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NASA NTRS1991

Gravitational microlensing by double stars and planetary systems

Almost all stars are in binary systems. When the separation between the two components is comparable to the Einstein ring radius corresponding to the combined mass of the binary acting as a gravitational lens, then an extra pair of images can be created, and the light curve of a lensed source becomes complicated. It is estimated that about 10 percent of all lensing episodes of the Galactic bulge stars will strongly display the binary nature of the lens. The effect is strong even if the companion is a planet. A massive search for microlensing of the Galactic bulge stars may lead to a discovery of the first extrasolar planetary systems.

Mao, Shunde↗

NASA NTRS1986

Gravitational microlensing by the galactic halo

A simple model of microlensing by massive objects that might be present in the halo of the Galaxy is presented. It is shown that in any nearby galaxy one star out of a million is strongly microlensed by a 'dark' object located in the Galactic halo, if the halo is made up of objects more massive than about 10 to the -8th solar mass. Monitoring the brightness of a few million stars in the Magellanic Clouds over a time scale between two hours and two years may lead to a discovery of 'dark halo' objects between 10 to the -6th and 10 to the -2nd solar mass, or it may put strong upper limits on the number of such objects.

Paczynski, B.↗

NASA NTRS1991

Gravitational microlensing of the Galactic bulge stars

The optical depth to microlensing on the ordinary disk stars is about 4 x 10 to the -7th for the Galactic bulge stars visible in Baade's window. This means that at any given time one out of about 2.5 x 10 to the 6th bulge stars must be brightened by at least 0.3 mag. The duration of events is proportional to the square root of mass of the lensing star, and it is in the range of 1 week to 1 month for the lensing stars of 0.1-1.0 solar mass. The average number of events with the amplitude exceeding 0.3 mag is expected to be about 4 per year per million bulge stars. If there are brown dwarfs in the Galactic disk with masses in the range 0.01-0.1 solar mass, with the total mass density equal to the total mass density of the ordinary stars, then the combined optical depth to microlensing of the bulge stars is about 8 x 10 to the -7th, the average number of events with the amplitude exceeding 0.3 mag is expected to be about 17 per year per million bulge stars, and the time scales of events are in the range of 3-20 days.

Paczynski, B.↗

NASA NTRS1991

Gravitational microlensing of high-redshift supernovae by compact objects

An analysis of the effect of microlensing by a cosmologically dominant density of compact objects is performed, using high-redshift Type Ia supernovae (SN Ia's) as probes. The compact objects are modeled as a three-dimensional distribution of point masses, and Monte Carlo simulations are done to calculate the resulting amplification probability distributions for several column densities and cosmologies. By combining these distributions with the intrinsic SN Ia luminosity function and comparing with the results for a perfectly smooth universe, estimates are made of the number of supernovae that would need to be observed to confirm or rule out this lensing scenario. It is found that about 1000 SN Ia's with redshifts of z = 1 would be needed to perform this test, which is beyond what current searches can hope to accomplish. Observations of many fewer high-redshift supernovae, used merely as standard candles, appears a promising way of distinguishing between different cosmological models.

Rauch, Kevin P.↗

NASA NTRS1991

Expected color variations of the gravitationally microlensed QSO 2237 + 0305

Typical light curves and the corresponding color curves are shown for the present model of QSO 2237 + 0305 A, the image that has been reported to vary. Probabilities are presented for color changes of certain amplitudes as functions of the observed magnitude changes for different intervals between the two observational epochs, different source sizes, and different source size ratios. It may be possible to find the ratio of the continuum source sizes in the two color bands, once a color change correlated with a continuum change is found.

Wambsganss, J.↗

NASA NTRS1994

Observational limits on Omega in stars, brown dwarfs, and stellar remnants from gravitational microlensing

Microlensing by compact objects with masses between approximately 0.001 solar masses and approximately 300 solar masses will amplify the continuum emission of a quasar, without significantly changing its line emission. Thus, compact objects with masses associated with stars, subdwarfs, and stellar remnants will reduce the apparent equivalent widths of quasar emission lines. It is possible to detect this population of lenses by searching for an increase in the number of small equivalent width quasars with redshift. This increase was looked for, but not found, in quasar samples taken from the Einstein Medium Sensitivity Survey and the Steidel & Sargent absorption-line studies. Thus, Omega(sub c), the cosmological density of compact objects relative to the critical density, is less than or approximately equal to 0.1 in the mass range 0.01 solar masses-20 solar masses (for Omega less than 0.6). For any value of Omega, Omega(sub c) less than or approximately equal to 0.2 in the larger mass range 0.001 solar masses-60 solar masses, and Omega(sub c) less than 1 for 0.001 solar masses-300 solar masses. Subdwarfs, stellar objects, or their remnants (e.g., MACHOS) cannot close the universe.

Dalcanton, Julianne J.↗

DOE OSTI2025

popclass: A Python Package for Classifying Microlensing Events

popclass is a Python package that provides a flexible, probabilistic framework for classifying the lens of a gravitational microlensing event. Gravitational microlensing occurs when a massive foreground object (e.g., a star, white dwarf or black hole) passes in front of and lenses the light from a distant background source. This causes an apparent brightening, and shift in position, of the background source. In most cases, characteristics of the microlensing signal do not contain enough information to definitively identify the lens type. Different lens types lie in different but overlapping regions of the characteristics of the microlensing signal. For example, black holes tend to be more massive than stars and therefore cause microlensing signals that are longer. Current Galactic simulations enable us to predict where different lens types lie in the observational space and can therefore be used to classify events (e.g., Lam et al., 2020). popclass allows the user to match the characteristics of a microlensing signal with a simulation of the Galaxy to calculate lens type probabilities for the event (see Figure 1). Constraints on any microlensing signal properties and any Galactic model can be used. popclass comes with an interface to ArviZ (Kumar et al., 2019) and PyMultiNest (Buchner et al., 2014) for microlensing signal constraints, as well as pre-loaded Galactic models, plotting functionality, and methods to quantify the classification uncertainty. The probabilistic framework for popclass was developed in Perkins et al. (2024), used in Fardeen et al. (2024) and has been applied to classifying events in Kaczmarek et al. (2025).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2004

Spitzer Space Telescope Observations of the aftermath of Microlensing Event MACHO-LMC-5

We have carried out photometry of the microlensing event MACHO-LMC-5 with Spitzer Infrared Array Camera (IRAC) 10 years after the magnification of the LMC source star was recorded. This event is unique in the annals of gravitational microlensing: the lensing star itself has been observed using the Hubble Space Telescope (once with WFPC2 and twice with ACS/HRC). Since the separation between the source and lens at the epoch of the Spitzer observations was ~0".24, the two stars cannot be resolved in the Spitzer images. However, the IRAC photometry clearly establishes that the lens is an M5 dwarf star from its infrared excess, which in turn yields a mass of ~0.2 Mө. This demonstrates the potential of Spitzer to detect the lenses in other gravitational microlensing events.

Stern, Daniel↗

NASA NTRSDate not supplied

Compressive Sensing Application for Transient Photometric Measurements

Compressive Sensing (CS) is a mathematical theory for simultaneous data acquisition and compression. Natural phenomena may be sparse in some physical or temporal domain. If we exploit this sparsity by applying the technique of CS to obtain information, how do our measurements change as a function of domain and measurement systematics? What are the specific implications for the science and for the sensing infrastructure? In this talk, we will discuss the generalized systematic effects consequent to the application of CS to time-series photometric measurements. We assess implications for observability, sparsification, and information loss in the detection, retrieval and reconstruction process. To study time-series photometry, we explore the field of gravitational microlensing. A source star, typically in the galactic bulge, gets microlensed when there is a precise alignment of a lensing star and its planetary system, with the source star. The microlensed source star changes in flux magnification as the lensing system crosses the precise path of alignment, resulting in a microlensing curve in time domain. A high-cadence, high-resolution system, which uses low power and bandwidth is essential to obtain valuable science measurements. Hence, we discuss application of CS to gravitational microlensing data sets, which in turn can be generalized to any time-ordered photometric measurements.

Asmita Abhay Korde↗

DOE OSTI2022

A Search for Predicted Astrometric Microlensing Events by Nearby Brown Dwarfs*

Gravitational microlensing has the potential to provide direct gravitational masses of single, free-floating brown dwarfs, independent of evolutionary and atmospheric models. The proper motions and parallaxes of nearby brown dwarfs can be used to predict close future alignments with distant background stars that cause a microlensing event. Targeted astrometric follow up of the predicted microlensing events permits the brown dwarf’s mass to be measured. Predicted microlensing events are typically found via searching for a peak threshold signal using an estimate of the lens mass. We develop a novel method that finds predicted events that instead will lead to a target lens-mass precision. The main advantage of our method is that it does not require a lens-mass estimate. We use this method to search for predicted astrometric microlensing events occurring between 2014 and 2032 using a catalog of 1225 low-mass star and brown-dwarf lenses in the Solar Neighborhood of spectral type M6 or later and a background source catalog from DECaLS Data Release 9. The background source catalog extends to g = 23.95, providing a more dense catalog compared to Gaia. Our search did not reveal any upcoming microlensing events. We estimate the rate of astrometric microlensing event for brown dwarfs in the Legacy Survey and find it to be low ~10 -5 yr -1 . We recommend carrying out targeted searches for brown dwarfs in front of the Galactic Bulge and Plane to find astrometric microlensing events that will allow the masses of single, free-floating brown dwarfs to be measured.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Discovery and Mass Measurements of a Cold, Sub-Neptune Mass Planet and Its Host Star

The gravitational microlensing exoplanet detection method is uniquely sensitive to cold, low-mass planets which orbit beyond the snow-line, where the most massive planets are thought to form. The early statistical results from microlensing indicate that Neptune-Saturn mass planets located beyond the snow-line are substantially more common than their counterparts in closer orbits that have found by the Doppler radial velocity method. We present the discovery of the planet MOA-2009-BLG-266Lb, which demonstrates that the gravitational microlensing method also has the capability to measure the masses of cold, low-mass planets. The mass measurements of the host star and the planet are made possible by the detection of the microlensing parallax signal due to the orbital motion or the Earth as well as observations from the EPOXI spacecraft in a Heliocentric orbit. The microlensing light curve indicates a planetary host star mass of M(sun) = 0.54 + / - 0.05M(sun) located at a distance of DL= 2.94 _ 0.21 kpc, orbited by a planet of mass mp= 9.8 +/-1.1M(Earth) with a semi-major axis of a = 3.1(+1.9-0.4)MAU.

Barry, Richard K., Jr.↗

NASA NTRS2016

Faint-Source-Star Planetary Microlensing: The Discovery of the Cold Gas-Giant Planet OGLE-2014-BLG-0676Lb

We report the discovery of a planet OGLE-2014-BLG-0676Lb via gravitational microlensing. Observations for the lensing event were made by the following groups: Microlensing Observations in Astrophysics; Optical Gravitational Lensing Experiment; Wise Observatory; RoboNETLas Cumbres Observatory Global Telescope; Microlensing Network for the Detection of Small Terrestrial Exoplanets; and -FUN. All analyses of the light-curve data favoura lens system comprising a planetary mass orbiting a host star. The most-favoured binary lens model has a mass ratio between the two lens masses of (4.78 +/- 0.13) 10(exp -3). Subject to some important assumptions, a Bayesian probability density analysis suggests the lens system comprises a 3.09(+1.02/-1.12) MJ planet orbiting a 0.62(+0.20/-0.22) solar mass host star at a deprojected orbital separation of 4.40(+2.16/-1.46) au. The distance to the lens system is 2.22(+0.96/-0.83) kpc. Planet OGLE-2014-BLG-0676Lb provides additional data to the growing number of cool planets discover redusing gravitational microlensing against which planetary formation theories may be tested. Most of the light in the baseline of this event is expected to come from the lens and thus high-resolution imaging observations could confirm our planetary model interpretation.

OGLE-2014-BLG-0676Lb↗

DOE OSTI2025

On Finding Black Holes in Photometric Microlensing Surveys

There are expected to be millions of isolated black holes in the galaxy resulting from the deaths of massive stars. Measuring the abundance and properties of this remnant population would shed light on the end stages of stellar evolution and the evolution paths of black hole systems. Detecting isolated black holes is currently only possible via gravitational microlensing, which has so far yielded one definitive detection. The difficulty in finding microlensing black holes lies in having to choose a small subset of events, based on characteristics of their light curves, to allocate expensive and scarce follow-up resources to confirm the identity of the lens. Current methods either rely on simple cuts in parameter space without using the full distribution information or are only effective on small subsets of events. In this paper, we present a new lens classification method. The classifier takes in posterior constraints on light-curve parameters and combines them with a Galactic simulation to estimate the lens class probability. This method is flexible and can be used with any set of microlensing light-curve parameters, making it applicable to large samples of events. We make this classification framework available via the popclass Python package. We apply the classifier to ~10,000 microlensing events from the Optical Gravitational Lensing Experiment survey and find 23 high-probability black hole candidates. Our classifier also suggests that the only known isolated black hole is an observational outlier, according to current Galactic models, and the allocation of astrometric follow-up on this event was a high-risk strategy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Disentangling the Black Hole Mass Spectrum with Photometric Microlensing Surveys

Abstract From the formation mechanisms of stars and compact objects to nuclear physics, modern astronomy frequently leverages surveys to understand populations of objects to answer fundamental questions. The population of dark and isolated compact objects in the Galaxy contains critical information related to many of these topics, but is only practically accessible via gravitational microlensing. However, photometric microlensing observables are degenerate for different types of lenses, and one can seldom classify an event as involving either a compact object or stellar lens on its own. To address this difficulty, we apply a Bayesian framework that treats lens type probabilistically and jointly with a lens population model. This method allows lens population characteristics to be inferred despite intrinsic uncertainty in the lens class of any single event. We investigate this method’s effectiveness on a simulated ground-based photometric survey in the context of characterizing a hypothetical population of primordial black holes (PBHs) with an average mass of 30 M ⊙ . On simulated data, our method outperforms current black hole (BH) lens identification pipelines and characterizes different subpopulations of lenses while jointly constraining the PBH contribution to dark matter to ≈25%. Key to robust inference, our method can marginalize over population model uncertainty. We find the lower mass cutoff for stellar origin BHs, a key observable in understanding the BH mass gap, particularly difficult to infer in our simulations. This work lays the foundation for cutting-edge PBH abundance constraints to be extracted from current photometric microlensing surveys.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1994

Magnification bias in galactic microlensing searches

It is shown that a significant amount of detectable gravitational microlensing events that could potentially be found by Massively Parallel Photometry (MAPP) project (such as the MACHO, EROS, and OGLE collaborations) will occur for stars too dim to be easily noticed individually by these projects. This is the result of a large magnification bias effect, a bias of including high-magnification events in any flux-limited sample. The probablility of detecting these events may be as high as 2.3 times the lensing probability of stars currently being monitored by MAPP collaborations.

Nemiroff, Robert J.↗

DOE OSTI2024

Primordial Black Hole Dark Matter Simulations Using PopSyCLE

Abstract Primordial black holes (PBHs), theorized to have originated in the early Universe, are speculated to be a viable form of dark matter. If they exist, they should be detectable through photometric and astrometric signals resulting from gravitational microlensing of stars in the Milky Way. Population Synthesis for Compact-object Lensing Events, or PopSyCLE , is a simulation code that enables users to simulate microlensing surveys, and is the first of its kind to include both photometric and astrometric microlensing effects, which are important for potential PBH detection and characterization. To estimate the number of observable PBH microlensing events, we modify PopSyCLE to include a dark matter halo consisting of PBHs. We detail our PBH population model, and demonstrate our PopSyCLE + PBH results through simulations of the Optical Gravitational Lensing Experiment-IV (OGLE-IV) and Nancy Grace Roman Space Telescope (Roman) microlensing surveys. We provide a proof-of-concept analysis for adding PBHs into PopSyCLE , and thus include many simplifying assumptions, such as f DM , the fraction of dark matter composed of PBHs, and m ¯ PBH , mean PBH mass. Assuming m ¯ PBH = 30 M ⊙ , we find ∼3.6 f DM times as many PBH microlensing events than stellar evolved black hole events, a PBH average peak Einstein crossing time of ∼91.5 days, estimate on order of 10 2 f DM PBH events within the 8 yr OGLE-IV results, and estimate Roman to detect ∼1000 f DM PBH microlensing events throughout its planned microlensing survey.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2022

An Isolated Mass-gap Black Hole or Neutron Star Detected with Astrometric Microlensing

We present the analysis of five black hole candidates identified from gravitational microlensing surveys. Hubble Space Telescope astrometric data and densely sampled light curves from ground-based microlensing surveys are fit with a single-source, single-lens microlensing model in order to measure the mass and luminosity of each lens and determine if it is a black hole. One of the five targets (OGLE-2011-BLG-0462/MOA-2011-BLG-191 or OB110462 for short) shows a significant >1 mas coherent astrometric shift, little to no lens flux, and has an inferred lens mass of 1.6–4.4 M ⨀ . This makes OB110462 the first definitive discovery of a compact object through astrometric microlensing and it is most likely either a neutron star or a low-mass black hole. This compact-object lens is relatively nearby (0.70–1.92 kpc) and has a slow transverse motion of <30 kms -1 . OB110462 shows significant tension between models well fit to photometry versus astrometry, making it currently difficult to distinguish between a neutron star and a black hole. Additional observations and modeling with more complex system geometries, such as binary sources, are needed to resolve the puzzling nature of this object. For the remaining four candidates, the lens masses are <2M ⨀ , and they are unlikely to be black holes; two of the four are likely white dwarfs or neutron stars. We compare the full sample of five candidates to theoretical expectations on the number of black holes in the Milky Way (∼10 8 ) and find reasonable agreement given the small sample size.

Astrophysical black holes↗

DOE OSTI2021

KMT-2019-BLG-1715: Planetary Microlensing Event with Three Lens Masses and Two Source Stars

We investigate the gravitational microlensing event KMT-2019-BLG-1715, the light curve of which shows two short-term anomalies from a caustic-crossing binary-lensing light curve: one with a large deviation and the other with a small deviation. We identify five pairs of solutions, in which the anomalies are explained by adding an extra lens or source component in addition to the base binary-lens model. We resolve the degeneracies by applying a method in which the measured flux ratio between the first and second source stars is compared with the flux ratio deduced from the ratio of the source radii. Applying this method leaves a single pair of viable solutions, in both of which the major anomaly is generated by a planetary-mass third body of the lens, and the minor anomaly is generated by a faint second source. A Bayesian analysis indicates that the lens comprises three masses: a planet-mass object with ∼2.6 M {sub J} and binary stars of K and M dwarfs lying in the galactic disk. We point out the possibility that the lens is the blend, and this can be verified by conducting high-resolution follow-up imaging for the resolution of the lens from the source.

79 ASTRONOMY AND ASTROPHYSICS↗