Search

Strongly gravitationally lensed supernovae (LSNe) are promising probes for providing absolute distance measurements using gravitational-lens time delays. Spatially unresolved LSNe offer an opportunity to enhance the sample size for precision cosmology. We predict that there will be approximately three times as many unresolved as resolved LSNe Ia in the Legacy Survey of Space and Time (LSST) by the Rubin Observatory. In this article, we explore the feasibility of detecting unresolved LSNe Ia from a pool of preclassified SNe Ia light curves using the shape of the blended light curves with deep-learning techniques. We find that ∼30% unresolved LSNe Ia can be detected with a simple 1D convolutional neural network (CNN) using well-sampled rizy-band light curves (with a false-positive rate of ∼3%). Even when the light curve is well observed in only a single band among r, i, and z, detection is still possible with false-positive rates ranging from ∼4 to 7% depending on the band. Furthermore, we demonstrate that these unresolved cases can be detected at an early stage using light curves up to ∼20 days from the first observation with well-controlled false-positive rates, providing ample opportunity to trigger follow-up observations. Additionally, we demonstrate the feasibility of time-delay estimations using solely LSST-like data of unresolved light curves, particularly for doubles, when excluding systems with low time delays and magnification ratios. However, the abundance of such systems among those unresolved in LSST poses a significant challenge. This approach holds potential utility for upcoming wide-field surveys, and overall results could significantly improve with enhanced cadence and depth in the future surveys. [ABSTRACT FROM AUTHOR]

Context. The gravitational lens system SDSS J1004+4112 was the first known example of a quasar lensed by a galaxy cluster. The interest in this system has been renewed following the publication of r-band light curves spanning 14.5 years and the determination of the time delays between the four brightest quasar images. Aims. We constrained the quasar accretion disk size and the fraction of the lens mass in stars using the signature of microlensing in the quasar image light curves. Methods. We built the six possible histograms of microlensing magnitude differences between the four quasar images and compared them with simulated model histograms, using a χ2 test to infer the model parameters. Results. We infer a quasar disk half-light radius of R1/2 = (0.70 ± 0.04)RE = (6.4 ± 0.4) √M/0.3M⊙ light-days at 2407 Å in the rest frame and stellar mass fractions at the quasar image positions of αA > 0.059, αB = 0.056+0.021-0.027, αC = 0.030+0.031-0.021, and αD = 0.072+0.034-0.016. Conclusions. The inferred disk size is broadly compatible with most previous estimates, and the stellar mass fractions are within the expected ranges for galaxy clusters. In the region where image C lies, the stellar mass fraction is compatible with a stellar contribution from the brightest cluster galaxy, galaxy cluster members, and intracluster light, but the values at images B, D, and especially A are slightly larger, possibly suggesting the presence of extra stellar components. [ABSTRACT FROM AUTHOR]

Evaluating the Kirchhoff–Fresnel diffraction integral is essential in studying wave effects in astrophysical lensing, but is often intractable because of the highly oscillatory integrand. A recent breakthrough was made by exploiting the Picard–Lefschetz theory: the integral can be performed along the 'Lefschetz thimbles' in the complex domain where the integrand is not oscillatory but rapidly converging. The application of this method, however, has been limited by both the unfamiliar concepts involved and the low numerical efficiency of the method used to find the Lefschetz thimbles. In this paper, we give simple examples of the Lefschetz thimbles and define the 'flow lines' that facilitate the understanding of the concepts. Based on this, we propose new ways to obtain the Lefschetz thimbles with high numerical efficiency, which provide an effective tool for studying wave effects in astrophysical lensing. [ABSTRACT FROM AUTHOR]

Gravitational lensing may render individual high-mass stars detectable out to cosmological distances, and several extremely magnified stars have in recent years been detected out to redshifts |$z\approx 6$|⁠. Here, we present Muspelheim, a model for the evolving spectral energy distributions of both metal-enriched and metal-free stars at high redshifts. Using this model, we argue that lensed stars will form a highly biased sample of the intrinsic distribution of stars across the Hertzsprung–Russell diagram, and that this bias will typically tend to favour the detection of lensed stars in evolved stages characterized by low effective temperatures, even though stars only spend a minor fraction of their lifetimes in such states. We also explore the prospects of detecting individual, lensed metal-free (Population III) stars at high redshifts using the James Webb Space Telescope (JWST). We find that very massive (⁠|$\gtrsim 100\ \mathrm{M}_\odot$|⁠) Population III stars at |$z\gtrsim 6$| may potentially be detected by JWST in surveys covering large numbers of strong-lensing clusters, provided that the Population III stellar initial mass function is sufficiently top-heavy, that these stars evolve to effective temperatures |$\le 15000$| K, and that the cosmic star formation rate density of Pop III stars reaches |$\gtrsim 10^{-4}\ \mathrm{M}_\odot$| cMpc |$^{-3}$| yr |$^{-1}$| at |$z\approx 6$| –10. Various ways to distinguish metal-free lensed stars from metal-enriched ones are also discussed. [ABSTRACT FROM AUTHOR]

Context. It is generally accepted that all massive galaxies host supermassive black holes (BHs) in their center and that mergers of two galaxies lead to the formation of BH binaries. The most interesting among them comprise the mergers in their final state, that is to say with parsec (3.2 light years) or sub-parsec orbital separations. It is possible to detect these systems with binary self-lensing. Aims. Here we report the potential detection of a central supermassive BH binary in the active galaxy (AGN) NGC 1566 based on a microlensing outburst. The light curve of the outburst – based on observations with the All Sky Automated Survey for SuperNovae – lasted from the beginning of 2017 until the beginning of 2020. The steep symmetric light curve as well as its shape look very different with respect to normal random variations in AGN. Results. However, the observations could be easily reproduced with a best-fit standard microlensing light curve. Based on the light curve, we derived a characteristic timescale of 155 days. During the outburst, the continuum as well as the broad line intensities varied; however, the narrow emission lines did not. This is an indication that the lensing object orbits the AGN nucleus between the broad line region (BLR) and the narrow line region (NLR), that is, at a distance on the order of 250 light days. The light curve can be reproduced by a lens with a BH mass of 5 × 105 M⊙. This implies a mass ratio to the central AGN on the order of 1–10. [ABSTRACT FROM AUTHOR]

Deep imaging of galaxy cluster fields have in recent years revealed tens of candidates for gravitationally lensed stars at redshifts z ≈ 1 − 6, and future searches are expected to reveal highly magnified stars from even earlier epochs. Multi-band photometric observations may be used to constrain the redshift, effective temperature Teff, and dust attenuation along the line of sight to such objects. When combined with an estimate of the likely magnification, these quantities may be converted into a constraint on the stellar luminosity and, for an adopted set of stellar evolutionary tracks, the initial stellar mass. Further characterisation is difficult, however, without spectroscopic observations, which at the typical brightness levels of high-redshift lensed stars becomes extremely challenging for even the largest existing telescopes. Here, we explore what spectral features one can realistically hope to detect in lensed stars with peak brightness in the range 26–28 AB mag, Teff = 4000 − 50 000 K, and redshifts z = 1 − 10, using spectroscopy with JWST and the forthcoming ELT. We find that a majority of detectable lines appear in the rest-UV range for stars with Teff ≥ 15 000 K. The strongest detectable spectral lines are the C IVλ1550 Å line and the Si IVλλ1393, 1403 Å-doublet at Teff = 30 000 K. For lower temperatures, the calcium H- and K-lines at Teff = 6000 K are among the most readily detectable. In limited wavelength ranges, ELT is expected to provide more sensitive spectroscopic observations, and with higher resolution than JWST. We find that variations in both mass-loss rate and metallicity lead to noticeable effects in the detectability of certain spectral lines with both JWST and ELT. [ABSTRACT FROM AUTHOR]

Gravitational microlensing with binary lensing is one of the channels for detecting exoplanets. Due to the degeneracy of the lens parameters for the binary microlensing, additional features such as parallax and finite-size effects need to identify the lens parameters. The frequency-shift effect as the relativistic analogy of the gravity assist for the photons, is an extra observation that provides additional constraint between the lens parameters. In this work, we extend the application of the frequency-shift effect to binary microlensing and derive the frequency shift during the lensing and caustic crossing. The frequency shift for the binary lens is of the order of |${\Delta \nu }/{\nu }\sim 10^{-12}$|⁠. We also investigate the feasibility of detecting this effect by employing cross-correlation methods. [ABSTRACT FROM AUTHOR]

We present the analysis of the microlensing event OGLE-2015-BLG-0845, which was affected by both the microlensing parallax and xallarap effects. The former was detected via the simultaneous observations from the ground and Spitzer , and the latter was caused by the orbital motion of the source star in a relatively close binary. The combination of these two effects led to a mass measurement of the lens object, revealing a low-mass (⁠|$0.14 \pm 0.05 \, \mathrm{ M}_{\odot }$|⁠) M dwarf at the bulge distance (⁠|$7.6 \pm 1.0$| kpc). The source binary consists of a late F-type subgiant and a K-type dwarf of |$\sim 1.2$| and |$\sim 0.9 \mathrm{ M}_{\odot }$|⁠ , respectively, and the orbital period is |$70 \pm 10$| d. OGLE-2015-BLG-0845 is the first single-lens event in which the lens mass is measured via the binarity of the source. Given the abundance of binary systems as potential microlensing sources, the xallarap effect may not be a rare phenomenon. Our work thus highlights the application of the xallarap effect in the mass determination of microlenses, and the same method can be used to identify isolated dark lenses. [ABSTRACT FROM AUTHOR]

This work studies microlensing effects in strongly lensed gravitational wave (GW) signals corresponding to global minima images in galaxy-scale lenses. We find that stellar microlenses alone are unable to introduce noticeable wave effects in the global minima GW signals at strong lensing magnification |$({\mu})\lt 50$| with match value between unlensed and lensed GW signals being above |${\sim }99.5~{{\ \rm per \, cent}}$| in |${\sim }90~{{\ \rm per \, cent}}$| of systems implying that GW signals corresponding to global minima can be treated as reference signal to determine the amount of microlensing in other strongly lensed counterparts. Since the stellar microlenses introduce negligible wave effects in global minima, they can be used to probe the intermediate-mass black hole (IMBH) lenses in the galaxy lens. We show that the presence of an IMBH lens with mass in the range |$[50,10^3]~{\rm M_\odot }$| such that the global minima lies within five Einstein radius of it, the microlensing effects at |$f\lt 10^2$| Hz are mainly determined by the IMBH lens for |${\mu} \lt 50$|⁠. Assuming that a typical strong lensing magnification of 3.8 and high enough signal-to-noise ratio (in the range |${\simeq }[10, 30]$|⁠) to detect the microlensing effect in GW signals corresponding to global minima, with non-detection of IMBH-led microlensing effects in |${\simeq }15~({\simeq }150)$| lensed GW signals, we can rule out dark matter fraction |$\gt 10~{{\ \rm per \, cent}}~(\gt 1~{{\ \rm per \, cent}})$| made of IMBH population inside galaxy lenses with mass values |$\gt 150~{\rm M_\odot }$| with |${\sim }$| 90 per cent confidence. Although we have specifically used IMBHs as an example, the same analysis applies to any subhalo (or compact objects) with lensing masses (i.e. the total mass inside Einstein radius) satisfying the above criterion. [ABSTRACT FROM AUTHOR]

Microlensing of the broad emission line region (BLR) in gravitationally lensed quasars produces line profile distortions that can be used to probe the BLR size, geometry, and kinematics. Based on single-epoch spectroscopic data, we analyzed the C IV line profile distortions due to microlensing in two quasars, SDSS J133907.13+131039.6 (J1339) and SDSS J113803.73+031457.7 (J1138), complementing previous studies of microlensing in the quasars Q2237+0305 and J1004+4112. J1339 shows a strong, asymmetric line profile deformation, while J1138 shows a more modest, symmetric deformation, confirming the rich diversity of microlensing-induced spectral line deformations. To probe the C IV BLR, we compared the observed line profile deformations to simulated ones. The simulations are based on three simple BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), of various sizes, inclinations, and emissivities. These models were convolved with microlensing magnification maps specific to the microlensed quasar images, which produced a large number of distorted line profiles. The models that best reproduce the observed line profile deformations were then identified using a Bayesian probabilistic approach. We find that the line profile deformations can be reproduced with the simple BLR models under consideration, with no need for more complex geometries or kinematics. The models with disk geometries (KD and EW) are preferred, while the PW model is definitely less likely. In J1339, the EW model is favored, while the KD model is preferred in Q2237+0305, suggesting that various kinematical models can dominate the C IV BLR. For J1339, we find the C IV BLR half-light radii to be r1/2 = 5.1−2.9+4.6 r 1 / 2 = 5. 1 − 2.9 + 4.6 $ r_{1/2} = 5.1^{+4.6}_{-2.9} $ light-days and r1/2 = 6.7−3.8+6.0 r 1 / 2 = 6. 7 − 3.8 + 6.0 $ r_{1/2} = 6.7^{+6.0}_{-3.8} $ light-days from spectra obtained in 2014 and 2017, respectively. They do agree within uncertainties. For J1138, the amplitude of microlensing is smaller and more dependent on the macro-magnification factor. From spectra obtained in 2005 (single epoch), we find r1/2 = 4.9−2.7+4.9 r 1 / 2 = 4. 9 − 2.7 + 4.9 $ r_{1/2} = 4.9^{+4.9}_{-2.7} $ light-days and r1/2 = 12−8+13 r 1 / 2 = 12 − 8 + 13 $ r_{1/2} = 12^{+13}_{-8} $ light-days for two extreme values of the macro-magnification factor. Combining these new measurements with those previously obtained for the quasars Q2237+0305 and J1004+4112, we show that the BLR radii estimated from microlensing do follow the C IV radius–luminosity relation obtained from reverberation mapping, although the microlensing radii seem to be systematically smaller, which could indicate either a selection bias or a real offset. [ABSTRACT FROM AUTHOR]

Aims. We investigated the nature of the anomalies appearing in four microlensing events KMT-2020-BLG-0757, KMT-2022-BLG-0732, KMT-2022-BLG-1787, and KMT-2022-BLG-1852. The light curves of these events commonly exhibit initial bumps followed by subsequent troughs that extend across a substantial portion of the light curves. Methods. We performed thorough modeling of the anomalies to elucidate their characteristics. Despite their prolonged durations, which differ from the usual brief anomalies observed in typical planetary events, our analysis revealed that each anomaly in these events originated from a planetary companion located within the Einstein ring of the primary star. It was found that the initial bump arouse when the source star crossed one of the planetary caustics, while the subsequent trough feature occurred as the source traversed the region of minor image perturbations lying between the pair of planetary caustics. Results. The estimated masses of the host and planet, their mass ratios, and the distance to the discovered planetary systems are (Mhost/M⊙, Mplanet/MJ, q/10−3, DL/kpc) = (0.58−0.30+0.33, 10.71−5.61+6.17, 17.61 ± 2.25, 6.67−1.30+0.93) for KMT-2020-BLG-0757, (0.53−0.31+0.31, 1.12−0.65+0.65, 2.01 ± 0.07, 6.66−1.84+1.19) for KMT-2022-BLG-0732, (0.42−0.23+0.32, 6.64−3.64+4.98, 15.07 ± 0.86, 7.55−1.30+0.89) for KMT-2022-BLG-1787, and (0.32−0.19+0.34, 4.98−2.94+5.42, 8.74 ± 0.49, 6.27−1.15+0.90) for KMT-2022-BLG-1852. These parameters indicate that all the planets are giants with masses exceeding the mass of Jupiter in our solar system and the hosts are low-mass stars with masses substantially less massive than the Sun. [ABSTRACT FROM AUTHOR]

Aims. We aim to investigate the nature of the short-term anomaly that appears in the lensing light curve of KMT-2023-BLG-1866. The anomaly was only partly covered due to its short duration of less than a day, coupled with cloudy weather conditions and a restricted nighttime duration. Methods. Considering the intricacy of interpreting partially covered signals, we thoroughly explored all potential degenerate solutions. Through this process, we identified three planetary scenarios that account for the observed anomaly equally well. These scenarios are characterized by the specific planetary parameters: (s, q)inner = [0.9740 ± 0.0083, (2.46 ± 1.07) × 10−5], (s, q)intermediate = [0.9779 ± 0.0017, (1.56 ± 0.25) × 10−5], and (s, q)outer = [0.9894 ± 0.0107, (2.31 ± 1.29) × 10−5], where s and q denote the projected separation (scaled to the Einstein radius) and mass ratio between the planet and its host, respectively. We identify that the ambiguity between the inner and outer solutions stems from the inner-outer degeneracy, while the similarity between the intermediate solution and the others is due to an accidental degeneracy caused by incomplete anomaly coverage. Results. Through Bayesian analysis utilizing the constraints derived from measured lensing observables and blending flux, our estimation indicates that the lens system comprises a very-low-mass planet orbiting an early M-type star situated approximately (6.2–6.5) kpc from Earth in terms of median posterior values for the different solutions. The median mass of the planet host is in the range of (0.48–0.51) M⊙, and that of the planet's mass spans a range of (2.6–4.0) ME, varying across different solutions. The detection of KMT-2023-BLG-1866Lb signifies the extension of the lensing surveys to very-low-mass planets that have been difficult to detect in earlier surveys. [ABSTRACT FROM AUTHOR]

Lensed quasars are powerful cosmic laboratories; they are used to simultaneously probe various astrophysical phenomena. Microlensing by stars within distant galaxies acts as strong gravitational lenses of multiply imaged quasars, and provides a unique and direct measurement of the lensed quasar internal structure. Microlensing of the continuum emitting region as well as the broad-line region (BLR) is well characterized by four observable indices, μcont, μBLR, WCI (wing-core), and RBI (red-blue), measured directly from the spectra. During the 2004−2007 monitoring period, image A of the quadruply lensed system Q2237+0305 underwent a strong microlensing amplification, while image D remained unaffected. We used 35 epochs of archival spectrophotometric data of Q2237+0305 obtained with the Very Large Telescope of the European Southern Observatory to develop an independent microlensing method for estimating the geometry and size of the BLR. We measured the index time series for the C IV line and the continuum emission at 1450 Å. We built a library of the simulated microlensing index time series that reproduce the observed times series based on three representative BLR models: Keplerian disk (KD), polar wind (PW), and equatorial wind (EW). After sampling the model parameter space, we find that KD is the predominant model, while PW and EW are less likely. We infer that the system is viewed at an intermediate viewing angle i ∼ 35°, and we estimate the most likely C IV BLR half-light radius r1/2 = 51 ± 23 light days. Our results are in good agreement with previous findings in the literature and extend the validity of the index-based approach to a temporal domain. [ABSTRACT FROM AUTHOR]

Microlensing of stars in strongly lensed galaxies can lead to temporary extreme magnification factors (μ> 1000), enabling their detection at high redshifts. Following the discovery of Icarus, several stars at cosmological distances (z > 1) have been observed using the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). This emerging field of gravitational lensing holds promise to study individual high redshift stars. It also offers the opportunity to study the substructure in the lens plane with implications for dark matter models, as more lensed stars are detected and analysed statistically. Due to the computational demands of simulating microlensing at large magnification factors, it is important to develop fast and accurate analytical approximations for the probability of magnification in such extreme scenarios. In this study, we consider different macro-model magnification and microlensing surface mass density scenarios and study how the probability of extreme magnification factors depends on these factors. To achieve this, we created state-of-the-art large simulations of the microlensing effect in these scenarios. Through the analysis of these simulations, we derived analytical scaling relationships that can bypass the need for expensive numerical simulations. Our results are useful to interpret current observations of stars at cosmic distances which are extremely magnified and under the influence of microlenses. [ABSTRACT FROM AUTHOR]

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 H 0 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. [ABSTRACT FROM AUTHOR]

Isolated black holes (BHs) and neutron stars (NSs) are largely undetectable across the electromagnetic spectrum. For this reason, our only real prospect of observing these isolated compact remnants is via microlensing; a feat recently performed for the first time. However, characterization of the microlensing events caused by BHs and NSs is still in its infancy. In this work, we perform N -body simulations to explore the frequency and physical characteristics of microlensing events across the entire sky. Our simulations find that every year we can expect |$88_{-6}^{+6}$| BH, |$6.8_{-1.6}^{+1.7}$| NS, and |$20^{+30}_{-20}$| stellar microlensing events which cause an astrometric shift larger than 2 mas. Similarly, we can expect |$21_{-3}^{+3}$| BH, |$18_{-3}^{+3}$| NS, and |$7500_{-500}^{+500}$| stellar microlensing events which cause a bump magnitude larger than 1 mag. Leveraging a more comprehensive dynamical model than prior work, we predict the fraction of microlensing events caused by BHs as a function of Einstein time to be smaller than previously thought. Comparison of our microlensing simulations to events in Gaia finds good agreement. Finally, we predict that in the combination of Gaia and Gaia NIR data there will be |$14700_{-900}^{+600}$| BH and |$1600_{-200}^{+300}$| NS events creating a centroid shift larger than 1 mas and |$330_{-120}^{+100}$| BH and |$310_{-100}^{+110}$| NS events causing bump magnitudes >1. Of these, <10 BH and |$5_{-5}^{+10}$| NS events should be detectable using current analysis techniques. These results inform future astrometric mission design, such as Gaia NIR, as they indicate that, compared to stellar events, there are fewer observable BH events than previously thought. [ABSTRACT FROM AUTHOR]

In this study, we investigate the impact of microlensing on gravitational wave (GW) signals in the LIGO−Virgo sensitivity band. Microlensing caused by an isolated point lens, with (redshifted) mass ranging from M Lz ∈ (1,  105) M⊙ and impact parameter y ∈ (0.01,  5), can result in a maximum mismatch of |$\sim 30~{{\ \rm per\ cent}}$| with their unlensed counterparts. When y < 1, it strongly anticorrelates with the luminosity distance enhancing the detection horizon and signal-to-noise ratio (SNR). Biases in inferred source parameters are assessed, with in-plane spin components being the most affected intrinsic parameters. The luminosity distance is often underestimated, while sky-localization and trigger times are mostly well-recovered. Study of a population of microlensed signals due to an isolated point lens primarily reveals: (i) using unlensed templates during the search causes fractional loss (20 per cent to 30 per cent) of potentially identifiable microlensed signals; (ii) the observed distribution of y challenges the notion of its high improbability at low values (y ≲ 1), especially for y ≲ 0.1; (iii) Bayes factor analysis of the population indicates that certain region in M Lz − y parameter space have a higher probability of being detected and accurately identified as microlensed. Notably, the microlens parameters for the most compelling candidate identified in previous microlensing searches, GW200208_130117, fall within a 1σ range of the aforementioned higher probability region. Identifying microlensing signatures from M Lz < 100 M⊙ remains challenging due to small microlensing effects at typical SNR values. Additionally, we also examined how microlensing from a population of microlenses influences the detection of strong lensing signatures in pairs of GW events, particularly in the posterior-overlap analysis. [ABSTRACT FROM AUTHOR]

Upcoming wide-field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-yr LSST survey, during which the quasar's inner accretion disc crosses a caustic feature produced by an ensemble of microlenses. Such caustic-crossing events offer the unique opportunity to probe the vicinity of the central supermassive black hole, especially when combined with high cadence, multi-instrument follow-up triggered by LSST monitoring. To simulate the high-cadence optical monitoring of caustic-crossing events, we use relativistic accretion disc models which leads to strong asymmetric features. We develop analysis methods to measure the innermost stable circular orbit (ISCO) crossing time of isolated caustic-crossing events and benchmark their performance on our simulations. We also use our simulations to train a convolutional neural network (CNN) to infer the black hole mass, inclination angle, and impact angle directly from these light curves. As a pilot application of our methods, we used archival caustic-crossings of QSO 2237+0305 to estimate the black hole mass and inclination angle. From these data, two of these methods called the second derivative and wavelet methods measure an ISCO crossing time of 48.5 and 49.5 d, corresponding to a Kerr black hole mass of M BH = (1.5 ± 1.2) × 109 and (1.5 ± 1.3) × 109  M⊙, respectively. The CNN inferred log10(M BH/M⊙) = 8.35 ± 0.30 when trained on Schwarzschild black hole simulations, and a moderate inclination of i  = 45 ± 23°. These measurements are found to be consistent with previous estimates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To better understand which sources contribute to optical passband fluxes of Q0957+561, we present and analyse light curves of the doubly imaged gravitationally lensed quasar from its discovery to 2023. After an early microlensing event, the difference light curves (describing delay-corrected flux ratios between the two quasar images) only show prominent microlensing gradients over the last 17 yr. In addition to these long time-scale gradients in the gr bands, we detect short time-scale, extrinsically induced differential variations that are highly correlated with the short time-scale intrinsic variability of the quasar in those bands. Both the accretion disc and the broad emission-line region (BELR) contribute to optical passband fluxes, and we also show that realistic contributions of the BELR account for the observed correlations in the gr bands. We would like to highlight that the BELR sources of optical passband fluxes of Q0957+561 should be taken into account when measuring accretion-disc source sizes from microlensing simulations. [ABSTRACT FROM AUTHOR]

We analyse 1602 microlensing events found in the VISTA Variables in the Via Lactea (VVV) near-infrared (NIR) survey data. We obtain spatially resolved, efficiency-corrected time-scale distributions across the Galactic bulge (|ℓ| < 10°, | b | < 5°), using a Bayesian hierarchical model. Spatially resolved peaks and means of the time-scale distributions, along with their marginal distributions in strips of longitude and latitude, are in agreement at a 1σ level with predictions based on the Besançon model of the Galaxy. We find that the event time-scales in the central bulge fields (|ℓ| < 5°) are on average shorter than the non-central (|ℓ| > 5°) fields, with the average peak of the lognormal time-scale distribution at 23.6 ± 1.9 d for the central fields and 29.0 ± 3.0 d for the non-central fields. Our ability to probe the structure of the bulge with this sample of NIR microlensing events is limited by the VVV survey's sparse cadence and relatively small number of detected microlensing events compared to dedicated optical surveys. Looking forward to future surveys, we investigate the capability of the Roman telescope to detect spatially resolved asymmetries in the time-scale distributions. We propose two pairs of Roman fields, centred on (ℓ = ±9, 5°, b  = −0.125°) and (ℓ = −5°, b  = ±1.375°) as good targets to measure the asymmetry in longitude and latitude, respectively. [ABSTRACT FROM AUTHOR]

A detailed analysis is presented of gravitational microlensing by intervening compact objects of the black hole shadows imaged by the Event Horizon Telescope (EHT). We show how the centre, size, and shape of the shadow depend on the Einstein angle relative to the true/unlensed shadow size, and how the location of the lens affects the shift, size, and asymmetry of the black hole shadow due to microlensing. Assuming a supermassive black hole (SMBH) casts a circular-shaped true shadow, microlensing can create an asymmetry of up to approximately 8 per cent, which is twice the asymmetry caused by the SMBH's spin and its tilt relative to us. Furthermore, the size can be enhanced by ∼50 per cent of the true shadow. Currently, the terrestrial baselines of EHT lack the resolution to detect microlensing signatures in the shadows. However, future expansions of EHT, including space-based baselines at the Moon and L2, could potentially enable the detection of microlensing events. For Sgr A*, an event rate of 0.0014 per year makes the microlensing phenomena difficult to observe even with space-based baselines for the stellar population in the stellar bulge and stellar disc for lens masses ∼ M ⊙. None the less, the presence of a cluster of 20 000 stellar-mass black holes in the central parsec of the Milky Way, expected to arise from dynamical friction acting on infalling stellar clusters, significantly boosts the event rate. Hence, continuously monitoring the shadow of Sgr A* could offer novel insights into the compact object population surrounding the Galactic Centre. [ABSTRACT FROM AUTHOR]

The article presents the results of long-term photometric monitoring of two binary gravitationally lensed quasars, SDSS J2124 1632 and SDSS J0806 2006, carried out at the Maidanak Observatory in 2017–2022. The obtained light curves of the lensed components of both systems are analyzed. The variability of SDSS J2124 1632 turned out to be quite large: up to for the system as a whole and up to for component A. Long-term microlensing was found against the background of a general increase in the apparent brightness of the quasar source. The brightness variations in SDSS J0806 2006 are less intense: the range is about for the system as a whole, and up to for both components. Analysis of the light curves did not show the presence of microlensing here. We also calculated the probable values of the time delay: days (component B is in the lead) and days (component A is in the lead) in SDSS J2124 1632 and SDSS J0806 2006, respectively. The value of for SDSS J2124 1632 is consistent with previously found time delays for binary gravitationally lensed systems. In the case of the second system, the time delay is consistent with earlier theoretical calculations, which suggested that the time delay should be about 50 days. [ABSTRACT FROM AUTHOR]

Analyses are given on four recent gravitational millilensing claims on gamma-ray bursts (GRBs): GRB 081122A, GRB 081126A, GRB 110517B, and GRB 210812A. Two tests, a light curve similarity test and a hardness similarity test, compare different temporal sections of a single GRB to see if they are statistically similar. The hardness similarity test shows that the ratio between the second and the first emission episodes in each energy channel differed from the same ratio averaged over all energy channels at above 90 per cent confidence level in GRB 081122A. Additionally, the light curve similarity test applied to GRB 081122A, GRB 081126A, and GRB 110517B separately indicated a high likelihood that the two emission episodes in each GRB were not from the same parent emission episode. This conclusion was reached with confidence levels of 4.8σ for GRB 081122A, 3.08σ for GRB 081126A, and 8.45σ for GRB 110517B. However, these tests did not detect a significant difference between the pulses of GRB 210812A. Consequently, our results suggest that while GRB 210812A could not be conclusively ruled out, the other three GRBs do not show clear evidence of millilensing. [ABSTRACT FROM AUTHOR]

It has been claimed that the variability of field quasars resembles gravitational lensing by a large cosmological population of free-floating planets with mass |$\sim\!\! 10\ {\rm M}_{\oplus }$|⁠. However, Galactic photometric monitoring experiments, on the other hand, exclude a large population of such planetary-mass gravitational lenses. These apparently contradictory pieces of evidence can be reconciled if the objects under consideration have a mean column density that lies between the critical column densities for gravitational lensing in these two contexts. Dark matter in that form is known to be weakly collisional, so a core develops in galaxy halo density profiles, and a preferred model has already been established. Here, we consider what such a model implies for Q2237+0305, which is the best-studied example of a quasar that is strongly lensed by an intervening galaxy. We construct microlensing magnification maps appropriate to the four macro-images of the quasar – all of which are seen through the bulge of the galaxy. Each of these maps exhibits a caustic network arising from the stars, plus many small, isolated caustics arising from the free-floating 'planets' in the lens galaxy. The 'planets' have little influence on the magnification histograms but a large effect on the statistics of the magnification gradients. We compare our predictions to the published Optical Gravitational Lensing Experiment (OGLE) photometry of Q2237+0305 and find that these data are consistent with the presence of the hypothetical 'planets'. However, the evidence is relatively weak because the OGLE data set is not well suited to testing our predictions and requires low-pass filtering for this application. New data from a large, space-based telescope are desirable to address this issue. [ABSTRACT FROM AUTHOR]

In this work, we update and develop algorithms for KMTNet tender-love care (TLC) photometry in order to create a new, mostly automated, TLC pipeline. We then start a project to systematically apply the new TLC pipeline to the historic KMTNet microlensing events, and search for buried planetary signals. We report the discovery of such a planet candidate in the microlensing event MOA-2019-BLG-421/KMT-2019-BLG-2991. The anomalous signal can be explained by either a planet around the lens star or the orbital motion of the source star. For the planetary interpretation, despite many degenerate solutions, the planet is most likely to be a Jovian planet orbiting an M or K dwarf, which is a typical microlensing planet. The discovery proves that the project can indeed increase the sensitivity of historic events and find previously undiscovered signals. [ABSTRACT FROM AUTHOR]

Strong gravitational lensing of quasars has the potential to unlock the poorly understood physics of these fascinating objects, as well as serve as a probe of the lensing mass distribution and of cosmological parameters. In particular, gravitational microlensing by compact bodies in the lensing galaxy can enable mapping of quasar structure to < 10 − 6 arcsec scales. Some of this potential has been realized over the past few decades, however the upcoming era of large sky surveys promises to bring this promise to full fruition. In this article, we review the theoretical framework of this field, describe the prominent current methods for parameter inference from quasar microlensing data across different observing modalities, and discuss the constraints so far derived on the geometry and physics of quasar inner structure. We also review the application of strong lensing and microlensing to constraining the granularity of the lens potential, i.e. the contribution of the baryonic and dark matter components, and the local mass distribution in the lens, i.e. the stellar mass function. Finally, we discuss the future of the field, including the new possibilities that will be opened by the next generation of large surveys and by new analysis methods now being developed. [ABSTRACT FROM AUTHOR]

Strong gravitational lensing and microlensing of supernovae (SNe) are emerging as a new probe of cosmology and astrophysics in recent years. We provide an overview of this nascent research field, starting with a summary of the first discoveries of strongly lensed SNe. We describe the use of the time delays between multiple SN images as a way to measure cosmological distances and thus constrain cosmological parameters, particularly the Hubble constant, whose value is currently under heated debates. New methods for measuring the time delays in lensed SNe have been developed, and the sample of lensed SNe from the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to provide competitive cosmological constraints. Lensed SNe are also powerful astrophysical probes. We review the usage of lensed SNe to constrain SN progenitors, acquire high-z SN spectra through lensing magnifications, infer SN sizes via microlensing, and measure properties of dust in galaxies. The current challenge in the field is the rarity and difficulty in finding lensed SNe. We describe various methods and ongoing efforts to find these spectacular explosions, forecast the properties of the expected sample of lensed SNe from upcoming surveys particularly the LSST, and summarize the observational follow-up requirements to enable the various scientific studies. We anticipate the upcoming years to be exciting with a boom in lensed SN discoveries. [ABSTRACT FROM AUTHOR]

The abundance of protoplanetary bodies ejected from their parent star system is presently poorly constrained. With only two existing optical observations of interstellar objects in the 108–1010 kg mass range and a small number of robust microlensing observations of free-floating planets (FFPs) in the 1024–1025 kg mass range, there is a large range of masses for which there are no existing measurements of the unbound population. The three primary microlensing surveys currently searching for FFPs operate at a cadence greater than 15 min, which limits their ability to observe events associated with bodies with a mass much below an Earth mass. We demonstrate that existing high-cadence observations of M31 with the Subaru Hyper Suprime-Cam place constraints on the abundance of unbound objects at sub-terrestrial masses, with peak sensitivity at 10−4 M⊕ for Milky Way lenses and 10−1 M⊕ for lenses in M31. For a fiducial |$\frac{dn}{dM}\propto M^{-2}$| mass distribution, we find that the abundance of unbound objects is constrained to |$n_\text{unbound} \lt 1.4 \times 10^{7} ~\rm {pc}^{-3}$| for masses within 1 dex of 10−4 M⊕. Additionally, we compute limits on an artificial 'monochromatic' distribution of unbound objects and compare to existing literature, demonstrating that the assumed spatial distribution of lenses has very significant consequences for the sensitivity of microlensing surveys. While the observations ultimately do not probe abundances suggested by current models of planetary formation, our limits place direct observational constraints on the unbound population in the sub-terrestrial mass range and motivate new observational strategies for microlensing surveys. [ABSTRACT FROM AUTHOR]

We report on three optically bright, ∼16th mag, point sources within 10 arcsec of each other that vanished within 1 h, based on two consecutive exposures at Palomar Observatory on 1952 July 19 (POSS I Red and Blue). The three point sources have continued to be absent in telescope exposures during 71 yr with detection thresholds of ∼21st mag. We obtained two deep exposures with the 10.4-m Gran Telescopio Canarias on 2023 April 25 and 27 in r and g band, both reaching magnitude 25.5 (3σ). The three point sources are still absent, implying they have dimmed by more than 10 mag within an hour back in 1952. When bright in 1952, the most isolated transient source has a profile nearly the same as comparison stars, implying the sources are subarcsec in angular size and they exhibit no elongation due to movement. This triple transient has observed properties similar to other cases where groups of transients ('multiple transients') have appeared and vanished in a small region within a plate exposure. The explanation for these three transients and the previously reported cases remains unclear. Models involving background objects that are optically luminous for less than 1 h coupled with foreground gravitational lensing seem plausible. If so, a significant population of massive objects with structure serving as the lenses, to produce three images, are required to explain the subhour transients. [ABSTRACT FROM AUTHOR]

Aims. We aim to reveal the sizes of the continuum and broad emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1004+4112 by analyzing the unique signatures of microlensing in this system. Through a comprehensive analysis of 20 spectroscopic observations acquired between 2003 and 2018, we studied the striking deformations of various BEL profiles and determined the sizes of their respective emitting regions. Methods. Our approach involves a detailed analysis of the magnitude differences in the BEL wings and their adjacent continua, and the implementation of a statistical model to quantify the distribution and impact of microlensing magnifications. To ensure a reliable baseline for no microlensing, we used the emission line cores as a reference. We then applied a Bayesian estimate to derive the size lower limits of the Lyα, Si IV, C IV, C III], and Mg II emitting regions, as well as the sizes of the underlying continuum-emitting sources. Results. We analyzed the outstanding microlensing-induced distortions in the line profiles of various BELs in the quasar image A, characterized by a prominent magnification of the blue part and a strong demagnification of the red part. From the statistics of microlensing magnifications and using Bayesian methods, we estimate the lower limit to the overall size of the regions emitting the BELs to be a few light-days across, which is significantly smaller than in typically lensed quasars. The asymmetric deformations in the BELs indicate that the broad-line region is generally not spherically symmetric, and is likely confined to a plane and following the motions of the accretion disk. Additionally, the inferred continuum-emitting region sizes are larger than predictions based on standard thin-disk theory by a factor of ∼3.6 on average. The size-wavelength relation is consistent with that of a geometrically thin and optically thick accretion disk. [ABSTRACT FROM AUTHOR]

With the detection of black hole mergers by the LIGO gravitational wave telescope, there has been increasing interest in the possibility that dark matter may be in the form of solar mass primordial black holes. One of the predictions implicit in this idea is that compact clouds in the broad emission line regions of high-redshift quasars will be microlensed, leading to changes in line structure and the appearance of new emission features. In this paper, the effect of microlensing on the broad emission line region is reviewed by reference to gravitationally lensed quasar systems where microlensing of the emission lines can be unambiguously identified. It is then shown that although changes in Seyfert galaxy line profiles occur on time-scales of a few years, they are too nearby for a significant chance that they could be microlensed, and are plausibly attributed to intrinsic changes in line structure. In contrast, in a sample of 53 high-redshift quasars, 9 quasars show large changes in line profile at a rate consistent with microlensing. These changes occur on a time-scale an order of magnitude too short for changes associated with the dynamics of the emission line region. The main conclusion of the paper is that the observed changes in quasar emission line profiles are consistent with microlensing by a population of solar mass compact bodies making up the dark matter, although other explanations like intrinsic variability are possible. Such bodies are most plausibly identified as primordial black holes. [ABSTRACT FROM AUTHOR]

Primordial black holes, which could have formed during the early Universe through overdensities in primordial density fluctuations during inflation, are potential candidates for dark matter. We explore the use of lensing parallax of gamma-ray bursts (GRBs), which results in different fluxes being observed from two different vantage points, in order to probe the abundance of primordial black holes in the unexplored window within the mass range 10−15 to 10−11  |$\mathrm{ {M}_\odot}$|⁠. We derive the optical depth for the lensing of GRBs with a distribution of source properties and realistic detector sensitivities. We comment on the ability of the proposed Indian twin satellite mission Daksha in its low Earth orbit to conduct this experiment. If the two Daksha satellites observe 10 000 GRBs simultaneously and the entirety of dark matter is made up of 10−15 to 10−12  |$\mathrm{ {M}_\odot}$| black holes, Daksha will detect non-zero lensing events with a probability ranging from 80 to 50 per cent at the bin edges, respectively. Non-detections will not conclusively rule out primordial black holes as dark matter in this mass range. However, we show that meaningful constraints can be obtained in such a case if the two satellites are separated by at least the Earth–Moon distance. [ABSTRACT FROM AUTHOR]

Currently, astrometric microlensing is the only tool that can directly measure the mass of a single star; it can also help us to detect compact objects such as isolated neutron stars and black holes. The number of microlensing events that are being predicted and reported is increasing. In this paper, potential lens stars are selected from three types of stars: high-proper-motion stars, nearby stars, and high-mass stars. For each potential lens star, we select a larger search scope to find possible matching sources and to avoid missing events as much as possible. Using data from Gaia Data Release 3, we predict 4500 astrometric microlensing events with δθ+ > 0.1 mas, which occur between J2010.0 and J2070.0, where 1664 events are different from those found previously. There are 293 lens stars that can cause two or more events, where five lens stars can cause more than 50 events. We find that 116 events have the distance of background stars from the proper motion path of lens stars more than 8 arcsec in the reference epoch, where the maximum distance is 16 |${_{.}^{\prime\prime}}$| 6. Thus, the cone search method of expanding the search range of sources for each potential lens star can reduce the possibility of missing events. [ABSTRACT FROM AUTHOR]

Two different temporal sections of a single gamma-ray burst (GRB) must be statistically similar to show an internal gravitational lensing signature. Here, two straightforward gravitational lensing tests are defined and applied: a light curve similarity test and a hardness similarity test. Gravitational millilensing has been claimed to be detected within several individual GRBs that contain two emission episodes separated by a time-delay. However, our analyses indicate that none of those claims satisfy both tests. The hardness similarity test performed on GRB 950830 and GRB 090717A found that the ratio between the second and the first emission episodes in each energy channel differed from the same ratio averaged over all detected energy channels at around 90 per cent confidence level. Also, a light curve similarity test performed on GRB 950830, GRB 090717A, and GRB 200716C separately found that it is unlikely that the two emission episodes in each GRB were drawn from a single parent emission episode for that GRB, with differences at the 3.0σ, 5.84σ, and 9.35σ confidence levels, respectively. [ABSTRACT FROM AUTHOR]

We present JWST/NIRSpec observations of a highly magnified star candidate at a photometric redshift of z phot ≃ 4.8, previously detected in JWST/NIRCam imaging of the strong lensing (SL) cluster MACS J0647+7015 (z  = 0.591). The spectroscopic observation allows us to precisely measure the redshift of the host arc at z spec = 4.758 ± 0.004, and the star's spectrum displays clear Lyman- and Balmer-breaks commensurate with this redshift. A fit to the spectrum suggests a B-type super-giant star of surface temperature |$T_{\mathrm{eff,B}}\simeq 15\, 000$|  K with either a redder F-type companion (⁠|$T_{\mathrm{eff,F}}\simeq 6\, 250$|  K) or significant dust attenuation (AV ≃ 0.82) along the line of sight. We also investigate the possibility that this object is a magnified young globular cluster rather than a single star. We show that the spectrum is in principle consistent with a star cluster, which could also accommodate the lack of flux variability between the two epochs. However, the lack of a counter image and the strong upper limit on the size of the object from lensing symmetry, r ≲ 0.5 pc, could indicate that this scenario is somewhat less likely – albeit not completely ruled out by the current data. The presented spectrum seen at a time when the Universe was only ∼1.2 Gyr old showcases the ability of JWST to study early stars through extreme lensing. [ABSTRACT FROM AUTHOR]

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects leading to distortion in the signals. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some follow-up analyses that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system by applying these analyses to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. These analyses cover the strong lensing, millilensing, and microlensing regimes. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations. [ABSTRACT FROM AUTHOR]

Gravitational lensing describes the bending of the trajectories of light and gravitational waves due to the gravitational potential of a massive object. Strong lensing by galaxies can create multiple images with different overall amplifications, arrival times, and image types. If, furthermore, the gravitational wave encounters a star along its trajectory, microlensing will take place. Previously, it has been shown that the effects of microlenses on strongly-lensed type-I images could be negligible in practice, at least in the low magnification regime. In this work, we study the same effect on type-II strongly-lensed images by computing the microlensing amplification factor. As opposed to being magnified, type-II images are typically demagnified. Moreover, microlensing on top of type-II images induces larger mismatches with un-microlensed waveforms than type-I images. These results are broadly consistent with recent literature and serve to confirm the findings. In addition, we investigate the possibility of detecting and analysing microlensed signals through Bayesian parameter estimation with an isolated point mass lens template, which has been adopted in recent parameter estimation literature. In particular, we simulate gravitational waves microlensed by a microlens embedded in a galaxy potential near moderately magnified type-I and II macroimages, with variable lens masses, source parameters and macromagnifcations. Generally, an isolated point mass model could be used as an effective template to detect a type-II microlensed image but not for type-I images, demonstrating the necessity for more realistic microlensing search templates. [ABSTRACT FROM AUTHOR]

Since the first detection of gravitational waves in 2015, gravitational-wave astronomy has emerged as a rapidly advancing field that holds great potential for studying the cosmos, from probing the properties of black holes to testing the limits of our current understanding of gravity. One important aspect of gravitational-wave astronomy is the phenomenon of gravitational lensing, where massive intervening objects can bend and magnify gravitational waves, providing a unique way to probe the distribution of matter in the Universe, as well as finding applications to fundamental physics, astrophysics, and cosmology. However, current models for gravitational-wave millilensing—a specific form of lensing where small-scale astrophysical objects can split a gravitational wave signal into multiple copies—are often limited to simple isolated lenses, which is not realistic for complex lensing scenarios. In this paper, we present a novel phenomenological approach to incorporate millilensing in data analysis in a model-independent fashion. Our approach enables the recovery of arbitrary lens configurations without the need for extensive computational lens modelling, making it a more accurate and computationally efficient tool for studying the distribution of matter in the Universe using gravitational-wave signals. When gravitational-wave lensing observations become possible, our method could provide a powerful tool for studying complex lens configurations in the future. [ABSTRACT FROM AUTHOR]

We study light variability of gravitationally magnified high-redshift star clusters induced by a foreground population of microlenses. This arises as the incoherent superposition of light variations from many source stars traversing the random magnification pattern on the source plane. The light curve resembles a scale-invariant, Gaussian process on time-scales of years to decades, while exhibits rapid and frequent micro-caustic crossing flares of larger amplitudes on time-scales of days to months. For a concrete example, we study a young Lyman-continuum-leaking star cluster in the Sunburst Arc at z = 2.37. We show that one magnified image happens to be intervened by a foreground galaxy, and hence should exhibit a variable flux at the 1-$2{{\ \rm per\ cent}}$ level, which is measurable in space with ∼1-$3\,$ ks exposures on the Hubble Space Telescope and more easily with the James Webb Space Telescope, or even from the ground using a ∼4-m telescope without adaptive optics. Detailed measurement of this variability can help determine the absolute macro magnification and hence the intrinsic mass and length scales of the star cluster, test synthetic stellar population models, and probe multiplicity of massive stars. Furthermore, monitoring the other lensed images of the star cluster, which are free from significant intervention by foreground microlenses, can allow us to probe planetary to stellar mass compact objects constituting as little as a few per cent of the dark matter. Given the typical surface density of intracluster stars, we expect this phenomenon to be relevant for other extragalactic star clusters lensed by galaxy clusters.

Aims. We investigate the discrepancy between the predicted size of accretion disks (ADs) in quasars and the observed sizes as deduced from gravitational microlensing studies. Specifically, we aim to understand whether the discrepancy is due to an inadequacy of current AD models or whether it can be accounted for by the contribution of diffuse broad-line region (BLR) emission to the observed continuum signal. Methods. We employed state-of-the-art emission models for quasars and high-resolution microlensing magnification maps and compared the attributes of their magnification-distribution functions to those obtained for pure Shakura-Sunyaev disk models. We tested the validity of our detailed model predictions by examining their agreement with published microlensing estimates of the half-light radius of the continuum-emitting region in a sample of lensed quasars. Results. Our findings suggest that the steep disk temperature profiles found by microlensing studies are erroneous as the data are largely affected by the BLR, which does not obey a temperature-wavelength relation. We show with a sample of 12 lenses that the mere contribution of the BLR to the continuum signal is able to account for the deduced overestimation factors as well as the implied size-wavelength relation. Conclusions. Our study points to a likely solution to the AD size conundrum in lensed quasars, which is related to the interpretation of the observed signals rather than to disk physics. Our findings significantly weaken the tension between AD theory and observations, and suggest that microlensing can provide a new means to probe the hitherto poorly constrained diffuse BLR emission around accreting black holes. [ABSTRACT FROM AUTHOR]

Under the perturbative picture of planetary microlensing, the planet is considered to act as a uniform-shear Chang–Refsdal lens on one of the two images produced by the host star that comes close to the angular Einstein radius of the planet, leaving the other image unaffected. However, this uniform-shear approximation is only valid for isolated planetary caustics and breaks down in the resonant regime. Recently, the planetary-caustic degeneracy arising from the above formalism is found to generalize to the regime of central and resonant caustics, indicating that the perturbative picture and Chang–Refsdal lens approximation may have been underexplored in the past. Here, I introduce a new variable-shear Chang–Refsdal lens approximation, which not only supports central and resonant caustics, but also enables full magnification maps to be calculated analytically. Moreover, I introduce the generalized perturbative picture, which relaxes the required proximity between the planet and the image being perturbed in the previous work. Specifically, the planet always perturbs the image in the same half of the lens plane as the planet itself, leaving the other image largely unaffected. It is demonstrated how this new framework results in the offset degeneracy as a consequence of physical symmetry. The generalized perturbative picture also points to an approach to solve the two-body lens equation semi-analytically. The analytic and semi-analytic microlensing solutions associated with this work may allow for substantially faster light-curve calculations and modelling of observed events. A Python implementation is provided. [ABSTRACT FROM AUTHOR]

We present the observations and analysis of a high-magnification microlensing planetary event, KMT-2022-BLG-0440, for which the weak and short-lived planetary signal was covered by both the KMTNet survey and follow-up observations. The binary-lens models with a central caustic provide the best fits, with a planet/host mass ratio, q  = 0.75–1.00 × 10−4 at 1σ. The binary-lens models with a resonant caustic and a brown-dwarf mass ratio are both excluded by Δχ2 > 70. The binary-source model can fit the anomaly well but is rejected by the 'colour argument' on the second source. From Bayesian analyses, it is estimated that the host star is likely a K or M dwarf located in the Galactic disc, the planet probably has a Neptune-mass, and the projected planet-host separation is |$1.9^{+0.6}_{-0.7}$| or |$4.6^{+1.4}_{-1.7}$|  au, subject to the close/wide degeneracy. This is the third q < 10−4 planet from a high-magnification planetary signal (A ≳ 65). Together with another such planet, KMT-2021-BLG-0171Lb, the ongoing follow-up program for the KMTNet high-magnification events has demonstrated its ability to detect high-magnification planetary signals for q < 10−4 planets, which are challenging for the current microlensing surveys. [ABSTRACT FROM AUTHOR]

We study the highly magnified arc SGAS J122651.3+215220 caused by a star-forming galaxy at zs = 2.93 crossing the lensing caustic cast by the galaxy cluster SDSS J1226+2152 (zl = 0.43), using Hubble Space Telescope observations. We report in the arc several asymmetric surface brightness features whose angular separations are a fraction of an arcsecond from the lensing critical curve and appear to be highly but unequally magnified image pairs of underlying compact sources, with one brightest pair having clear asymmetry consistently across four filters. One explanation of unequal magnification is microlensing by intracluster stars, which induces independent flux variations in the images of individual or groups of source stars in the lensed galaxy. For a second possibility, intracluster dark matter subhaloes invisible to telescopes effectively perturb lensing magnifications near the critical curve and give rise to persistently unequal image pairs. Our modelling suggests, at least for the most prominent identified image pair, that the microlensing hypothesis is in tension with the absence of notable asymmetry variation over a six-year baseline, while subhaloes of ∼106-$10^8\, \mathrm{ M}_\odot$ anticipated from structure formation with cold dark matter typically produce stationary and sizable asymmetries. We judge that observations at additional times and more precise lens models are necessary to stringently constrain temporal variability and robustly distinguish between the two explanations. The arc under this study is a scheduled target of a Director's Discretionary Early Release Science program of the James Webb Space Telescope, which will provide deep images and a high-resolution view with integral field spectroscopy.

Most transit microlensing events due to very low mass lens objects suffer from extreme finite-source effects. While modelling their light curves, there is a known continuous degeneracy between their relevant lensing parameters, i.e. the source angular radius normalized to the angular Einstein radius ρ⋆, the Einstein crossing time t E, the lens impact parameter u 0, the blending parameter, and the stellar apparent magnitude. In this work, I numerically study the origin of this degeneracy. I find that these light curves have five observational parameters (i.e. the baseline magnitude, the maximum deviation in the magnification factor, the full width at half-maximum |$\rm {FWHM}=2 \mathit{ t}_{\rm {HM}}$|⁠ , the deviation from a top-hat model, and the time of the maximum time derivative of microlensing light curves |$T_{\rm {max}}=t_{\rm E}\sqrt{\rho _{\star }^{2}-u_{0}^{2}}$|⁠). For extreme finite-source microlensing events due to uniform source stars, we get t HM ≃ T max and the deviation from the top-hat model tends to zero, which both cause the known continuous degeneracy. When either ρ⋆ ≲ 10 or the limb-darkening effect is considerable, t HM and T max are two independent observational parameters. I use a numerical approach, i.e. random forests containing 100–120 decision trees, to study how these observational parameters are efficient in yielding the lensing parameters. These machine learning models find the mentioned five lensing parameters for finite-source microlensing events from uniform and limb-darkened source stars with the average R 2-scores of 0.87 and 0.84, respectively. R 2-score for evaluating the lens impact parameter gets worse on adding limb darkening, and for extracting the limb-darkening coefficient itself this score falls as low as 0.67. [ABSTRACT FROM AUTHOR]

We report the discovery of a transient seen in a strongly lensed arc at redshift z s = 1.2567 in Hubble Space Telescope imaging of the Abell 370 galaxy cluster. The transient is detected at 29.51 ± 0.14 AB mag in a WFC3/UVIS F200LP difference image made using observations from two different epochs, obtained in the framework of the Flashlights programme, and is also visible in the F350LP band (m F350LP ≈ 30.53 ± 0.76 AB mag). The transient is observed on the negative-parity side of the critical curve at a distance of ∼0.6 arcsec from it, greater than previous examples of lensed stars. The large distance from the critical curve yields a significantly smaller macromagnification, but our simulations show that bright, O/B-type supergiants can reach sufficiently high magnifications to be seen at the observed position and magnitude. In addition, the observed transient image is a trailing image with an observer-frame time delay of ∼+0.8 d from its expected counterpart, so that any transient lasting for longer than that should have also been seen on the minima side and is thus excluded. This, together with the blue colour we measure for the transient (m F200LP − m F350LP ≈ [−0.3, −1.6] AB), rules out most other transient candidates such as (kilo)novae, for example, and makes a lensed star the prime candidate. Assuming that the transient is indeed a lensed star as suggested, many more such events should be detected in the near future in cluster surveys with the Hubble Space Telescope and JWST. [ABSTRACT FROM AUTHOR]

Gravitational microlensing is a powerful method for detecting and characterizing free-floating planetary-mass objects (FFPs). FFPs could have exomoons rotating them. In this work, we study the probability of realizing these systems (i.e. free-floating moon-planet ones) through microlensing observations. These systems make mostly close caustic configurations with a considerable finite-source effect. We investigate finite-source microlensing light curves owing to free-floating moon-planet systems. We conclude that crossing planetary caustics causes an extensive extra peak at light curves' wing that only changes its width if the source star does not cross the central caustic. If the source trajectory is normal to the moon-planet axis, the moon-induced perturbation has a symmetric shape with respect to the magnification peak, and its light curve is similar to a single-lens one with a higher finite-source effect. We evaluate the Roman efficiency for realizing moon-induced perturbations, which is |$\left[0.002-0.094\right]\ \mathrm{ per\, cent}$| by assuming a log-uniform distribution for moon-planet mass ratio in the range ∈ [ −9,   −2]. The highest detection efficiency (i.e. |$\simeq 0.094~{{\ \rm per\ cent}}$|⁠) happens for Saturn-mass planets when moon-planet distance is ∼43 R p, where R p is the Saturn radius. Enhancing planetary mass extends the event's time-scale and decreases the finite-source effect, but it reduces the projected moon-planet distance normalized to the Einstein radius s (R E) which in turn decreases the size of planetary caustics and takes them away from the host planet's position in close caustic configurations. [ABSTRACT FROM AUTHOR]

We present K2-2016-BLG-0005Lb, a densely sampled, planetary binary caustic-crossing microlensing event found from a blind search of data gathered from Campaign 9 of the Kepler K2 mission (K2 C9). K2-2016-BLG-0005Lb is the first bound microlensing exoplanet discovered from space-based data. The event has caustic entry and exit points that are resolved in the K2 C9 data, enabling the lens-source relative proper motion to be measured. We have fitted a binary microlens model to the Kepler data and to simultaneous observations from multiple ground-based surveys. Whilst the ground-based data only sparsely sample the binary caustic, they provide a clear detection of parallax that allows us to break completely the microlensing mass-position-velocity degeneracy and measure the planet's mass directly. We find a host mass of 0.58 ± 0.04 M⊙ and a planetary mass of 1.1 ± 0.1 MJ. The system lies at a distance of 5.2 ± 0.2 kpc from Earth towards the Galactic bulge, more than twice the distance of the previous most distant planet found by Kepler. The sky-projected separation of the planet from its host is found to be 4.2 ± 0.3 au which, for circular orbits, deprojects to a host separation |$a = 4.4^{+1.9}_{-0.4}$|  au and orbital period |$P = 13^{+9}_{-2}$|  yr. This makes K2-2016-BLG-0005Lb a close Jupiter analogue orbiting a low-mass host star. According to current planet formation models, this system is very close to the host mass threshold below which Jupiters are not expected to form. Upcoming space-based exoplanet microlensing surveys by NASA's Nancy Grace Roman Space Telescope and, possibly, ESA's Euclid mission, will provide demanding tests of current planet formation models. [ABSTRACT FROM AUTHOR]

We examine a caustic-straddling arc at z = 0.9397 in the field of the galaxy cluster MACS J0416.1-2403 (z = 0.397) using archival multiband Hubble Space Telescope images and show that its surface brightness exhibits anomalies that can be explained by a single highly magnified star undergoing microlensing. First, we show that the surface brightness pattern is not perfectly symmetric across the cluster critical curve, which is inconsistent with a locally smooth lens model; the location of the candidate star exhibits the most significant asymmetry. Second, our analysis indicates that the asymmetric feature has ∼30% higher flux in the 2012 visits compared to the Frontier Fields program visits in 2014. Moreover, the variable asymmetric feature shows an anomalous color between the F814W and F105W filters in 2014. These anomalies are naturally explained by microlensing-induced variability of a caustic-transiting blue supergiant in a star-forming region, with a mean magnification factor around μ ∼ 200. We extend this study to a statistical analysis of the whole arc image and find tentative evidence of the increased mismatch of the two images in the proximity of the critical line. Robust detection of one or multiple caustic-transiting stars in this arc will enable detailed follow-up studies that can shed light on the small-scale structure of the dark matter inside the cluster halo.

KOI-3278 is a self-lensing stellar binary consisting of a white dwarf secondary orbiting a Sun-like primary star. Kruse & Agol noticed small periodic brightenings every 88.18 days in the Kepler photometry and interpreted these as the result of microlensing by a white dwarf with about 63% of the mass of the Sun. We obtained two sets of spectra for the primary that allowed us to derive three sets of spectroscopic estimates for its effective temperature, surface gravity, and metallicity for the first time. We used these values to update the Kruse & Agol Einsteinian microlensing model, resulting in a revised mass for the white dwarf of 0.539-0.020+0.022 M o. The spectra also allowed us to determine radial velocities and derive orbital solutions, with good agreement between the two independent data sets. An independent Newtonian dynamical MCMC model of the combined velocities yielded a mass for the white dwarf of 0.5122-0.0058+0.0057 M o. The nominal uncertainty for the Newtonian mass is about four times better than for the Einsteinian, ± 1.1% versus ± 4.1%, and the difference between the two mass determinations is 5.2%. We then present a joint Einsteinian microlensing and Newtonian radial velocity model for KOI-3278, which yielded a mass for the white dwarf of 0.5250-0.0089+0.0082M o. This joint model does not rely on any white dwarf evolutionary models or assumptions on the white dwarf mass-radius relation. We discuss the benefits of a joint model of self-lensing binaries, and how future studies of these systems can provide insight into the mass-radius relation of white dwarfs.