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Abstract Astrometry, the precise measurement of star motions, offers an alternative avenue to investigate low-frequency gravitational waves through the spatial deflection of photons, complementing pulsar timing arrays reliant on timing residuals. Upcoming data from Gaia, Theia, and Roman can not only cross-check pulsar timing array findings but also explore the uncharted frequency range bridging pulsar timing arrays and LISA. We present an analytical framework to evaluate the feasibility of detecting a gravitational wave background, considering measurement noise and the intrinsic variability of the stochastic background. Furthermore, we highlight astrometry's crucial role in uncovering key properties of the gravitational wave background, such as spectral index and chirality, employing information-matrix analysis. Finally, we simulate the emergence of quadrupolar correlations, commonly referred to as the generalized Hellings-Downs curves. 

Abstract The first James Webb Space Telescope (JWST) Near InfraRed Camera imaging in the field of the galaxy cluster PLCK G165.7+67.0 (z= 0.35) uncovered a Type Ia supernova (SN Ia) atz= 1.78, called “SN H0pe.” Three different images of this one SN were detected as a result of strong gravitational lensing, each one traversing a different path in spacetime, thereby inducing a relative delay in the arrival of each image. Follow-up JWST observations of all three SN images enabled photometric and rare spectroscopic measurements of the two relative time delays. Following strict blinding protocols which oversaw a live unblinding and regulated postunblinding changes, these two measured time delays were compared to the predictions of seven independently constructed cluster lens models to measure a value for the Hubble constant,H₀ =  71.8 + 9.2 − 8.1 km s⁻¹Mpc⁻¹. The range of admissibleH₀values predicted across the lens models limits further precision, reflecting the well-known degeneracies between lens model constraints and time delays. It has long been theorized that a way forward is to leverage a standard candle, but this has not been realized until now. For the first time, the lens models are evaluated by their agreement with the SN absolute magnifications, breaking degeneracies and producing our best estimate,H₀ =  ${75.7}_{-5.5}^{+8.1}$km s⁻¹Mpc⁻¹. This is the first precise measurement ofH₀from a multiply imaged SN Ia and only the second from any multiply imaged SN. 

Recent observations of caustic-crossing galaxies at redshift 0.7 ≲ z ≲ 1 show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicts such events should be common near the critical curves (CCs) of galaxy clusters (“near region”), but some are found relatively far away from these CCs (“far region”). We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal in the far region. We study the combined magnification from the macrolens, millilenses, and microlenses (“3M lensing”), when the macromodel magnification is relatively low (common in the far region). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead, we find that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of microlensing events found near and far from the CC. By measuringβ(the exponent of the adopted power law LF,dN/dL = ϕ(L)∝(1/L)^β), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive-imaging regime whereβ > 2 and the number density of events is greater around substructures, and (ii) negative-imaging regime whereβ < 2 and the number density of microlensing events is reduced around substructures. This technique opens a new window to map the distribution of dark-matter substructure down to ∼10³ M_⊙. We study the particular case of seven microlensing events found in the Flashlights program in the Dragon arc (z = 0.725). A population of supergiant stars having a steep LF withβ = 2.55_−0.56^+0.72fits the distribution of these events in the far and near regions. We also find that the new microlensing events from JWST observations in this arc imply a surface mass density substructure of Σ_∗= 54M_⊙pc⁻², consistent with the expected population of stars from the intracluster medium. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of ∼1.3 × 10⁸ M_⊙(within its Einstein radius) in the galaxy cluster. 

Strong gravitational magnification enables the detection of faint background sources and allows researchers to resolve their internal structures and even identify individual stars in distant galaxies. Highly magnified individual stars are useful in various applications, including studies of stellar populations in distant galaxies and constraining dark matter structures in the lensing plane. However, these applications have been hampered by the small number of individual stars observed, as typically one or a few stars are identified from each distant galaxy. Here, we report the discovery of more than 40 microlensed stars in a single galaxy behind Abell 370 at redshift of 0.725 (dubbed ‘the Dragon arc’) when the Universe was half of its current age, using James Webb Space Telescope observations with the time-domain technique. These events were found near the expected lensing critical curves, suggesting that these are magnified stars that appear as transients from intracluster stellar microlenses. Through multi-wavelength photometry, we constrained their stellar types and found that many of them are consistent with red giants or supergiants magnified by factors of hundreds. This finding reveals a high occurrence of microlensing events in the Dragon arc and demonstrates that time-domain observations by the James Webb Space Telescope could lead to the possibility of conducting statistical studies of high-redshift stars. 

In this work, we present a constraint on the abundance of supergiant (SG) stars at redshiftz ≈ 1, based on recent observations of a strongly lensed arc at this redshift. First we derived a free-form model of MACS J0416.1-2403 using data from the Beyond Ultra-deep Frontier Fields and Legacy Observations (BUFFALO) program. The new lens model is based on 72 multiply lensed galaxies that produce 214 multiple images, making it the largest sample of spectroscopically confirmed lensed galaxies on this cluster. The larger coverage in BUFFALO allowed us to measure the shear up to the outskirts of the cluster, and extend the range of lensing constraints up to ∼1 Mpc from the central region, providing a mass estimate up to this radius. As an application, we make predictions for the number of high-redshift multiply lensed galaxies detected in future observations with theJames WebbSpace Telescope (JWST). Then we focus on a previously known lensed galaxy atz = 1.0054, nicknamed Spock, which contains four previously reported transients. We interpret these transients as microcaustic crossings of SG stars and explain how we computed the probability of such events. Based on simplifications regarding the stellar evolution, we find that microlensing (by stars in the intracluster medium) of SG stars atz = 1.0054 can fully explain these events. The inferred abundance of SG stars is consistent with either (1) a number density of stars with bolometric luminosities beyond the Humphreys-Davidson (HD) limit (L_max ≈ 6 × 10⁵ L_⊙for red stars), which is below ∼400 stars kpc⁻², or (2) the absence of stars beyond the HD limit but with a SG number density of ∼9000 kpc⁻²for stars with luminosities between 10⁵ L_⊙and 6 × 10⁵ L_⊙. This is equivalent to one SG star per 10 × 10 pc². Finally, we make predictions for future observations with JWST’s NIRcam. We find that in observations made with theF200Wfilter that reach 29 mag AB, if cool red SG stars exist atz ≈ 1 beyond the HD limit, they should be easily detected in this arc.