0$ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modelling. We propose and quantitatively assess the use of galaxy–galaxy shear measurements to break the MSD in the strong lensing mass modelling. We use stacked galaxy–galaxy lensing profiles and corresponding covariance matrices from Huang et al. to constrain the MSD in lens mass modelling with a highly flexible mass profile. Our analyses show that if ideally all galaxy–galaxy lensing measurements from the Hyper Suprime-Cam survey can be used to constrain the MSD, we can achieve $\sim 10~{{\ \rm per\ cent}}$ precision on the MSD constraint. We forecast that galaxy–galaxy lensing measurements from Legacy Survey of Space and Time (LSST)-like surveys can in general constrain the MSD with $\sim 1\,\mathrm{ per\,cent}-3~{{\ \rm per\ cent}}$ precision. Furthermore, if we push weak lensing measurements to a lower angular scale of $\sim 0.04\,\rm Mpc$, a survey like LSST can provide $\sim 1~{{\ \rm per\ cent}}$ precision on the MSD constraint, enabling a measurement of $H_0$ at the 1 per cent level. We demonstrate that galaxy–galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone.

The missing quasar image in the gravitationally lensed quasar HE0230−2130: Implications for the cored lens mass distribution and dark satellites

Strongly lensed systems with peculiar configurations allow us to probe the local properties of the deflecting lens mass while simultaneously testing general profile assumptions. The quasar HE0230−2130 is lensed by two galaxies at similar redshifts (Δz ∼ 0.003) into four observed images. Using modeled quasar positions from fitting the brightness of the quasar images in ground-based imaging data from the Magellan telescope, we find that lens-mass models where each of these two galaxies is parametrized with a singular power-law (PL) profile predict five quasar images. One of the predicted images is unobserved despite it being distinctively offset from the lensing galaxies and likely bright enough to be observable. This missing image gives rise to new opportunities to study the mass distribution of these galaxies. To interpret the quad configuration of the system, we tested 12 different profile assumptions with the aim of obtaining lens-mass models that correctly predict only four observed images. We tested the effects of adopting: cored profiles for the lensing galaxies; external shear; and additional profiles to represent a dark matter clump. We find that half of our model classes can produce the correct image multiplicity. By comparing the Bayesian evidence of different model parametrizations, we favor two model classes: (i) one that incorporates two singular PL profiles for the lensing galaxies and a cored isothermal sphere in the region of the previously predicted fifth image (rNIS profile), and (ii) one with a bigger lensing galaxy parametrized by a singular PL profile and the smaller galaxy by a cored PL profile with external shear. We estimated the mass of the rNIS clump for each candidate model of our final Markov chain Monte Carlo sample, and find that only 2% are in the range of 106 M⊙ ≤ MrNIS ≤ 109 M⊙, which is the predicted mass range of dark matter subhalos in cold dark matter simulations, or the mass of dark-matter-dominated and low-surface-brightness galaxies. We therefore favor the models with a cored mass distribution for the lens galaxy close to the predicted fifth image. Our study further demonstrates that lensed quasar images are sensitive to the dark matter structure in the gravitational lens. We are able to describe this exotic lensing configuration with relatively simple models, which demonstrates the power of strong lensing for studying galaxies and lens substructure.

Gravitational imaging through a triple source plane lens: revisiting the ΛCDM-defying dark subhalo in SDSSJ0946+1006

ABSTRACT The ΛCDM paradigm successfully explains the large-scale structure of the Universe, but is less well constrained on subgalactic scales. Gravitational lens modelling has been used to measure the imprints of dark substructures on lensed arcs, testing the small-scale predictions of ΛCDM. However, the methods required for these tests are subject to degeneracies among the lens mass model and the source light profile. We present a case study of the unique compound gravitational lens SDSSJ0946+1006, wherein a dark, massive substructure has been detected, whose reported high concentration would be unlikely in a ΛCDM universe. For the first time, we model the first two background sources in both I- and U-band HST imaging, as well as VLT-MUSE emission line data for the most distant source. We recover a lensing perturber at a 5.9σ confidence level with mass $\log _{10}(M_\mathrm{sub}/{\rm M}_{\odot })=9.2^{+0.4}_{-0.1}$ and concentration $\log _{10}c=2.4^{+0.5}_{-0.3}$. The concentration is more consistent with CDM subhaloes than previously reported, and the mass is compatible with that of a dwarf satellite galaxy whose flux is undetectable in the data at the location of the perturber. A wandering black hole with mass $\log _{10}(M_\mathrm{BH}/{\rm M}_{\odot })=8.9^{+0.2}_{-0.1}$ is a viable alternative model. We systematically investigate alternative assumptions about the complexity of the mass distribution and source reconstruction; in all cases the subhalo is detected at around the ≥5σ level. However, the detection significance can be altered substantially (up to 11.3σ) by alternative choices for the source regularization scheme.

A new step forward in realistic cluster lens mass modelling: analysis of Hubble Frontier Field Cluster Abell S1063 from joint lensing, X-ray, and galaxy kinematics data

ABSTRACT We present a new method to simultaneously and self-consistently model the mass distribution of galaxy clusters that combines constraints from strong lensing features, X-ray emission, and galaxy kinematics measurements. We are able to successfully decompose clusters into their collisionless and collisional mass components thanks to the X-ray surface brightness, as well as use the dynamics of cluster members, to obtain more accurate masses exploiting the fundamental plane of elliptical galaxies. Knowledge from all observables is included through a consistent Bayesian approach in the likelihood or in physically motivated priors. We apply this method to the galaxy cluster Abell S1063 and produce a mass model that we publicly release with this paper. The resulting mass distribution presents different ellipticities for the intra-cluster gas and the other large-scale mass components as well as deviation from elliptical symmetry in the main halo. We assess the ability of our method to recover the masses of the different elements of the cluster using a mock cluster based on a simplified version of our Abell S1063 model. Thanks to the wealth of mutliwavelength information provided by the mass model and the detected X-ray emission, we also found evidence for an ongoing merger event with gas sloshing from a smaller infalling structure into the main cluster. In agreement with previous findings, the total mass, gas profile, and gas mass fraction are all consistent with small deviations from the hydrostatic equilibrium. This new mass model for Abell S1063 is publicly available, as the lenstool extension used to construct it.

Andromeda’s Parachute: Time Delays and Hubble Constant

The gravitational lens system PS J0147+4630 (Andromeda’s Parachute) consists of four quasar images ABCD and a lensing galaxy. We obtained r-band light curves of ABCD in the 2017−2022 period from monitoring with two 2 m class telescopes. Applying state-of-the-art curve-shifting algorithms to these light curves led to measurements of time delays between images, and the three independent delays relative to image D are accurate enough to be used in cosmological studies (uncertainty of about 4%): Δt AD = −170.5 ± 7.0, Δt BD = −170.4 ± 6.0, and Δt CD = −177.0 ± 6.5 days, where image D is trailing all the other images. Our finely sampled light curves and some additional fluxes in the years 2010−2013 also demonstrated the presence of significant microlensing variations. From the measured delays relative to image D and typical values of the external convergence, recent lens mass models yielded a Hubble constant that is in clear disagreement with currently accepted values around 70 km s−1 Mpc−1. We discuss how to account for a standard value of the Hubble constant without invoking the presence of an extraordinary high external convergence.

Mass Reconstruction of Galaxy-scale Strong Gravitational Lenses Using a Broken Power-law Model

With mock strong gravitational lensing images, we investigate the performance of the broken power-law (BPL) model proposed by Du et al. () on the mass reconstruction of galaxy-scale lenses. An end-to-end test is carried out, including the creation of mock strong lensing images, the subtraction of lens light, and the reconstruction of lensed images, where the lenses are selected from the galaxies in the Illustris-1 simulation. We notice that, regardless of the adopted mass models (the BPL model or its special cases), the Einstein radius can be robustly determined from imaging data alone, and the median bias is typically less than 1%. Away from the Einstein radius, the lens mass distribution tends to be harder to measure, especially at radii where there are no lensed images detected. We find that, with rigid priors, the BPL model can clearly outperform the single power-law models by achieving <5% median bias on the radial convergence profile within the Einstein radius. As for the source light reconstructions, they are found to be sensitive to both lens light contamination and lens mass models, where the BPL model with rigid priors still performs best when there is no lens light contamination. We show that, by correcting for the projection effect, the BPL model can estimate the aperture and luminosity weighted line-of-sight velocity dispersions to an accuracy of ∼6% scatter. These results highlight the great potential of the BPL model in strong lensing related studies.

Characteristic Features of Gravitational Wave Lensing as Probe of Lens Mass Model

AbstractTo recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, the lensing of gravitational waves is studied in the context of LISA sources and wave‐optics regime. While different papers before the studied microlensing effects enhanced by simultaneous strong lensing, the focus is on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed signal. It is shows how, in the interference regime (i.e., when interference patterns are present in the lensed image), one is able to i) distinguish a lensed waveform from an unlensed one, and ii) differentiate between different lens models. In pure wave‐optics, on the other hand, the feasibility of the study depends on the signal‐to‐noise ratio of the signal and/or the amplitude of the lensing effect. To achieve these goals, the phase of the amplification factor of the different lens models and its effect on the unlensed waveform is studied, and the signal‐to‐noise calculation to provide some quantitative examples is exploited.

Angular structure and gravitational imaging

AbstractIn gravitational imaging, the mass model for the main lensing galaxy is one of the main sources of systematic uncertainty. We use subhalo detection models with increasing levels of angular complexity in the lens mass model to analyse 100 HST mock observations. We find that perturbations of just 1% are enough to cause a 20% false positive subhalo detection rate, with order 3 multipoles having the strongest effect. The area in an observation where a substructure can be detected drops by a factor of 10 if multipoles up to 3 per cent amplitude are included in the lens model. The mass of the smallest detectable substructure however is not affected. We find a detection limit of M&gt;108.2M⊙ at 5σ in all models. In order for strong lensing searches for dark matter objects to remain reliable in the future, angular structure beyond the elliptical power-law must be included.

First JWST observations of a gravitational lens

We present our lens mass model of SMACS J0723.3−7327, the first strong gravitational lens observed by the James Webb Space Telescope (JWST). We use data from the Hubble Space Telescope and the Multi Unit Spectroscopic Explorer (MUSE) to build our ‘pre-JWST’ lens model and then refine it with newly available JWST near-infrared imaging in our JWST model. To reproduce the positions of all multiple lensed images with good accuracy, the adopted mass parameterisation consists of one cluster-scale component, accounting mainly for the dark matter distribution, the galaxy cluster members, and an external shear component. The pre-JWST model has, as constraints, 19 multiple images from six background sources, of which four have secure spectroscopic redshift measurements from this work. The JWST model has more than twice the number of constraints: 30 additional multiple images from another 11 lensed sources. Both models can reproduce the multiple image positions very well, with a δrms of 0.​​″39 and 0.​​″51 for the pre-JWST and JWST models, respectively. The total mass estimates within a radius of 128 kpc (roughly the Einstein radius) are 7.9−0.2+0.3 × 1013 M⊙ and 8.7−0.2+0.2 × 1013 M⊙ for the pre-JWST and JWST models, respectively. We predict with our mass models the redshifts of the newly detected JWST sources, which is crucial information, especially for systems without spectroscopic measurements, for further studies and follow-up observations. Interestingly, one family detected with JWST is found to be at a very high redshift, z &gt; 7.5 (68% confidence level), and with one image that has a lensing magnification of |μ| = 9.5−0.8+0.9, making it an interesting case for future studies. The lens models, including magnification maps and redshifts estimated from the model, are made publicly available, along with the full spectroscopic redshift catalogue from MUSE.

Deep learning method for testing the cosmic distance duality relation* *Supported by the National Natural Science Fund of China (11873001 and 12147102), and the Fundamental Research Funds for the Central Universities of China (2022CDJXY-002)

The cosmic distance duality relation (DDR) is constrained by a combination of type-Ia supernovae (SNe Ia) and strong gravitational lensing (SGL) systems using the deep learning method. To make use of the full SGL data, we reconstruct the luminosity distance from SNe Ia up to the highest redshift of SGL using deep learning, and then, this luminosity distance is compared with the angular diameter distance obtained from SGL. Considering the influence of the lens mass profile, we constrain the possible violation of the DDR in three lens mass models. The results show that, in the singular isothermal sphere and extended power-law models, the DDR is violated at a high confidence level, with the violation parameter and , respectively. In the power-law model, however, the DDR is verified within a 1σ confidence level, with the violation parameter . Our results demonstrate that the constraints on the DDR strongly depend on the lens mass models. Given a specific lens mass model, the DDR can be constrained at a precision of using deep learning.

Systematic Errors Induced by the Elliptical Power-law model in Galaxy–Galaxy Strong Lens Modeling

The elliptical power-law model of the mass in a galaxy is widely used in strong gravitational lensing analyses. However, the distribution of mass in real galaxies is more complex. We quantify the biases due to this model mismatch by simulating and then analyzing mock Hubble Space Telescope imaging of lenses with mass distributions inferred from SDSS-MaNGA stellar dynamics data. We find accurate recovery of source galaxy morphology, except for a slight tendency to infer sources to be more compact than their true size. The Einstein radius of the lens is also robustly recovered with 0.1% accuracy, as is the global density slope, with 2.5% relative systematic error, compared to the 3.4% intrinsic dispersion. However, asymmetry in real lenses also leads to a spurious fitted “external shear” with typical strength γ ext = 0.015. Furthermore, time delays inferred from lens modeling without measurements of stellar dynamics are typically underestimated by ∼5%. Using such measurements from a sub-sample of 37 lenses would bias measurements of the Hubble constant H 0 by ∼9%. Although this work is based on a particular set of MaNGA galaxies, and the specific value of the detected biases may change for another set of strong lenses, our results strongly suggest the next generation cosmography needs to use more complex lens mass models.

VLT/MUSE Observations of SDSS J1029+2623: Toward a High-precision Strong Lensing Model*

Abstract We present a strong lensing analysis of the galaxy cluster SDSS J1029+2623 at z = 0.588, one of the few currently known lens clusters with multiple images of a background (z = 2.1992) quasar with a measured time delay. We use archival Hubble Space Telescope multiband imaging and new Multi Unit Spectroscopic Explorer follow-up spectroscopy to build an accurate lens mass model, a crucial step toward future cosmological applications. The spectroscopic data enable the secure identification of 57 cluster members and of two nearby perturbers along the line of sight. We estimate the inner kinematics of a subset of 20 cluster galaxies to calibrate the scaling relations parameterizing the sub-halo mass component. We also reliably determine the redshift of four multiply imaged sources, provide a tentative measurement for one system, and report the discovery of a new four-image system. The final catalog comprises 26 multiple images from seven background sources, spanning a wide redshift range, from 1.02 to 5.06. We present two parametric lens models, with slightly different cluster mass parameterizations. The observed positions of the multiple images are accurately reproduced within approximately 0.″2, the three image positions of the quasar within only ∼0.″1. We estimate a cluster projected total mass of M(&lt;300 kpc) ∼ 2.1 × 1014 M ⊙, with a statistical uncertainty of a few percent. Both models, which include a small galaxy close to one of the quasar images, predict magnitude differences and time delays between the quasar images that are consistent with the observations.

On the cosmic distance duality relation and strong gravitational lens power law density profile

Many new strong gravitational lensing (SGL) systems have been discovered in the last two decades with the advent of powerful new space and ground-based telescopes. The effect of the lens mass model (usually the power-law mass model) on cosmological parameters constraints has been performed recently in literature. In this paper, by using SGL systems and Supernovae type Ia observations, we explore if the power-law mass density profile (ρ ∝ r-γ) is consistent with the cosmic distance duality relation (CDDR), DL (1+z)-2/DA = η(z) = 1, by considering different lens mass intervals. It has been obtained that the verification of the CDDR validity is significantly dependent on lens mass interval considered: the sub-sample with σap ≥ 300 km/s (where σap is the lens apparent stellar velocity dispersion) is in full agreement with the CDDR validity, the sub-sample with intermediate σap values (200 ≤ σap < 300) km/s is marginally consistent with η = 1 and, finally, the sub-sample with low σap values (σap < 200 km/s) ruled out the CDDR validity with high statistical confidence. Therefore, if one takes the CDDR as guarantee, our results suggest that using a single density profile is not suitable to describe lens with low σap values and it is only an approximate description to lenses with intermediate mass interval.

Hierarchical Inference with Bayesian Neural Networks: An Application to Strong Gravitational Lensing

Abstract In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope–quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training set’s interim prior. Simultaneously, we can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys (https://github.com/swagnercarena/ovejero).

Exotic image formation in strong gravitational lensing by clusters of galaxies – I. Cross-section

ABSTRACT In a recent paper, we have discussed the higher order singularities in gravitational lensing. We have shown that a singularity map, comprising A3- lines and unstable (point) singularities (A4 and D4), is a compact representation of high magnification regions corresponding to a given lens model for all possible source redshifts. It marks all the optimal locations for deep surveys in the lens plane. Here, we present singularity maps for 10 different clusters lenses selected from the Hubble Frontier fields (HFF) and the Reionization Lensing Cluster Survey (RELICS) surveys. We have identified regions in the lens plane with a high magnification for sources up to redshift 10. To determine the dependence of unstable (point) singularities on lens mass model reconstruction techniques, we compared singularity maps corresponding to the different mass models (provided by various groups in the HFF survey) for each cluster lens. We find that the non-parametric (free-form) method of lens mass reconstruction yields the least number of point singularities. In contrast, mass models reconstructed by various groups using a parametric approach have a significantly larger number of point singularities. We also estimate the number of galaxies lying near these unstable (point) singularities, which can be observed with the James Webb Space Telescope (JWST). We find that we expect to get at least one hyperbolic umbilic and one swallowtail image formation for a source at z &amp;gt; 1 for every five clusters with JWST. These numbers are much higher than earlier estimates.

Could Quasar Lensing Time Delays Hint to a Core Component in Halos, Instead of H0 Tension?

Abstract The time delay measured between the images of gravitationally lensed quasars probes a combination of the angular diameter distance to the source-lens system and the mass density profile of the lens. Observational campaigns to measure such systems have reported a determination of the Hubble parameter H 0 that shows significant tension with independent determination based on the cosmic microwave background (CMB) and large-scale structure (LSS). We show that lens mass models that exhibit a cored component, coexisting with a cusp, probe a degenerate direction in the lens model parameter space, being an approximate mass sheet transformation. This family of lens models has not been considered by the cosmographic analyses. Once added to the model, the cosmographic error budget should become dependent on stellar kinematics uncertainties. We propose that a core component coexisting with a cusp could bring the lensing measurements of H 0 into accordance with the CMB/LSS value.

Truth or Delusion? A Possible Gravitational Lensing Interpretation of the Ultraluminous Quasar SDSS J010013.02+280225.8 at z = 6.30

Abstract Gravitational lensing sometimes dominates the observed properties of apparently very bright objects. We present morphological properties in the high-resolution (FWHM ∼ 0.″15) Atacama Large Millimeter/submillimeter Array (ALMA) 1 mm map for an ultraluminous quasar at z = 6.30, SDSS J010013.02+280225.8 (hereafter J0100+2802), whose black hole (BH) mass M BH is the most massive (∼1.2 × 1010 M ⊙) at z &gt; 6 ever known. We find that the continuum emission of J0100+2802 is resolved into a quadruple system within a radius of 0.″2, which can be interpreted as either multiple dusty star-forming regions in the host galaxy or multiple images due to strong gravitational lensing. The Mg ii absorption and the potential Lyα line features have been identified at z = 2.33 in the near-infrared spectroscopy toward J0100+2802, and a simple mass model fitting well reproduces the positions and flux densities of the quadruple system, both of which are consistent with the latter interpretation. Although a high-resolution map taken in the Advanced Camera for Survey on board Hubble Space Telescope (HST) shows a morphology with an apparently single component, in our fiducial lens mass model it can simply be explained by a ∼50 pc scale offset between the ALMA and HST emission regions. In this case, the magnification factor for the observed HST emission is obtained to ∼450, reducing the intrinsic M BH estimate to below 109 M ⊙. The confirmation or the rejection of the gravitational lensing scenario is important for our understanding of the supermassive BHs in the early universe.

Discovery of an unusually compact lensed Lyman-break galaxy from the Hyper Suprime-Cam Survey

ABSTRACT We report the serendipitous discovery of HSC J0904–0102, a quadruply lensed Lyman-break galaxy (LBG) in the Survey of Gravitationally-lensed Objects in Hyper Suprime-Cam Imaging (SuGOHI). Owing to its point-like appearance, the source was thought to be a lensed active galactic nucleus. We obtained follow-up spectroscopic data with the Gemini Multi-Object Spectrographs on the Gemini South Telescope, which confirmed this to be a lens system. The deflecting foreground galaxy is a typical early-type galaxy at a high redshift of $z_{\ell}=0.957$ with stellar velocity dispersion $\sigma_v=259\pm56$ km s−1. The lensed source is identified as an LBG at $z_{\rm s}=3.403$, based on the sharp drop bluewards of Lyα and other absorption features. A simple lens mass model for the system, assuming a singular isothermal ellipsoid, yields an Einstein radius of $\theta_{\rm Ein}=1.23$ arcsec and a total mass within the Einstein radius of $M_{\rm Ein}=(5.55\pm0.24)\times10^{11}\rm M_{\odot}$ corresponding to a velocity dispersion of $\sigma_{\rm SIE}=283\pm3$ km s−1, which is in good agreement with the value derived spectroscopically. The most isolated lensed LBG image has a magnification of $\sim 6.5$. In comparison with other lensed LBGs and typical $z\sim4$ LBG populations, HSC J0904–0102 is unusually compact, an outlier at $&amp;gt;2\sigma$ confidence. Together with a previously discovered SuGOHI lens, HSC J1152+0047, which is similarly compact, we believe that the HSC survey is extending LBG studies down to smaller galaxy sizes.