Welcome

• Kenneth Wong

Cosmology and Stellar Physics with Lensed Supernovae

• Sherry Suyu

Strongly lensed supernovae (SNe) provide great opportunities for constraining cosmological parameters and SN progenitors. The time delays between the multiple images of a lensed SN allow a measurement of the Hubble constant (H0), which is complementary to lensed-quasar studies. An independent measurement of H0 is important for assessing the current H0 tension and the possible need for new physics. I will present the results of a new program on lensed SNe, including recent developments in the search for these rare events, and new techniques for analyzing such systems for cosmography. The time delays also facilitate early-phase observations of SNe, which are crucial for deciphering SN progenitors. Using various models of SN explosions, I will quantify the impact of microlensing on SN for both progenitor and cosmological studies. I will show the bright prospects of lensed SNe as an independent and competitive probe of cosmology and SN progenitors.

Lessons learned from iPTF16geu

• Ariel Goobar

Wide-field time domain surveys are well-suited to find strongly lensed systems, without the need for high spatial resolution, as demonstrated by the discovery of the first multiply-imaged Type Ia supernova, iPTF16geu. Yet, in spite of significant efforts, four years have passed without a sequel. I will summarize the circumstances surrounding the discovery of SN2016geu using the Palomar Transient Facility and the follow-up with HST and ground-based facilities, with focus on the observational challenges.

Lens Searches for transients and variable sources

• Anupreeta More

I will give an overview of systematic lens searches (including machine learning based approaches) being conducted in the ongoing imaging surveys to find transients or variable sources which can allow us to put constraints on cosmological parameters or often times, give insight into the astrophysics. I will also talk about new methods proposed to be used in upcoming surveys such as LSST, their strengths, complementarity and possible directions for improvements.

Lens searches with Gaia and variability

• Cameron Lemon

Lens searches with Gaia and variability

Galaxy lens models with offset mass components: implications for time delays and H0.

• Liliya Williams

Accurate determination of the Hubble parameter from strong lensing depends critically on the mass model of the lensing galaxy. There is evidence that the commonly used elliptically symmetric lenses may not adequately represent the lens galaxy population. I will discuss the recent modeling of the quad Supernova iPTF16geu. Simple models suffer from a few deficiencies: the center and the position angle of the recovered mass are not the same as those of the observed light, and the density profile required by microlensing considerations is rather shallow. We model the lensing galaxy as a superposition of two mass components; allowing them to be offset from each other by up to 0.25 kpc alleviates most of the problems of simple models, and leads to predictions for microlensing magnification and time delays that differ from those of simple models. I will discuss the implications of two offset components lens modeling for H0 estimation.

Constraining the Hubble constant -- some lessons learnt from using lensing simulations

• Dandan Xu

Time-domain lensing observations and modeling have turn out to serve an increasingly important role in providing independent constraints on the Hubble constant and cosmology. A couple of issues regarding the modeling technique remain not entirely clear and many good efforts have been made in order to understand various possible key systematics. In this talk, I will briefly discuss a few interesting and potentially important lessons that we learnt from using lensing simulations.

Where my DAEMON hides -- one explanation to rule all lens models

• Jenny Wagner

"A big obstacle to efficiently determine H0 from time-delay cosmography is the lens modelling. When choosing a mass density profile as lens model, we have to select from a multitude of lens model classes and ranges for the model parameter values. A specific choice may bias the confidence bounds on H0 low, a marginalisation over many model classes and parameter ranges is computationally very intensive. As a first step towards one general mass density profile that replaces the heuristically inferred fitting function lens models, I will introduce the ""DArk Emergent Matter halO explanatioN"" (DAEMON) which is able to explain the self-similar dark matter halo morphologies forming under scale-free gravitational interaction. DAEMON thus allows us to base the power-law mass density profiles and composites thereof, like the famous Navarro-Frenk-White profile on sound mathematically and physically fundamental principles. Consequently, choosing and marginalising over classes of lens models can be simplified to reduce computational costs and obtain realistic confidence bounds on H0 at the same time."

Auto-identification of unphysical source reconstructions in strong lens modelling

• Jacob Maresca

With the advent of next-generation surveys and the expectation of discovering huge numbers of strong gravitational lens systems, much effort is being invested into developing automated procedures for handling the data. The several orders of magnitude increase in the number of strong galaxy-galaxy lens systems is an insurmountable challenge for traditional modelling techniques. Whilst machine learning techniques have dramatically improved the efficiency of lens modelling, parametric modelling of the lens mass profile remains an important tool for dealing with complex lensing systems. In particular, source reconstruction methods are necessary to cope with the irregular structure of high-redshift sources. In this paper, we consider a Convolutional Neural Network (CNN) that analyses the outputs of semi-analytic methods which parametrically model the lens mass and linearly reconstruct the source surface brightness distribution. We show the unphysical source reconstructions that arise as a result of incorrectly initialised lens models can be effectively caught by our CNN. Furthermore, the CNN predictions can be used to automatically re-initialise the parametric lens model, avoiding unphysical source reconstructions. The CNN accurately classifies source reconstructions with a precision P>0.99 and recall R>0.99. Using the CNN predictions to re-initialise the lens modelling procedure, we achieve a 69 per cent decrease in the occurrence of unphysical source reconstructions. This combined CNN and parametric modelling approach can greatly improve the automation of lens modelling.

Real-time cosmology with lensed repeating Fast Radio Bursts

• Adi Zitrin

Real-time cosmology refers to measuring the evolution of the universe in real time. Given the short human lifetime compared to the age of the universe, measuring such changes is very challenging. Thanks to their short duration and the typical time delays involved, lensed repeating FRBs may offer a unique opportunity to do so. I will review this possibility and discuss its feasibility using existing and upcoming facilities.

Large-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

• Ji Won Park

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time-delay gravitational lenses for Hubble constant (H0) determination. Our BNN was trained on synthetic HST-quality images of strongly lensed active galactic nuclei (AGN) with lens galaxy light included. The BNN can accurately characterize the posterior PDFs of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into ensemble H0 inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of 9.3\% per lens in the inferred H0. A simple combination of 200 test-set lenses results in a precision of 0.5 km s−1 Mpc−1 (0.7%), with no detectable bias in this H0 recovery test. The computation time for the entire pipeline -- including the training set generation, BNN training, and H0 inference -- translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for H0 inference.

Panel Discussion: Time-Delay Cosmography

• Liliya Williams
• Nan Li
• Dominique Sluse
• Simon Birrer
• Sherry Suyu
• Tommaso Treu

Recent studies on the propagation velocity of lensed gravitational waves

• Ryuichi Takahashi

In this talk, we briefly review the propagation velocity of lensed gravitational waves in general relativity, based on recent papers (listed below). We mainly discuss the velocity difference between GWs and electromagnetic waves (EMWs) in the presence of a lens. The lensing of EMWs is usually studied in geometrical optics, while the lensing of GWs should be studied in wave optics if the wavelength is larger than the Schwarzschild radius of the lens. The recent studies reveal that the phase and group velocities of GWs can exceed the velocity of EMWs, but the wave front never arrives before the EMWs if both waves were emitted simultaneously from the source. Finally, we discuss an observational possibility to detect the arrival-time difference. References: RT (2017), Morita & Soda (2019), Suyama (2020), Ezquiaga+ (2020)

Using transients at extreme magnifications to constrain dark matter

• Jose Diego

Events at cosmological distances, undergoing extreme magnifications have become a reality since the discovery of Icarus, the first strongly lensed star at redshift larger than 1. Since the discovery of Icarus, similar events have been observed in the last years, and many more are expected in the upcoming years. The large magnification factors present in these events allow to study not only the background source, but also the small-scale perturbations in the lens plane. This type of observations allow to constrain certain models of dark matter, like those postulating that primordial black holes with masses similar to those found by LIGO/Virgo can account fro a fraction of the dark matter. In this talk I will review some of the possibilities offered by extreme magnified events to constrain the abundance of primordial black holes. In particular I will consider the case of extremely magnified stars, supernovae and gravitational waves.

The effect of dark matter substructure on strong lensing measurements of the Hubble constant

• Daniel Gilman

The particle nature of dark matter manifests in the abundance and density profiles of dark matter structure on sub galactic scales, both in the form of subhalos and field halos along the the line of sight. The lensing effects of these structures leaves subtle imprints on the arrival time delays and flux ratios between images in quadruply imaged quasars (quads). I will describe recent work that quantifies the effects of dark substructure on strong lensing measurements of the Hubble constant, showing that substructure contributes an small additional source of uncertainty - but does not bias - strong lensing measurements of H0. Time permitting, I will also describe an analysis framework that constrains the particle nature of dark matter by forward modeling flux ratios in quads, with an emphasis on how it can be applied to a variety of structure formation scenarios based on dark matter theory.

Beyond-WIMP DM models and constraints from anomalous strong-lens systems

• Ayuki Kamada

"A weakly interacting massive particle (WIMP) from electroweak-scale new physics have been a promising candidate of cold dark matter (CDM). Meanwhile beyond-WIMP DM models attract interests partially because they may explain the possible issues in CDM: tension between early and late cosmology in H0; and challenges in explaining the observed Galactic-scale structure. I overview beyond-WIMP DM models and their cosmological implications, particularly explaining a relatively new possibility: late-decaying dark matter (LDDM). I stress that anomalous strong-lens systems have a good potential to probe beyond-WIMP DM models, by showing the constraints from existing data."

Phase shift of lensed gravitational waves

• Liang Dai

Several gravitational wave signals of binary black hole coalescence in LIGO/Virgo O2 are found to show surprisingly coincident intrinsic and extrinsic parameters. Could they be multiple images of a gravitationally lensed source? Lensed gravitational waveforms are subject to a topological phase shift called the Morse phase shift. While the absolute Morse phase is degenerate with the source orbital phase, the relative Morse phase is measurable under the lensing hypothesis. We find that the candidate signals have relative Morse phases consistent with geometrical lensing, but the results point toward a peculiar configuration of multiple lensed images that are rarely realized by galaxy or galaxy cluster lenses. The Morse phase information will help with lens reconstruction for future detection of lensed gravitational waves.

Gravitational Lensing of Gravitational Waves: Effect of Microlensing Population

• Anuj Mishra

In this work, we investigate the effect of microlensing in strongly lensed gravitational wave signals due to the population of microlenses present in lensing galaxies. We consider a wide range of realistic strong lens magnification and the corresponding density values of the microlens population. We find that the effects of microlensing become increasingly significant with the increase in the strong lens magnification for both minima and saddle type of images. Hence, for notable microlensing features in the gravitational wave signals, the strong lensing magnification also needs to be substantial. The mismatch analyses suggest that only in very rare scenarios, the waveforms will be missed; otherwise, only its parameter estimation will be affected. We also study the effects of different IMFs (Salpeter and Chabrier) on the amplification curve caused by the corresponding microlens population.

Panel Discussion: Dark Matter Science with Upcoming Surveys/Telescopes

• Thomas Collett
• Ariel Goobar
• Dandan Xu
• Ayuki Kamada
• Jose Diego
• Kaiki Inoue

Microlensing in lensed quasars

• Veronica Motta

"The observation of gravitationally microlensed quasars provides direct measurements of the accretion disk structure. The flux variations of the quasar images, induced by the source crossing through the microlens caustics, produce variations on timescales of years. There are two techniques to measure those variations: photometric monitoring and single epoch spectroscopy/photometry. The first one measures the magnification changes by comparing the light curves of the lensed images after correcting by the time delay between the images. The second one uses emission lines (or a smooth macrolens model) as a reference to estimate the microlensing variability. These techniques have been successfully applied to investigate the inner structure of a few dozen of systems, improving the analysis of systematic uncertainties. In the upcoming decade, with the discovery of thousands of new systems, quasar microlensing could offer a comprehensive view of the accretion disk structure."

Extremely Magnified Stars and Flashlights

• Patrick Kelly

Observations with the Hubble Space Telescope (HST) have now definitively identified two blue supergiant stars, Icarus and Warhol, at cosmological distances which are extremely magnified by foreground Hubble Frontier Field (HFF) galaxy clusters. Moreover, several less well characterized stars have also been detected briefly when their magnification temporarily increased due to microlensing by an object in a foreground cluster. I will discuss the two-cycle Flashlights 192-orbit HST program, which is obtaining two epochs of ultra-deep, unfiltered imaging of all six HFF cluster fields. These observations, with a single-visit five-sigma limiting magnitude of 31 AB, can be expected to increase the current sample of microlensing events of extremely magnified stars substantially, and detect a sizable sample of pairs of stellar images. If only 2% of dark matter consists of primordial black holes across a broad ranges of masses, then the rate of of detected microlensing peaks should be significantly increased. The pairs of stellar images should stringently test lens models, probe the abundance of low-mass dark-matter halos, and evaluate predictions for dark matter as ultra-light bosons.

Summary / closing

• Masamune Oguri