Gravitational microlensing can detect isolated stellar-mass black holes (BHs), which are believed to be the dominant form of Galactic BHs according to population synthesis models. Previous searches for BH events in microlensing data focused on long-timescale events with significant microlensing parallax detections. Here we show that, although BH events preferentially have long timescales, the microlensing parallax amplitudes are so small that in most cases the parallax signals cannot be detected statistically significantly. We then identify OGLE-2006-BLG-044 to be a candidate BH event because of its long timescale and small microlensing parallax. Our findings have implications to future BH searches in microlensing data.
Motivated by the ongoing Spitzer observational campaign, and the forecoming K2 one, we revisit, working in an heliocentric reference frame, the geometrical foundation for the analysis of the microlensing parallax, as measured with the simultaneous observation of the same microlensing event from two observers with relative distance of order AU. For the case of observers at rest we discuss the well known fourfold microlensing parallax degeneracy and determine an equation for the degenerate directions of the lens trajectory. For the case of observers in motion, we write down an extension of the G…
The impact of the free-floating planet (FFP) mass function on the event rate for the accurate microlensing parallax determination: application to Euclid and Roman parallax observation
In gravitational microlensing, binary systems may act as lenses or sources. Identifying lens binarity is generally easy especially in events characterized by caustic crossing since the resulting light curve exhibits strong deviations from smooth single-lensing light curve. On the contrary, light curves with minor deviations from a Paczyński behaviour do not allow one to identify the source binarity. A consequence of the gravitational microlensing is the shift of the position of the multiple image centroid with respect to the source star location - the so called astrometric microlensing signal.…
The microlens parallax is a crucial observable for conclusively identifying the nature of lens systems in microlensing events containing or composed of faint (even dark) astronomical objects such as planets, neutron stars, brown dwarfs, and black holes. With the commencement of a new era of microlensing in collaboration with space-based observations, the microlens parallax can be routinely measured. In addition, space-based observations can provide opportunities to verify the microlens parallax measured from ground-only observations and to find a unique solution of the lensing lightcurve analy…
Uncertainty in the initial-final mass relation (IFMR) has long been a problem in understanding the final stages of massive star evolution. One of the major challenges of constraining the IFMR is the difficulty of measuring the mass of non-luminous remnant objects (i.e. neutron stars and black holes). Gravitational wave detectors have opened the possibility of finding large numbers of compact objects in other galaxies, but all in merging binary systems. Gravitational lensing experiments using astrometry and photometry are capable of finding compact objects, both isolated and in binaries, in the…
I show that when the observables $(\vec π_{\rm E},t_{\rm E},θ_{\rm E},π_s,\vec μ_s)$ are well measured up to a discrete degeneracy in the microlensing parallax vector $\vec π_{\rm E}$, the relative likelihood of the different solutions can be written in closed form $P_i = K H_i B_i$, where $H_i$ is the number of stars (potential lenses) having the mass and kinematics of the inferred parameters of solution $i$ and $B_i$ is an additional factor that is formally derived from the Jacobian of the transformation from Galactic to microlensing parameters. The Jacobian term $B_i$ constitutes an explici…
The event rate and the efficiency of mass estimation for free-floating planet (FFP) microlensing events were determined from the simulation of the simultaneous parallax observations by Euclid, WFIRST, and LSST. The stellar population from the Besançon Galactic model toward $(l, b)=(1^{\circ},-1.^{\circ}75)$ was applied to our 3D microlensing model, and 30,000 parallax observations were simulated for each following FFP lens masses: Jupiter-mass, Neptune-mass, and Earth-mass assuming the population of one FFP per star. The interstellar dust, unresolved stellar background, nearby star blending we…
We present the analysis of the binary gravitational microlensing event MOA-2015-BLG-020. The event has a fairly long timescale (about 63 days) and thus the light curve deviates significantly from the lensing model that is based on the rectilinear lens-source relative motion. This enables us to measure the microlensing parallax through the annual parallax effect. The microlensing parallax parameters constrained by the ground-based data are confirmed by the Spitzer observations through the satellite parallax method. By additionally measuring the angular Einstein radius from the analysis of the r…
We introduce MulensModel, a software package for gravitational microlensing modeling. The package provides a framework for calculating microlensing model magnification curves and goodness-of-fit statistics for microlensing events with single and binary lenses as well as a variety of higher-order effects: extended sources with limb-darkening, annual microlensing parallax, satellite microlensing parallax, and binary lens orbital motion. The software could also be used for analysis of the planned microlensing survey by the NASA flag-ship WFIRST satellite. MulensModel is available at https://githu…
Most stellar remnants so far have been found in binary systems, where they interact with matter from their companions. Isolated neutron stars and black holes are difficult to find as they are dark, yet they are predicted to exist in our Galaxy in vast numbers. We explored the OGLE-III database of 150 million objects observed in years 2001-2009 and found 59 microlensing events exhibiting a parallax effect due to the Earth's motion around the Sun. Combining parallax and brightness measurements from microlensing light curves with expected proper motions in the Milky Way, we identified 13 microlen…
In this work, we use $13$ microlensing candidates with dark lenses from OGLE III catalogue \cite{2016MNRAS.458.3012W} and cross-match them with the GAIA catalogue. We identify the microlensing source stars in the GAIA catalogue by comparing the coordinate and the magnitude of stars and using the proper motion and the parallax parameters of the source stars. Combining with the microlensing light curves as well as the microlensing parallax effect, we determine the mass and the distance of lenses from Earth. We conclude that the lens for this set of microlensing events for the massive lenses are …
Gravitational microlensing may detect dark stellar remnants - black holes or neutron stars - even if they are isolated. However, it is challenging to estimate masses of isolated dark stellar remnants using solely photometric data for microlensing events. A recent analysis of OGLE-III long-timescale microlensing events exhibiting the annual parallax effects claimed that a number of bright events were due to "mass-gap" objects (with masses intermediate between those of neutron stars and black holes). Here, we present a detailed description of the updated and corrected method that can be used to …
I present a novel method for measuring lens masses for microlensing events. By combining a measured lens flux with the microlens parallax vector pi_E, it is possible to derive the mass of the lens system without knowing the angular size of the Einstein ring, theta_E. This enables mass and distance measurements for single, luminous lenses, as well as binary and planetary lenses without caustic crossings. I discuss applications of this method in the contexts of the Spitzer, Kepler, and WFIRST microlensing missions.
Augmenting the \emph{WFIRST} microlensing campaigns with intensive observations from a ground-based network of wide-field survey telescopes would have several major advantages. First, it would enable full two-dimensional (2-D) vector microlens parallax measurements for a substantial fraction of low-mass lenses as well as planetary and binary events that show caustic crossing features. For a significant fraction of the free-floating planet (FFP) events and all caustic-crossing planetary/binary events, these 2-D parallax measurements directly lead to complete solutions (mass, distance, transvers…
We have redetermined the parallax and proper motion of the nearby isolated neutron star RX~J185635-3754. We used eight observations with the high resolution camera of the HST/ACS taken from 2002 through 2004. We performed the astrometric fitting using five independent methods, all of which yielded consistent results. The mean estimate of the distance is 123 (+11, -15) pc (1 sigma), in good agreement with our earlier published determination.
We present limits on the lens flux of OGLE-2007-BLG-224 based on MagAO imaging taken seven years after the microlensing event. At the time of the observations, the lens should have been separated from the microlensing source by 292 mas. However, no new sources are detected with MagAO. We place an upper limit on the lens flux of $H>20.57$. This measurement supports the conclusion of Gould et al. (2009) that the lens in this event should be a brown dwarf. This is the first test of a prediction based on the terrestrial microlens parallax effect and the first AO confirmation of a sub-stellar/dark …
The kinematics of isolated brown dwarfs in the Galaxy, beyond the solar neighborhood, is virtually unknown. Microlensing has the potential to probe this hidden population, as it can measure both the mass and five of the six phase-space coordinates (all except the radial velocity) even of a dark isolated lens. However, the measurements of both the microlens parallax and finite-source effects are needed in order to recover the full information. Here, we combine $Spitzer$ satellite parallax measurement with the ground-based light curve, which exhibits strong finite-source effects, of event OGLE-2…
We report the analysis of microlensing event OGLE-2017-BLG-1038, observed by the Optical Gravitational Lensing Experiment, Korean Microlensing Telescope Network, and Spitzer telescopes. The event is caused by a giant source star in the Galactic Bulge passing over a large resonant binary lens caustic. The availability of space-based data allows the full set of physical parameters to be calculated. However, there exists an eightfold degeneracy in the parallax measurement. The four best solutions correspond to very-low-mass binaries near ($M_1 = 170^{+40}_{-50} M_J$ and $M_2 = 110^{+20}_{-30} M_J…
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 mass for this event. Sahu et al. (2022) inferred a lens mass of 7.1 $\pm$ 1.3 Msun, consistent with a BH, while Lam…
Context: Gravitational microlensing is sensitive to compact-object lenses in the Milky Way, including white dwarfs, neutron stars or black holes, and could potentially probe a wide range of stellar remnant masses. However, the mass of the lens can be determined only in very limited cases, due to missing information on both source and lens distances and their proper motions. Aims: We aim at improving the mass estimates in the annual parallax microlensing events found in the 8 years of OGLE-III observations towards the Galactic Bulge (Wyrzykowski et al. 2016) with the use of Gaia Data Release 2 …
Microlensing is a powerful and unique technique to probe isolated objects in the Galaxy. To study the characteristics of these interesting objects based on the microlensing method, measurement of the microlens parallax is required to determine the properties of the lens. Of the various methods to measure microlens parallax, the most robust way is to make simultaneous ground- and space-based observations, i.e., by measuring the space-based microlens parallax. However, space-based campaigns usually require "expensive" resources. Gould & Yee (2012) proposed an idea called the "cheap space-based m…
Terrestrial microlens parallax is one of the very few methods that can measure the mass and number density of isolated dark low-mass objects, such as old free-floating planets and brown dwarfs. Terrestrial microlens parallax can be measured whenever a microlensing event differs substantially as observed from two or more well-separated sites. If the lens also transits the source during the event, then its mass can be measured. We derive an analytic expression for the expected rate of such events and then use this to derive two important conclusions. First the rate is directly proportional to th…
We report the mass and distance measurements of two single-lens events from the 2017 Spitzer microlensing campaign. The ground-based observations yield the detection of finite-source effects, and the microlens parallaxes are derived from the joint analysis of ground-based observations and Spitzer observations. We find that the lens of OGLE-2017-BLG-1254 is a $0.60 \pm 0.03 M_{\odot}$ star with $D_{\rm LS} = 0.53 \pm 0.11~\text{kpc}$, where $D_{\rm LS}$ is the distance between the lens and the source. The second event, OGLE-2017-BLG-1161, is subject to the known satellite parallax degeneracy, a…
We analyze the gravitational binary-lensing event OGLE-2016-BLG-0156, for which the lensing light curve displays pronounced deviations induced by microlens-parallax effects. The light curve exhibits 3 distinctive widely-separated peaks and we find that the multiple-peak feature provides a very tight constraint on the microlens-parallax effect, enabling us to precisely measure the microlens parallax $π_{\rm E}$. All the peaks are densely and continuously covered from high-cadence survey observations using globally located telescopes and the analysis of the peaks leads to the precise measurement…
The longest microlensing events provide enough information to estimate the mass and distance of the lens. Among hundreds of millions of stars which were monitored for many years by the OGLE project we selected those with clear parallax effect and derived the mass function of lensing objects in the Milky Way. We also found candidates for microlensing stellar-mass single black holes. We discuss how Gaia superb astrometry will help in measuring masses of remnants in currently on-going and future microlensing events.
Mass measurements of gravitational microlenses require one to determine the microlens parallax $\pie$, but precise $\pie$ measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which $\pie$ is measured with a dramatically improved precision using additional data from space-based $Spitzer$ observations. We find that while the parallax model based on the ground-based…
Astrometric microlensing probes of the isolated neutron star population with Roman
Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文中心）；Space Science Institute, Lawrence Livermore National Laboratory（空间科学研究所，劳伦斯利弗莫尔国家实验室）；Georgia Institute of Technology（佐治亚理工学院）
Our knowledge of the birth mass function of neutron stars and black holes is based on observations of binary systems but the binary evolution likely affects the final mass of the compact object. Gravitational microlensing allows us to detect and measure masses of isolated stellar remnants, which are nearly impossible to obtain with other techniques. Here, we analyze a sample of 4360 gravitational microlensing events detected during the third phase of the OGLE survey. We select a subsample of 87 long-timescale low-blending events. We estimate the masses of lensing objects by combining photometr…
Two independent groups reported the discovery of an isolated dark stellar remnant in the microlensing event OGLE-2011-BLG-0462 based on photometric ground-based observations coupled with astrometric measurements taken with the Hubble Space Telescope. These two analyses yielded discrepant mass measurements, with the first group reporting that the lensing object is a black hole of 7.1 +/- 1.3 solar masses whereas the other concluded that the microlensing event was caused by either a neutron star or a low-mass black hole (1.6-4.4 solar masses). Here, we scrutinize the available photometric and as…
We report the lens mass and distance measurements of the nearby microlensing event TCP J05074264+2447555. We measure the microlens parallax vector $π_{\rm E}$ using Spitzer and ground-based light curves with constraints on the direction of lens-source relative proper motion derived from Very Large Telescope Interferometer (VLTI) GRAVITY observations. Combining this $π_{\rm E}$ determination with the angular Einstein radius $θ_{\rm E}$ measured by VLTI GRAVITY observations, we find that the lens is a star with mass $M_{\rm L} = 0.495 \pm 0.063~M_{\odot}$ at a distance $D_{\rm L} = 429 \pm 21~{\…
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, neutron stars, and almost the only way to study isolated stellar-mass black holes. The majority of previous efforts to search for gravitational microlensing events have concentrated towards 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 lens mass estimate…
We present the analysis of the binary-lens microlensing event OGLE-2017-BLG-0537. The light curve of the event exhibits two strong caustic-crossing spikes among which the second caustic crossing was resolved by high-cadence surveys. It is found that the lens components with a mass ratio $\sim 0.5$ are separated in projection by $\sim 1.3\thetae$, where $\thetae$ is the angular Einstein radius. Analysis of the caustic-crossing part yields $\thetae=1.77\pm 0.16$~mas and a lens-source relative proper motion of $μ=12.4\pm 1.1~{\rm mas}~{\rm yr}^{-1}$. The measured $μ$ is the third highest value am…
"Industrial-Scale" Black Hole Selection without a Satellite
Peking University（北京大学）；Kavli Institute of Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；National Astronomical Observatories, Chinese Academy of Science（中国科学院国家天文台）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）；Ohio State University（俄亥俄州立大学）；University of Warsaw（华沙大学）；European Southern Observatory（欧洲南方天文台）
Astrometric microlensing can be used to make precise measurements of the masses of lens stars that are independent of their assumed internal physics. Such direct mass measurements, obtained purely by observing the gravitational effects of the stars on external objects, are crucial for validating theoretical stellar models. Specifically, astrometric microlensing provides a channel to direct mass measurements of single stars for which so few measurements exist. To use the astrometric solutions and photometric measurements of ~1.7 billion stars from Gaia Data Release 2 to predict microlensing eve…
We present the first space-based microlens parallax measurement of an isolated star. From the striking differences in the lightcurve as seen from Earth and from Spitzer (~1 AU to the West), we infer a projected velocity v_helio,projected ~ 250 km/s, which strongly favors a lens in the Galactic Disk with mass M=0.23 +- 0.07 M_sun and distance D_L=3.1 +- 0.4 kpc. An ensemble of such measurements drawn from our ongoing program could be used to measure the single-lens mass function including dark objects, and also is necessary for measuring the Galactic distribution of planets since the ensemble r…
The masses of stars including stellar remnants are almost exclusively known from binary systems. In this work, we study gravitational microlensing of faint background galaxies by isolated neutron stars (pulsars). We show that the resulting surface brightness distortions can be used to determine the masses of neutron star. Due to different evolutionary histories, isolated neutron stars may have different masses from those in binary systems, and thus provide unique insight into their equation of states under extreme physical conditions. We search for existing pulsar catalogs and find one promisi…
We search for microlensing events in the zero-latitude area of the Galactic Bulge using the VVV Survey near-IR data. We have discovered a total sample of $N=630$ events within an area covering $20.68 deg^2$ between the years 2010 and 2015. In this paper we describe the search and present the data for the final sample, including near-IR magnitudes, colors and proper motions, as well as the standard microlensing parameters. We use the near-IR Color-Magnitude and Color-Color Diagram to select $N_{RC}=290$ events with red-clump sources to analyze the extinction properties of the sample in the cent…
Massive galactic lenses with large Einstein Radii should cause a measurable astrometric microlensing effect, i.e. the light centroid shift due to the motion of the two images. Such a shift in the position of a background star due to microlensing was not included in the $Gaia$ astrometric model, therefore significant deviation should cause $Gaia$'s astrometric parameters to be determined incorrectly. Here we studied one of the photometric microlensing events reported in the $Gaia$ DR3, GaiaDR3-ULENS-001, for which poor goodness of $Gaia$ fit and erroneous parallax could indicate the presence of…
In this article we review the astrophysical application of gravitational microlensing. After introducing the history of gravitational lensing, we present the key equations and concept of microlensing. The most frequent microlensing events are single-lens events and historically it has been used for searching dark matter in the form of compact astrophysical halo objects in the Galactic halo. We discuss about the degeneracy problem in the parameters of lens and perturbation effects that can partially break the degeneracy between the lens parameters. The rest of paper is about the astrophysical a…
Due to the nature depending on only the gravitational field, microlensing, in principle, provides an important tool to detect faint and even dark brown dwarfs. However, the number of identified brown dwarfs is limited due to the difficulty of the lens mass measurement that is needed to check the substellar nature of the lensing object. In this work, we report a microlensing brown dwarf discovered from the analysis of the gravitational binary-lens event OGLE-2014-BLG-1112. We identify the brown-dwarf nature of the lens companion by measuring the lens mass from the detections of both microlens-p…
Light curves of microlensing events involving stellar binaries and planetary systems can provide information about the orbital elements of the system due to orbital modulations of the caustic structure. Accurately measuring the orbit in either the stellar or planetary case requires detailed modeling of subtle deviations in the light curve. At the same time, the natural, Cartesian parameterization of a microlensing binary is partially degenerate with the microlens parallax. Hence, it is desirable to perform independent tests of the predictions of microlens orbit models using radial velocity tim…
We present an analysis of microlensing event OGLE-2016-BLG-0693, based on the survey-only microlensing observations by the OGLE and KMTNet groups. In order to analyze the light curve, we consider the effects of parallax, orbital motion, and baseline slope, and also refine the result using a Galactic model prior. From the microlensing analysis, we find that the event is a binary composed of a low-mass brown dwarf 49+-20 M_J companion and a K- or G-dwarf host, which lies at a distance 5.0+-0.6 kpc toward the Galactic bulge. The projected separation between the brown dwarf and its host star is le…
Context. Gaia DR2 offers unparalleled precision on stars' parallaxes and proper motions. This allows the prediction of microlensing events for which the lens stars (and any planets they possess) are nearby and may be well studied and characterised. Aims. We identify a number of potential microlensing events that will occur before the year 2035.5, 20 years from the Gaia DR2 reference epoch. Methods. We query Gaia DR2 for potential lenses within 100 pc, extract parallaxes and proper motions of the lenses and background sources, and identify potential lensing events. We estimate the lens masses f…
We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E~270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462 (hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry of MOA-11…
We present a new Milky Way microlensing simulation code, dubbed PopSyCLE (Population Synthesis for Compact object Lensing Events). PopSyCLE is the first resolved microlensing simulation to include a compact object distribution derived from numerical supernovae explosion models and both astrometric and photometric microlensing effects. We demonstrate the capabilities of PopSyCLE by investigating the optimal way to find black holes (BHs) with microlensing. Candidate BHs have typically been selected from wide-field photometric microlensing surveys, such as OGLE, by selecting events with long Eins…
We report the result of the analysis of the light curve of a caustic-crossing binary-lens microlensing event OGLE-2009-BLG-023/MOA-2009-BLG-028. Even though the event was observed solely by survey experiments, we could uniquely determine the mass of the lens and distance to it by simultaneously measuring the Einstein radius and lens parallax. From this, we find that the lens system is composed of M-type dwarfs with masses $(0.50\pm 0.07) \ M_\odot$ and $(0.15\pm 0.02)\ M_\odot$ located in the Galactic disk with a distance of $\sim 1.8$ kpc toward the Galactic bulge direction. The event demonst…
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 no…
We report on the mass and distance measurements of two single-lens events from the 2015 \emph{Spitzer} microlensing campaign. With both finite-source effect and microlens parallax measurements, we find that the lens of OGLE-2015-BLG-1268 is very likely a brown dwarf. Assuming that the source star lies behind the same amount of dust as the Bulge red clump, we find the lens is a $45\pm7$ $M_{\rm J}$ brown dwarf at $5.9\pm1.0$ kpc. The lens of of the second event, OGLE-2015-BLG-0763, is a $0.50\pm0.04$ $M_\odot$ star at $6.9\pm1.0$ kpc. We show that the probability to definitively measure the mas…
