Time-delay Cosmography Research Articles

Image formation near hyperbolic umbilic in strong gravitational lensing

Hyperbolic umbilic (HU) is a point singularity of the gravitational lens equation, giving rise to a ring-shaped image formation made of four highly magnified images, off-centred from the lens centre. Recent observations have revealed new strongly lensed image formations near HU singularities, and many more are expected in ongoing and future observations. Like fold/cusp, image formations near HU also satisfy magnification relation (), i.e., the signed magnification sum of the four images equals zero. Here, we study how deviates from zero as a function of area () covered by the image formation near HU and the distance ( d) of the central maxima image (which is part of the HU image formation) from the lens centre for ideal single- and double-component cluster-scale lenses. For lens ellipticity values ≥0.3, the central maxima image will form sufficiently far from the lens centre ( d≳5″), similar to the observed HU image formations with . We also find that, in some cases, double-component and actual cluster-scale lenses can lead to large cross-sections for HU image formations for sources at z≳5, effectively increasing the chances to observe HU image formation at high redshifts. Finally, we study the time delay distribution in the observed HU image formation, finding that not only are these images highly magnified, but the relative time delay between various pairs of HU characteristic image formation has a typical value of ∼100 days, an order of magnitude smaller than generic five-image formations in cluster lenses, making such image formations optimal targets for time delay cosmography studies.

TDCOSMO

Context. Time-delay cosmography is a technique for measuring H0 with strong gravitational lensing. It requires a correction for line-of-sight perturbations, and thus it is necessary to build tools to assess populations of these lines of sight efficiently. Aims. We demonstrate the techniques necessary to analyze line-of-sight effects at a population level, and investigate whether strong lenses fall in preferably overdense environments. Methods. We analyzed a set of 25 galaxy-galaxy lens lines of sight in the Strong Lensing Legacy Survey sample using standard techniques, then performed a hierarchical analysis to constrain the population-level parameters. We introduce a new statistical model for these posteriors that may provide insight into the underlying physics of the system. Reults. We find the median value of κext in the population model to be 0.033 ± 0.010. The median value of κext for the individual lens posteriors is 0.008 ± 0.015. Both approaches demostrate that our systems are drawn from an overdense sample. The different results from these two approaches show the importance of population models that do not multiply the effect of our priors.

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.

Image Deconvolution and Point-spread Function Reconstruction with STARRED: A Wavelet-based Two-channel Method Optimized for Light-curve Extraction

We present starred, a point-spread function (PSF) reconstruction, two-channel deconvolution, and light-curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data is targeted rather than an infinite one, thereby minimizing deconvolution artifacts. In addition, starred performs a joint deconvolution of all available data, accounting for epoch-to-epoch variations of the PSF and decomposing the resulting deconvolved image into a point source and an extended source channel. The output is a high-signal-to-noise-ratio, high-resolution frame combining all data and the photometry of all point sources in the field of view as a function of time. Of note, starred also provides exquisite PSF models for each data frame. We showcase three applications of starred in the context of the imminent LSST survey and of JWST imaging: (i) the extraction of supernovae light curves and the scene representation of their host galaxy; (ii) the extraction of lensed quasar light curves for time-delay cosmography; and (iii) the measurement of the spectral energy distribution of globular clusters in the “Sparkler,” a galaxy at redshift z = 1.378 strongly lensed by the galaxy cluster SMACS J0723.3-7327. starred is implemented in jax, leveraging automatic differentiation and graphics processing unit acceleration. This enables the rapid processing of large time-domain data sets, positioning the method as a powerful tool for extracting light curves from the multitude of lensed or unlensed variable and transient objects in the Rubin-LSST data, even when blended with intervening objects.

How to break the mass sheet degeneracy with the light curves of microlensed Type Ia supernovae

ABSTRACT The standardizable nature of gravitationally lensed Type Ia supernovae (glSNe Ia) makes them an attractive target for time-delay cosmography, since a source with known luminosity breaks the mass sheet degeneracy. It is known that microlensing by stars in the lensing galaxy can add significant stochastic uncertainty to the unlensed luminosity, which is often much larger than the intrinsic scatter of the Type Ia population. In this work, we show how the temporal microlensing variations as the supernova (SN) disc expands can be used to improve the standardization of glSNe Ia. We find that SNe are standardizable if they do not cross caustics as they expand. We estimate that this will be the case for ≈6 doubly imaged systems and ≈0.3 quadruply imaged systems per year from the Vera Rubin Observatory (LSST). At the end of the 10 yr LSST survey, these systems should enable us to test for systematics in H0 due to the mass sheet degeneracy at the $1.00^{+0.07}_{-0.06}$ per cent level, or 1.8 ± 0.2 per cent if we can only extract time delays from the third of systems with counter-images brighter than i = 24 mag.

Lensed Type Ia Supernova “Encore” at z = 2: The First Instance of Two Multiply Imaged Supernovae in the Same Host Galaxy

A bright (m F150W,AB = 24 mag), z = 1.95 supernova (SN) candidate was discovered in JWST/NIRCam imaging acquired on 2023 November 17. The SN is quintuply imaged as a result of strong gravitational lensing by a foreground galaxy cluster, detected in three locations, and remarkably is the second lensed SN found in the same host galaxy. The previous lensed SN was called “Requiem,” and therefore the new SN is named “Encore.” This makes the MACS J0138.0−2155 cluster the first known system to produce more than one multiply imaged SN. Moreover, both SN Requiem and SN Encore are Type Ia SNe (SNe Ia), making this the most distant case of a galaxy hosting two SNe Ia. Using parametric host fitting, we determine the probability of detecting two SNe Ia in this host galaxy over a ∼10 yr window to be ≈3%. These observations have the potential to yield a Hubble constant (H 0) measurement with ∼10% precision, only the third lensed SN capable of such a result, using the three visible images of the SN. Both SN Requiem and SN Encore have a fourth image that is expected to appear within a few years of ∼2030, providing an unprecedented baseline for time-delay cosmography.

GausSN: Bayesian time-delay estimation for strongly lensed supernovae

ABSTRACT We present gausSN, a Bayesian semiparametric Gaussian Process (GP) model for time-delay estimation with resolved systems of gravitationally lensed supernovae (glSNe). gausSN models the underlying light curve non-parametrically using a GP. Without assuming a template light curve for each SN type, gausSN fits for the time delays of all images using data in any number of wavelength filters simultaneously. We also introduce a novel time-varying magnification model to capture the effects of microlensing alongside time-delay estimation. In this analysis, we model the time-varying relative magnification as a sigmoid function, as well as a constant for comparison to existing time-delay estimation approaches. We demonstrate that gausSN provides robust time-delay estimates for simulations of glSNe from the Nancy Grace Roman Space Telescope and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (Rubin-LSST). We find that up to 43.6 per cent of time-delay estimates from Roman and 52.9 per cent from Rubin-LSST have fractional errors of less than 5 per cent. We then apply gausSN to SN Refsdal and find the time delay for the fifth image is consistent with the original analysis, regardless of microlensing treatment. Therefore, gausSN maintains the level of precision and accuracy achieved by existing time-delay extraction methods with fewer assumptions about the underlying shape of the light curve than template-based approaches, while incorporating microlensing into the statistical error budget. gausSN is scalable for time-delay cosmography analyses given current projections of glSNe discovery rates from Rubin-LSST and Roman.

Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies

We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combines time-delay cosmography in lens galaxy clusters with pure samples of ‘cosmic chronometers’ by probing the member galaxies. The former makes use of the measured time delays between the multiple images of time-varying sources strongly lensed by galaxy clusters, while the latter exploits the most massive and passive cluster member galaxies to measure the differential time evolution of the Universe. We applied two different statistical techniques, adopting realistic errors on the measured quantities, to assess the accuracy and the gain in precision on the values of the cosmological parameters. We demonstrate that the proposed combined method allows for a robust and accurate measurement of the value of the Hubble constant. In addition, this provides valuable information on the other cosmological parameters thanks to the complementarity between the two different probes in breaking parameter degeneracies. Finally, we showcased the immediate observational feasibility of the proposed joint method by taking advantage of the existing high-quality spectro-photometric data for several lens galaxy clusters.

Augmenting the power of time-delay cosmography in lens galaxy clusters by probing their member galaxies

We present a simple and promising new method to measure the expansion rate and the geometry of the universe that combines observations related to the time delays between the multiple images of time-varying sources, strongly lensed by galaxy clusters, and Type Ia supernovae, exploding in galaxies belonging to the same lens clusters. By means of two different statistical techniques that adopt realistic errors on the relevant quantities, we quantify the accuracy of the inferred cosmological parameter values. We show that the estimate of the Hubble constant is robust and competitive, and depends only mildly on the chosen cosmological model. Remarkably, the two probes separately produce confidence regions on the cosmological parameter planes that are oriented in complementary ways, thus providing in combination valuable information on the values of the other cosmological parameters. We conclude by illustrating the immediate observational feasibility of the proposed joint method in a well-studied lens galaxy cluster, with a relatively small investment of telescope time for monitoring from a 2 to 3 m class ground-based telescope.

TDCOSMO

Context. Time-delay cosmography uses strong gravitational lensing of a time-variable source to infer the Hubble constant. The measurement is independent from both traditional distance ladder and CMB measurements. An accurate measurement with this technique requires considering the effects of objects along the line of sight outside the primary lens, which is quantified by the external convergence (κext). In absence of such corrections, H0 will be biased towards higher values in overdense fields and lower values in underdense fields. Aims. We discuss the current state of the methods used to account for environment effects. We present a new software package built for this kind of analysis and others that can leverage large astronomical survey datasets. We apply these techniques to the SDSS J0924+0219 strong lens field. Methods. We infer the relative density of the SDSS J0924+0219 field by computing weighted number counts for all galaxies in the field, and comparing to weighted number counts computed for a large number of fields in a reference survey. We then compute weighted number counts in the Millennium Simulation and compare these results to infer the external convergence of the lens field. Results. Our results show the SDSS J0924+0219 field is a fairly typical line of sight, with median κext = −0.012 and standard deviation σκ = 0.028.

Hierarchical Inference of the Lensing Convergence from Photometric Catalogs with Bayesian Graph Neural Networks

We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence (κ) from photometric measurements of galaxies along a given line of sight (LOS). The method is of particular interest in strong gravitational time-delay cosmography (TDC), where characterizing the “external convergence” (κ ext) from the lens environment and LOS is necessary for precise Hubble constant (H 0) inference. Starting from a large-scale simulation with a κ resolution of ∼1′, we introduce fluctuations on galaxy–galaxy lensing scales of ∼1″ and extract random sight lines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1000 sight lines, the BGNN infers the individual κ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of κ precisely and without bias (within the 2σ credible interval), resulting in a contribution to the H 0 error budget well under 1%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sight line, extracts a stronger κ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the κ ext characterization for precision TDC. The code is available as a public Python package, Node to Joy ⏬.

Peculiar velocity effects on the Hubble constant from time-delay cosmography

Peculiar velocity effects on the Hubble constant from time-delay cosmography

TDCOSMO

Strong-lensing time delays enable the measurement of the Hubble constant (H0) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H0, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy Dd = 865−81+85 Mpc and the time-delay distance DΔt = 2180−271+472 Mpc, giving H0 = 77.1−7.1+7.3 km s−1 Mpc−1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system (H0 = 78.3−3.3+3.4 km s−1 Mpc−1) and for seven lenses (H0 = 74.2−1.6+1.6 km s−1 Mpc−1), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us (H0 = 73.3−5.8+5.8 km s−1 Mpc−1). This agreement corroborates the methodology of time-delay cosmography.

Large data set of lensed quasars: higher accuracy on H0? The angular structures viewpoint

AbstractThanks to forthcoming large-scale surveys, a tremendous number of strong lenses will be discovered in the coming years. The gain in accuracy on H0 from such a large population of lensed quasars is a key question for the future of time-delay cosmography. In such context, lensed systems will have to be modeled in an automated way, with models that are sufficiently generic to apply to every lens. I explore the biases that may arise from unaccounted-for azimuthal structures in mass models. The non-modeled twists in lensing galaxies are expected to bias the shear inference but not H0. Disregarded ellipticity gradients, boxyness and discyness may impact the cosmological inference on a lens-by-lens basis. Nevertheless, the diversity of azimuthal mass profile in lenses balances the bias at a population level and the H0 inference can thus benefits from such large surveys.

Accounting for population-level systematic effects using a hierarchical strategy

AbstractOne of the largest sources of systematics in time-delay cosmography arises from Mass Sheet Transformation (MST). The degeneracy associated with this transformation is often broken by an assumed profile shape, such as a power-law. A hierarchical strategy has been developed which constrains the global profile shape on a population level, constrained collectively by the kinematics measurements of the lenses. This framework allows one to include non-time-delay lenses to provide constraints to the global profile, improving the H0 constraints. This work tests the hierarchical framework using analytical profiles, and additionally tests the capacity to combine two populations which come from the same profiles but probe different radii due to a change in source redshift. We find that the hierarchical framework is able to compensate for this effect, and the addition of non-time-delay lenses improves the H0 constraint, even though these lenses have different Einstein radii than their time-delay counterparts.

TDCOSMO

The importance of alternative methods for measuring the Hubble constant, such as time-delay cosmography, is highlighted by the recent Hubble tension. It is paramount to thoroughly investigate and rule out systematic biases in all measurement methods before we can accept new physics as the source of this tension. In this study, we perform a check for systematic biases in the lens modelling procedure of time-delay cosmography by comparing independent and blind time-delay predictions of the system WGD 2038−4008 from two teams using two different software programs: GLEE and LENSTRONOMY. The predicted time delays from the two teams incorporate the stellar kinematics of the deflector and the external convergence from line-of-sight structures. The un-blinded time-delay predictions from the two teams agree within 1.2σ, implying that once the time delay is measured the inferred Hubble constant will also be mutually consistent. However, there is a ∼4σ discrepancy between the power-law model slope and external shear, which is a significant discrepancy at the level of lens models before the stellar kinematics and the external convergence are incorporated. We identify the difference in the reconstructed point spread function (PSF) to be the source of this discrepancy. When the same reconstructed PSF was used by both teams, we achieved excellent agreement, within ∼0.6σ, indicating that potential systematics stemming from source reconstruction algorithms and investigator choices are well under control. We recommend that future studies supersample the PSF as needed and marginalize over multiple algorithms or realizations for the PSF reconstruction to mitigate the systematics associated with the PSF. A future study will measure the time delays of the system WGD 2038−4008 and infer the Hubble constant based on our mass models.

STRIDES: automated uniform models for 30 quadruply imaged quasars

ABSTRACT Gravitational time delays provide a powerful one-step measurement of H0, 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 (105–106 CPU hours and ∼0.5–1 yr, respectively). Major improvements in modelling 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, we develop an automated modelling pipeline and apply it to a sample of 31 lens systems, 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 the Fermat potential (proportional to time delay) with respect to modelling choices. We find that for 10/30 lenses, our models are cosmography or nearly cosmography grade (<3 per cent and 3–5 per cent variations). For 6/30 lenses, the models are close to cosmography grade (5–10 per cent). These results utilize informative priors and will need to be confirmed by further analysis. However, they are also likely to improve by extending the pipeline modelling sequence and options. In conclusion, we show that uniform cosmography grade modelling of large strong lens samples is within reach.

TDCOSMO

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of H0. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the H0 bias associated with model choice to find H0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower z, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of H0 which is both more precise (σ ∼ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of H0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

Revealing the late-time transition of H0: relieve the Hubble crisis

Abstract The discrepancy between the value of the Hubble constant H0 measured from the local distance ladder and from the cosmic microwave background is the most serious challenge to the standard ΛCDM model. Various models have been proposed to solve or relieve it, but no satisfactory solution has been given until now. Here, we report a late-time transition of H0, i.e. H0 changes from a low value to a high one from early to late cosmic time, by investigating the Hubble parameter H($\mathit{ z}$) data based on the Gaussian process (GP) method. This finding effectively reduces the Hubble crisis by 70 per cent. Our results are also consistent with the descending trend of H0 measured using time-delay cosmography of lensed quasars at 1 σ confidence level, and support the idea that the Hubble crisis arises from new physics beyond the standard ΛCDM model. In addition, in the ΛCDM model and $w$CDM model, there is no transition behaviour of H0.

A lensed radio jet at milliarcsecond resolution I: Bayesian comparison of parametric lens models

ABSTRACT 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 bias 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.