Gravitational Microlensing Events Research Articles

Limits on Planetary-mass Primordial Black Holes from the OGLE High-cadence Survey of the Magellanic Clouds

Observations of the Galactic bulge revealed an excess of short-timescale gravitational microlensing events that are generally attributed to a large population of free-floating or wide-orbit exoplanets. However, in recent years, some authors suggested that planetary-mass primordial black holes (PBHs) comprising a substantial fraction (1%–10%) of the dark matter in the milky Way may be responsible for these events. If that was the case, a large number of short-timescale microlensing events should also be seen toward the Magellanic Clouds. Here, we report the results of a high-cadence survey of the Magellanic Clouds carried out from 2022 October through 2024 May as part of the Optical Gravitational Lensing Experiment. We observed almost 35 million source stars located in the central regions of the Large and Small Magellanic Clouds and found only one long-timescale microlensing event candidate. No short-timescale events were detected despite high sensitivity to such events. That allows us to infer the strongest available limits on the frequency of planetary-mass PBHs in dark matter. We find that PBHs and other compact objects with masses from 1.4 × 10−8 M ⊙ (half of the Moon mass) to 0.013 M ⊙ (planet/brown dwarf boundary) may comprise at most 1% of dark matter. That rules out the PBH origin hypothesis for the short-timescale events detected toward the Galactic bulge and indicates they are caused by the population of free-floating or wide-orbit planets.

Casting Light on Degeneracies: A Comprehensive Study of Lightcurve Variations in Microlensing Events OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192

This study investigates orbital parallax in gravitational microlensing events, focusing on OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192. For events with timescales ≤60 days, a Jerk-Parallax degeneracy arises due to high Jerk velocity ( vj˜ ), causing a fourfold continuous parallax degeneracy. OGLE-2017-BLG-0103, after incorporating orbital parallax, reveals four discrete degenerate parallax solutions, while OGLE-2017-BLG-0192 exhibits four discrete solutions without degeneracy. The asymmetric lightcurve of OGLE-2017-BLG-0103 suggests a more probable model where Xallarap is added to the parallax model, introducing tension. The galactic model analysis predicts a very low-mass stellar lens for OGLE-2017-BLG-0192. For OGLE-2017-BLG-0103, degenerate solutions suggest a low-mass star or a darker lens in the disk, while the Xallarap+Parallax model also predicts a stellar lens in the bulge, with the source being a solar-type star orbited by a dwarf star. This study presents five degenerate solutions for OGLE-2017-BLG-0103, emphasizing the potential for confirmation through high-resolution Adaptive Optics observations with Extremely Large Telescopes in the future. The complexities of degenerate scenarios in these microlensing events underscore the need to analyze special single-lens events in the Roman Telescope Era.

No massive black holes in the Milky Way halo.

The gravitational wave detectors have shown a population of massive black holes that do not resemble those observed in the Milky Way1-3 and whose origin is debated4-6. According to a possible explanation, these black holes may have formed from density fluctuations in the early Universe (primordial black holes)7-9, and they should comprise several to 100% of dark matter to explain the observed black hole merger rates10-12. If these black holes existed in the Milky Way dark matter halo, they would cause long-timescale gravitational microlensing events lasting years13. The previous experiments were not sufficiently sensitive to such events14-17. Here we present the results of the search for long-timescale microlensing events among the light curves of nearly 80 million stars located in the Large Magellanic Cloud that were monitored for 20 years by the Optical Gravitational Lensing Experiment survey18. We did not find any events with timescales longer than 1 year, whereas all shorter events detected may be explained by known stellar populations. We find that compact objects in the mass range from 1.8 × 10-4M⊙ to 6.3M⊙ cannot make up more than 1% of dark matter, and those in the mass range from 1.3 × 10-5M⊙ to 860 M⊙ cannot make up more than 10% of dark matter. Thus, primordial black holes in this mass range cannot simultaneously explain a substantial fraction of dark matter and gravitational wave events.

New mechanism for primordial black hole formation from the QCD axion

We present a new mechanism for the primordial black hole (PBH) production within the QCD axion framework. We take the case where the Peccei-Quinn symmetry breaks during inflation, resulting in a NDW=1 string-wall network that reenters the horizon sufficiently late. Therefore, closed axion domain walls naturally arising in the network are sufficiently large to collapse into PBHs. Our numerical simulation shows that ∼0.3% of the total wall area is in the form of closed walls. In addition, the relic abundance of dark matter is dominantly accounted for by free axions from the collapse of open walls bounded by strings. In this framework, the abundance of PBH within dark matter is calculated to be ∼0.9%. This fraction remains unaffected by axion parameters or the reentering horizon temperature, as it is determined by the fixed proportion of closed walls in the network, governed by the principles of percolation theory. The resultant PBHs uniformly share the same mass, which spans from about 10−9 to 1 solar mass, corresponding to the classical QCD axion mass window 10−5–10−2 eV and the reentering horizon temperature 300−1 MeV. Intriguingly, PBHs in this mechanism can naturally account for the ultrashort-timescale gravitational microlensing events observed by the OGLE collaboration. Published by the American Physical Society 2024

Blending from binarity in microlensing searches toward the Large Magellanic Cloud

Context. Studies of gravitational microlensing effects require the estimation of their detection efficiency as soon as one wants to quantify the massive compact objects along the line of sight of source targets. This is particularly important for setting limits on the contribution of massive compact objects to the Galactic halo. These estimates of detection efficiency must not only account for the blending effects of accidentally superimposed sources in crowded fields, but also for possible mixing of light from stars belonging to multiple gravitationally bound stellar systems. Aims. Until now, only blending due to accidental alignment of stars had been studied, in particular as a result of high-resolution space images. In this paper, we address the impact of unresolved binary sources that are physically gravitationally bound and not accidentally aligned, in the case of microlensing detection efficiencies toward the Large Magellanic Cloud (LMC). Methods. We used the Gaia catalog of nearby stars to constrain the local binarity rate, which we extrapolated to the distance of the LMC. Then we estimated an upper limit to the impact of this binarity on the detection efficiency of microlensing effects, as a function of lens mass. Results. We find that a maximum of 6.2% of microlensing events on LMC sources due to halo lenses heavier than 30 M⊙ could be affected as a result of the sources belonging to unresolved binary systems. This number is the maximum fraction of events for which the source is a binary system separated by about one angular Einstein radius or more in a configuration where light-curve distortion could affect the efficiency of some detection algorithms. For events caused by lighter lenses on LMC sources, our study shows that the chances of blending effects by binary systems is likely to be higher and should be studied in more detail to improve the accuracy of efficiency calculations.

Exploring Exoplanets at the Nanoscale: A Novel Approach Through Transmission Electron Microscopy

This paper explains the theoretical basis and potential efficacy of utilizing TEM for exoplanet discovery. TEM, in order to capture high-resolution images of the internal structure of thin samples, necessitates the passage of an electron beam through them. The innovative concept behind this application exploits the gravitational micro-lensing phenomenon, triggered when a sizable exoplanet transits in front of a distant star, resulting in a discernible gravitational distortion that becomes visible through high-resolution imaging. The effectiveness of this method is intertwined with the unique challenges posed by exoplanet detection. Conventional approaches grapple with limitations related to factors such as planetary size, distance from the host star, and background noise. TEM's exceptional high resolution offers a means to overcome some of these obstacles, enabling direct imaging of exoplanets and their atmospheric characteristics. Nevertheless, numerous challenges persist, including the necessity for an extensive network of synchronized TEM equipment and intricate data analysis techniques to differentiate gravitational micro-lensing events from other forms of distortion, as well as accurately ascertain their size. To gain a comprehensive grasp of TEM's potential and limitations in reshaping our comprehension of exoplanetary systems, further research, collaborative initiatives, and technological advancements are imperative.

A Binary Origin for the First Isolated Stellar-mass Black Hole Detected with Astrometric Microlensing

The Milky Way is believed to host hundreds of millions of quiescent stellar-mass black holes (BHs). In the last decade, some of these objects have been potentially uncovered via gravitational microlensing events. All these detections resulted in a degeneracy between the velocity and the mass of the lens. This degeneracy has been lifted, for the first time, with the recent astrometric microlensing detection of OB110462. However, two independent studies reported very different lens masses for this event. Sahu et al. inferred a lens mass of 7.1 ± 1.3 M ⊙, consistent with a BH, while Lam et al. inferred 1.6–4.2 M ⊙, consistent with either a neutron star or a BH. Here, we study the landscape of isolated BHs formed in the field. In particular, we focus on the mass and center-of-mass speed of four subpopulations: isolated BHs from single-star origin, disrupted BHs of binary-star origin, main-sequence stars with a compact object companion, and double compact object mergers. Our model predicts that most (≳70%) isolated BHs in the Milky Way are of binary origin. However, noninteractions lead to most massive BHs (≳15–20 M ⊙) being predominantly of single origin. Under the assumption that OB110462 is a free-floating compact object, we conclude that it is more likely to be a BH originally belonging to a binary system. Our results suggest that low-mass BH microlensing events can be useful to understand binary evolution of massive stars in the Milky Way, while high-mass BH lenses can be useful to probe single stellar evolution.

Application of Compressive Sensing in the Presence of Noise for Transient Photometric Events

Compressive sensing is a simultaneous data acquisition and compression technique, which can significantly reduce data bandwidth, data storage volume, and power. We apply this technique for transient photometric events. In this work, we analyze the effect of noise on the detection of these events using compressive sensing (CS). We show numerical results on the impact of source and measurement noise on the reconstruction of transient photometric curves, generated due to gravitational microlensing events. In our work, we define source noise as background noise, or any inherent noise present in the sampling region of interest. For our models, measurement noise is defined as the noise present during data acquisition. These results can be generalized for any transient photometric CS measurements with source noise and CS data acquisition measurement noise. Our results show that the CS measurement matrix properties have an effect on CS reconstruction in the presence of source noise and measurement noise. We provide potential solutions for improving the performance by tuning some of the properties of the measurement matrices. For source noise applications, we show that choosing a measurement matrix with low mutual coherence can lower the amount of error caused due to CS reconstruction. Similarly, for measurement noise addition, we show that by choosing a lower expected value of the binomial measurement matrix, we can lower the amount of error due to CS reconstruction.

Microlensing model inference with normalising flows and reversible jump MCMC

The estimation of parameters for gravitational microlensing events typically proceeds by fitting proposed lens models to observed data. A problem arises in this approach when alternate parameter values or models produce similar representations, since some comparison must be made between them. This is a challenging problem which has been frequently tackled via Bayesian model selection. Previously this was impractical since the gravitational microlensing joint model posterior is multi-modal and the computational expense required to sample an accurate discretisation prohibitive. Recently Zhang et al. (2021) showed how a neural network can be used to quickly approximate the model dependent posterior distribution of gravitational microlensing data. We show how in combination with Bayesian statistics this can be used to estimate marginal model probabilities from gravitational microlensing data. By using a similar neural network construction to generate approximate posteriors for each candidate lens model, we detail a reversible jump Metropolis–Hastings sampling algorithm which refines these posteriors to the joint-model posterior within a computationally feasible time frame. This is applied to simulated ROMAN events. We intend for this paper to serve as a proof-of-concept for the further development of Bayesian statistics in application to gravitational microlensing model inference.

Compressive Sensing Based Space Flight Instrument Constellation for Measuring Gravitational Microlensing Parallax

In this work, we provide a compressive sensing architecture for implementing on a space based observatory for detecting transient photometric parallax caused by gravitational microlensing events. Compressive sensing (CS) is a simultaneous data acquisition and compression technique, which can greatly reduce on-board resources required for space flight data storage and ground transmission. We simulate microlensing parallax observations using a space observatory constellation, based on CS detectors. Our results show that average CS error is less than 0.5% using 25% Nyquist rate samples. The error at peak magnification time is significantly lower than the error for distinguishing any two microlensing parallax curves at their peak magnification. Thus, CS is an enabling technology for detecting microlensing parallax, without causing any loss in detection accuracy.

KMT-2021-BLG-0171Lb and KMT-2021-BLG-1689Lb: two microlensing planets in the KMTNet high-cadence fields with followup observations

ABSTRACT Follow-up observations of high-magnification gravitational microlensing events can fully exploit their intrinsic sensitivity to detect extrasolar planets, especially those with small mass ratios. To make followup observations more uniform and efficient, we develop a system, HighMagFinder, to automatically alert possible ongoing high-magnification events based on the real-time data from the Korea Microlensing Telescope Network (KMTNet). We started a new phase of follow-up observations with the help of HighMagFinder in 2021. Here we report the discovery of two planets in high-magnification microlensing events, KMT-2021-BLG-0171 and KMT-2021-BLG-1689, which were identified by the HighMagFinder. We find that both events suffer the ‘central-resonant’ caustic degeneracy. The planet-host mass-ratio is q ∼ 4.7 × 10−5 or q ∼ 2.2 × 10−5 for KMT-2021-BLG-0171, and q ∼ 2.5 × 10−4 or q ∼ 1.8 × 10−4 for KMT-2021-BLG-1689. Together with two other events, four cases that suffer such degeneracy have been discovered in the 2021 season alone, indicating that the degenerate solutions may have been missed in some previous studies. We also propose a quantitative factor to weight the probability of each solution from the phase space. The resonant interpretations for the two events are disfavoured under this consideration. This factor can be included in future statistical studies to weight degenerate solutions.

X-Ray Observations of the Isolated Black Hole Candidate OGLE-2011-BLG-0462 and Other Collapsed Objects Discovered through Gravitational Microlensing

Isolated black holes and neutron stars can be revealed through the observation of long-duration gravitational microlensing events. A few candidates have been found in surveys of stars in the direction of the Galactic bulge. Recently, thanks to the addition of astrometric information at milliarcsecond level, it has been possible to reduce the uncertainties in the masses and distances for some of these “dark” gravitational lenses and select the most promising candidates. These isolated compact objects might emit X-rays powered by accretion from the interstellar medium. Using data of the Chandra, XMM-Newton, and INTEGRAL satellites, we searched for X-ray emission in the isolated black hole candidate OGLE-2011-BLG-0462, and in several other putative collapsed objects found with gravitational microlensing. OGLE-2011-BLG-0462 has been recently interpreted as a 7.1 M ⊙ black hole at a distance of 1.6 kpc, although a different group obtained a mass range (1.6–4.4 M ⊙) that cannot exclude a massive neutron star. We have derived upper limits on the flux from OGLE-2011-BLG-0462 of 9 × 10−15 erg cm−2 s−1 in the 0.5–7 keV range and ∼2 × 10−12 erg cm−2 s−1 in the 17–60 keV range. The implied X-ray luminosity is consistent with the small radiative efficiency expected for a black hole and disfavors a neutron star interpretation. Limits down to a factor of about five lower are obtained for the soft X-ray flux of other candidates, but their interpretation is affected by larger uncertainties in the masses, distances, and spatial velocities.

A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV

Modern surveys of gravitational microlensing events have progressed to detecting thousands per year, and surveys are capable of probing Galactic structure, stellar evolution, lens populations, black hole physics, and the nature of dark matter. One of the key avenues for doing this is the microlensing Einstein radius crossing time (t E) distribution. However, systematics in individual light curves as well as oversimplistic modeling can lead to biased results. To address this, we developed a model to simultaneously handle the microlensing parallax due to Earth's motion, systematic instrumental effects, and unlensed stellar variability with a Gaussian process model. We used light curves for nearly 10,000 OGLE-III and -IV Milky Way bulge microlensing events and fit each with our model. We also developed a forward model approach to infer the t E distribution by forward modeling from the data rather than using point estimates from individual events. We find that modeling the variability in the baseline removes a source of significant bias in individual events, and the previous analyses overestimated the number of t E > 100 day events due to their oversimplistic model ignoring parallax effects. We use our fits to identify the hundreds filling a regime in the microlensing parameter space that are 50% pure of black holes. Finally, we have released the largest-ever catalog of Markov Chain Monte Carlo parameter estimates for microlensing events.

Microlensing Events in the Galactic Plane Using the Zwicky Transient Facility

Abstract Microlensing is a powerful technique to study the Galactic population of “dark” objects such as exoplanets both bound and unbound, brown dwarfs, low-luminosity stars, old white dwarfs, and neutron stars, and it is almost the only way to study isolated stellar-mass black holes. The majority of previous efforts to search for gravitational microlensing events have concentrated toward high-density fields such as the Galactic bulge. Microlensing events in the Galactic plane have the advantage of closer proximity and better constrained relative proper motions, leading to better constrained estimates of lens mass at the expense of a lower optical depth, than events toward the Galactic bulge. We use the Zwicky Transient Facility Data Release 5 compiled from 2018–2021 to survey the Galactic plane in the region of ∣b∣ < 20°. We find a total of 60 candidate microlensing events including three that show a strong microlensing parallax effect. The rate of events traces Galactic structure, decreasing exponentially as a function Galactic longitude with scale length ℓ 0 ∼ 37°. On average, we find Einstein timescales of our microlensing events to be about three times as long (∼60 days) as those toward the Galactic bulge (∼20 days). This pilot project demonstrates that microlensing toward the Galactic plane shows strong promise for characterization of dark objects within the Galactic disk.

Application of compressive sensing for gravitational microlensing events

Compressive sensing (CS) is a unique mathematical technique for simultaneous data acquisition and compression. This technique is particularly apt for time-series photometric measurements; we apply CS to time-series photometric measurements specifically obtained due to gravitational microlensing events. We show the error sensitivity in detecting microlensing event parameters through simulation modeling. Particularly, we show the relation of both the amount of error and its impact on the microlensing parameters of interest. We derive statistical error bounds to apply those as a baseline for analyzing the effectiveness of CS application. Our results of single and binary microlensing events conclude that we can obtain error less than 1% over a three-pixel radius of the center of the microlensing star by using 25% Nyquist rate measurements.

Microlensing constraints on axion stars including finite lens and source size effects

A fraction of light scalar dark matter, especially axions, may organize into Bose-Einstein condensates, gravitationally bound clumps, "boson stars", and be present in large number in galactic halos today. We compute the expected number of gravitational microlensing events of clumps composed of the ordinary QCD axion and axion-like-particles and derive microlensing constraints from the EROS-2 survey and the Subaru Hyper Suprime-Cam observation. We perform a detailed lensing calculation, including the finite lens and source size effects in our analysis. We constrain the axion mass in terms of the fraction of dark matter collapsed into clumps, the individual clump densities, and the axion self-coupling. We also consider and constrain clumps composed of a generic scalar dark matter candidate with repulsive self-interactions. Our analysis opens up a new window for the potential discovery of dark matter.

Modelling the projected separation of microlensing events using systematic time-series feature engineering

Gravitational microlensing events have led to the discovery of more than 80 planets. In anticipation of the launch of the NASA Nancy Grace Roman Space Telescope, observations of gravitational microlensing events are expected to become much more numerous, and current manual techniques for their analysis will become insufficient. As a first step towards the automated estimated of microlensing event parameters, we present a workflow for identifying characteristics of light curves to estimate the projected separation from microlensing observations. We based this method on systematic time-series feature analysis of simulated light curves and validated it for a parameter space reduced to the planet–star separation. We determined a set of seven time-series features for making accurate predictions of the separation parameter. This reduced feature space of light curves serves as reliable input to both parametric and nonparametric regression models. Specifically, we validated a Random Forest regressor with respect to noise and data outages, which are common to current microlensing data, and found that the model is very robust. For this purpose, we created an empirical noise model from known microlensing events and introduced a model for simulating missing data due to data outages. Furthermore, we present an implementation of Bayesian Linear Regression on polynomial combinations of these seven light curve features, which computes probability distributions for recovered planet–star separations. The Random Forest and Bayesian Linear Regression regressors have an out-of-sample mean absolute error of 0.00057 R E and 0.00110 R E , respectively. The presented feature extraction workflow is expected to open new opportunities for mapping observed light curves to the large parameter space of microlensing events, which will be very useful for analysing the data from the Roman telescope mission.

Alternative way to detect and measure parameters of compact dark matter object as a component of a binary system

Various compact dark matter objects (CDOs) were discussed in the literature. Typically parameters of CDOs, such as the mass and the distance, were evaluated by using the gravitational microlensing effect. However, this method has limitations. We propose an alternative method for detecting and measuring parameters of CDOs. It is based on the scenario where there is a star having one planet, such that the orbital plane of the planet does not contain the star. This indicates the presence of a gravitating object located far away at the axis directed from the star to the planetary orbital plane. If in this direction there is no visible star, this could mean that the distant gravitating object is a CDO. We derived analytical expressions for determining the unknown mass of the CDO and its unknown distance from the star based on the parameters of the planetary orbit. We believe that this method could help obtaining additional observational data on the CDOs in particular and therefore on dark matter in general.

Microlensing Optical Depth and Event Rate in the OGLE-IV Galactic Plane Fields

Abstract Searches for gravitational microlensing events are traditionally concentrated on the central regions of the Galactic bulge but many microlensing events are expected to occur in the Galactic plane, far from the Galactic Center. Owing to the difficulty in conducting high-cadence observations of the Galactic plane over its vast area, which are necessary for the detection of microlensing events, their global properties were hitherto unknown. Here, we present results of the first comprehensive search for microlensing events in the Galactic plane. We searched an area of almost 3000 square degrees along the Galactic plane ( , 0° < l < 50°, 190° < l < 360°) observed by the Optical Gravitational Lensing Experiment (OGLE) during 2013–2019 and detected 630 events. We demonstrate that the mean Einstein timescales of Galactic plane microlensing events are on average three times longer than those of Galactic bulge events, with little dependence on the Galactic longitude. We also measure the microlensing optical depth and event rate as a function of Galactic longitude and demonstrate that they exponentially decrease with the angular distance from the Galactic Center (with the characteristic angular scale length of 32°). The average optical depth decreases from 0.5 × 10−6 at l = 10° to 1.5 × 10−8 in the Galactic anticenter. We also find that the optical depth in the longitude range 240° < l < 330° is asymmetric about the Galactic equator, which we interpret as a signature of the Galactic warp.

Constraining Black Hole Populations in Globular Clusters Using Microlensing: Application to Omega Centauri

Abstract We estimate the rate of gravitational microlensing events of cluster stars due to black holes (BHs) in the globular cluster NGC 5139 (ωCen). Theory and observations both indicate that ωCen may contain thousands of BHs, but their mass spectrum and exact distribution are not well constrained. In this Letter we show that one may observe microlensing events on a timescale of years in ωCen, and such an event sample can be used to infer the BH distribution. Direct detection of BHs will, in the near future, play a major role in distinguishing binary BH merger channels. Here we explore how gravitational microlensing can be used to put constraints on BH populations in globular clusters.