BINARY ASTROMETRIC MICROLENSING WITHGAIA

We investigate properties of astrometric microlensing of distant sources (such as quasi-stellar objects [QSOs] and radio galaxies) caused by stars in the Galaxy, mainly focusing on application of the VERA (VLBI Exploration of Radio Astrometry) project. Assuming typical parameters for the Galactic disk and bulge, we show that the maximum optical depth for astrometric shift of the 10 μas level is 8.9 × 10-2 for the QSO-disk lensing case and 3.8 × 10-2 for the QSO-bulge lensing case. We also find that the maximum optical depth for QSO-disk lensing is larger by an order of magnitude than that for disk-disk or bulge-disk lensing (assuming a typical source distance of 8-10 kpc). In addition to optical depth, we also calculate the event rate and find that the maximum event rate for the QSO-disk lensing case is 1.2 × 10-2 events yr-1, which is about 30 times greater than that for disk-disk lensing. This high event rate implies that if one monitors 10 QSOs behind the Galactic center region for 10 yr, at least one astrometric microlensing event should be detected. Therefore, monitoring distant radio sources with VERA can be a new tool to study astrometric microlensing caused by stars in the Galaxy. We also study the event duration of astrometric microlensing and find that the mean event duration for QSO-disk lensing is 7.5 yr for QSOs located near the Galactic center. This event duration for QSO-disk lensing is reasonably short compared to the project lifetime of VERA, which is anticipated to be ~20 yr. We also find that while the minimum event duration for bulge-bulge lensing is as short as 2.6 yr, the event duration for disk-disk lensing cannot be shorter than 15 yr. Thus, although astrometric microlensing of bulge sources/lenses can be studied by optical astrometric missions like SIM and GAIA, detections of disk events with the space astrometric missions are fairly difficult because of the limited project lifetime (typically ~5 yr) as well as the heavy dust extinction. Therefore, for studying astrometric microlensing by disk stars, VERA can be a powerful tool based on observations of distant sources like QSOs and radio galaxies. We discuss the implications of astrometric microlensing for VERA by focusing on estimating the lens mass, and we also present some possible candidates of radio sources toward which astrometric microlensing events should be searched for with VERA.

We present Hubble Space Telescope data of the low-reddening Sagittarius window in the Galactic bulge. The Sagittarius Window Eclipsing Extrasolar Planet Search field (3'x3'), together with three more Advanced Camera for Surveys and eight Wide Field Camera 3 fields, were observed in the F606W and F814W filters, approximately every two weeks for two years, with the principal aim of detecting a hidden population of isolated black holes and neutron stars through astrometric microlensing. Proper motions were measured with an accuracy of ~0.1 mas/yr (~4 km/s) at F606W~25.5 mag, and better than ~0.5 mas/yr (20 km/s) at F606W~28 mag, in both axes. Proper-motion measurements allowed us to separate disk and bulge stars and obtain a clean bulge color-magnitude diagram. We then identified for the first time a white dwarf (WD) cooling sequence in the Galactic bulge, together with a dozen candidate extreme horizontal branch stars. The comparison between theory and observations shows that a substantial fraction of the WDs (30%) are systematically redder than the cooling tracks for CO-core H-rich and He-rich envelope WDs. This evidence would suggest the presence of a significant number of low-mass WDs and WD - main sequence binaries in the bulge. This hypothesis is further supported by the finding of two dwarf novae in outburst, two short-period (P < 1 d) ellipsoidal variables, and a few candidate cataclysmic variables in the same field.

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.

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 km s−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 (∼108) and find reasonable agreement given the small sample size.

Because of dramatic improvements in the precision of astrometric measurements, the observation of light centroid shifts in observed stars due to intervening massive compact objects (astrometric microlensing) will become possible in the near future. Upcoming space missions, such as SIM and GAIA, will provide measurements with an accuracy of 4-60 mu as depending on the magnitude of the observed stars, and an accuracy of similar to 1 mu as is expected to be achieved in the more distant future. There are two different ways in which astrometric microlensing signals can be used to infer information: one possibility is to perform astrometric follow-up observations on photometrically detected microlensing events, and the other is to perform a survey based on astrometric observations alone. After the predictable effects of the Sun and the planets, stars in the Galactic disk play the dominant role in astrometric microlensing. The probability that the disk stars introduce a centroid shift larger than the threshold delta(T) at a given time for a given source in the Galactic bulge toward Baade's window reaches 100% for a threshold of delta(T) = 0.7 mu as, while this probability is similar to 2% for delta(T) = 5 mu as. However, this centroid shift does not vary much during the time in which a typical photometric microlensing event differs from baseline. So astrometric follow-ups (e.g., with SIM) are not expected to be disturbed by the statistical astrometric microlensing due to disk stars, so that it is possible to infer additional information about the nature of the lens that caused the photometric event, as suggested. The probability of observing astrometric microlensing events within the Galaxy turns out to be large compared to photometric microlensing events. The probability of seeing a variation by more than 5 mu as within 1 yr and reaching the closest angular approach between lens and source is similar to 10(-4) for a bulge star toward Baade's window, while this reduces to similar to 6 x 10(-6) for a direction perpendicular to the Galactic plane. For the upcoming mission GAIA, we expect similar to 1000 of the observed stars to show a detectable astrometric microlensing signal within its 5 yr lifetime. These events can be used to determine accurate masses of the lenses, and to derive the mass and the scale parameters (length and height) of the Galactic disk.

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 6 yr, reveals a clear relativistic astrometric deflection of the background star’s apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462 shows a parallactic signature of the effect of Earth’s motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 ± 1.3 M ⊙ and a distance of 1.58 ± 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic disk stars at similar distances by an amount corresponding to a transverse space velocity of ∼45 km s−1, suggesting that the BH received a “natal kick” from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial velocity measurements of Galactic X-ray binaries and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first for an isolated stellar-mass BH using any technique.

Populations of massive stars are directly reflective of the physics of stellar evolution. Counts of subtypes of massive stars and ratios of massive stars in different evolutionary states have been used ubiquitously as diagnostics of age and metallicity effects. While the binary fraction of massive stars is significant, inferences are often based upon models incorporating only single-star evolution. In this work, we utilize custom synthetic stellar populations from the Binary Population and Stellar Synthesis code to determine the effect of stellar binaries on number count ratios of different evolutionary stages in both young massive clusters and galaxies with massive stellar populations. We find that many ratios are degenerate in metallicity, age, and/or binary fraction. We develop diagnostic plots using these stellar count ratios to help break this degeneracy, and use these plots to compare our predictions to observed data in the Milky Way and the Local Group. These data suggest a possible correlation between the massive star binary fraction and metallicity. We also examine the robustness of our predictions in samples with varying levels of completeness. We find including binaries and imposing a completeness limit can both introduce ≳0.1 dex changes in inferred ages. Our results highlight the impact that binary evolution channels can have on the massive star population.

We investigate lens orbital motion in astrometric microlensing and its detectability. In microlensing events, the light centroid shift in the source trajectory (the astrometric trajectory) falls off much more slowly than the light amplification as the source distance from the lens position increases. As a result, perturbations developed with time such as lens orbital motion can make considerable deviations in astrometric trajectories. The rotation of the source trajectory due to lens orbital motion produces a more detectable astrometric deviation because the astrometric cross-section is much larger than the photometric one. Among binary microlensing events with detectable astrometric trajectories, those with stellar-mass black holes have most likely detectable astrometric signatures of orbital motion. Detecting lens orbital motion in their astrometric trajectories helps to discover further secondary components around the primary even without any photometric binarity signature as well as resolve close/wide degeneracy. For these binary microlensing events, we evaluate the efficiency of detecting orbital motion in astrometric trajectories and photometric light curves by performing Monte Carlo simulation. We conclude that astrometric efficiency is 87.3 per cent whereas the photometric efficiency is 48.2 per cent.

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∣ &lt; 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.

In a low-mass X-ray binary (LMXB), an intense stellar wind from the mass donor may be a consequence of the absorption of X-rays from the mass-accreting neutron star or black hole, and such a wind could change the evolution of these binaries dramatically compared with the evolution of cataclysmic variables (CVs), which are close binaries in which the accretor is a white dwarf. An analytical study and numerical models show that, in the closest and brightest LMXBs, a relativistic companion can capture up to ~10% of the mass lost in the induced stellar wind (ISW) from the main-sequence or subgiant donor, and this is enough to keep the X-ray luminosity of a typical LMXB on the level of LX ~ 5000 L☉ and to accelerate the rotation of an old neutron star with a low magnetic field into the millisecond-period range. A self-sustained ISW may exist even if the donor does not fill its Roche lobe, but the system can be bright (LX > 100 L☉) only if the radius of the donor is a substantial fraction ( 0.8) of the Roche lobe radius. A lower limit on the Roche lobe filling factor follows from the circumstance that both the rate Ėwind at which work must be done to lift wind matter off the donor and the rate Ėabs at which the donor absorbs X-ray energy are proportional to ISW (the ISW mass-loss rate) and from the requirement that Ėwind 3 hr. In Algol-like LMXBs in the Galactic disk, the timescale for the evaporation (caused by the ISW) of the donor with a low-mass, degenerate helium core can be smaller than the timescale for the radial expansion of the donor owing to nuclear evolution, and the donor may never fill its Roche lobe. However, if progenitor binaries are initially wide enough, the donor may escape evaporation as a main-sequence star, and significant mass transfer may not occur until the secondary evolves into a giant with a degenerate helium core of large mass and fills its Roche lobe. In globular clusters, as a result of capture and exchange reactions, semidetached Algol-like LMXBs can be formed in which the donor can fill its Roche lobe even when its degenerate helium core is of small mass, and Roche lobe mediated mass transfer driven by the nuclear evolution of the donor can dominate over capture from the ISW. The numerical models formally imply the possible presence in the Galaxy of ~104 dim (LX ~ 1-100 L☉), long-period LMXBs or radio pulsars with low-mass ( ~0.05 M☉) companions. Since there are few, if any, known observational counterparts of these systems, it is necessary to invoke a mechanism or mechanisms to destroy their formal progenitors. Possible destruction mechanisms include: (1) evaporation driven by the radiation from the rapidly rotating pulsar into which the accretor has been transformed by accretion during the bright LMXB phase, and (2) a dynamical instability arising when the donor is almost completely convective and fills its Roche lobe. In the case of dynamical disruption, the donor may be transformed into the envelope of a Thorne-Żytkow (1975) object with a neutron star or black hole core or into a planet-forming disk around the neutron star or black hole. A few short-period (Porb < 3 hr) LMXBs do exist, and, in them, the donor may be a helium white dwarf of mass less than ~0.09 M☉. An ISW operating before the donor fills its Roche lobe may be responsible for reducing the mass of the white dwarf from an initial value of ≥0.13 M☉ to a value of ≤0.09 M☉, thus permitting stable mass exchange (at a rate smaller than the Eddington limiting rate) and evolution to longer periods to occur after the donor fills its Roche lobe. Another scenario relies on the collapse of a massive oxygen-neon white dwarf, which has accreted from a Roche lobe filling helium white dwarf. Problems that must be explored further in order to acquire a better understanding of the evolution of LMXBs include the formation of a corona around an irradiated low-mass main-sequence or degenerate dwarf star, accretion of ISW matter by a neutron star or black hole companion, the effect of an ISW on the MSW, formation of millisecond pulsars, complete evaporation of low-mass donors, disruption by tidal forces of a low-mass main-sequence star or a degenerate dwarf companion into a gas disk around the accretor, and the formation of planetary systems in the disk around neutron stars and or black holes in post-LMXB systems.

Context. 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. Microlensing events that also exhibit a detectable photometric signature provide even stronger lens mass constraints. Aims. I use the astrometric solutions and photometric measurements of ~1.7 billion stars provided by Gaia Data Release 2 (GDR2) to predict microlensing events during the nominal Gaia mission and beyond. This will enable astronomers to observe the entirety of each event, including the peak, with appropriate observing resources. The data collected will allow precise lens mass measurements for white dwarfs and low-mass main sequence stars (K and M dwarfs) helping to constrain stellar evolutionary models. Methods. I search for source-lens pairs in GDR2 that could potentially lead to microlensing events between 25th July 2014 and 25th July 2026. I estimate the lens masses using GDR2 photometry and parallaxes, and appropriate model stellar isochrones. Combined with the source and lens parallax measurements from GDR2, this allows the Einstein ring radius to be computed for each source-lens pair. By considering the source and lens paths on the sky, I calculate the microlensing signals that are to be expected. Results. I present a list of 76 predicted microlensing events. Nine and five astrometric events will be caused by the white dwarf stars LAWD 37 and Stein 2051 B, respectively. A further nine events will exhibit detectable photometric and astrometric signatures. Of the remaining events, ten will exhibit astrometric signals with peak amplitudes above 0.5 mas, while the rest are low-amplitude astrometric events with peak amplitudes between 0.131 and 0.5 mas. Five and two events will reach their peaks during 2018 and 2019, respectively. Five of the photometric events have the potential to evolve into high-magnification events, which may also probe for planetary companions to the lenses.

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. Our aim is to improve the mass estimates in the annual parallax microlensing events found in the eight years of OGLE-III observations towards the Galactic Bulge with the use of Gaia Data Release 2 (DR2). Methods. We use Gaia DR2 data on distances and proper motions of non-blended sources and recompute the masses of lenses in parallax events. We also identify new events in that sample which are likely to have dark lenses; the total number of such events is now 18. Results. The derived distribution of masses of dark lenses is consistent with a continuous distribution of stellar-remnant masses. A mass gap between neutron star and black hole masses in the range between 2 and 5 solar masses is not favoured by our data, unless black holes receive natal kicks above 20−80 km s−1. We present eight candidates for objects with masses within the putative mass gap, including a spectacular multi-peak parallax event with mass of 2.4−1.3+1.9 M⊙ located just at 600 pc. The absence of an observational mass gap between neutron stars and black holes, or conversely the evidence of black hole natal kicks if a mass gap is assumed, can inform future supernova modelling efforts.

The kinematics of black hole and neutron star X-ray binaries in the Galaxy should help to know their birth place and constrain their evolution. We have used multiple tools of modern astronomy to determine the trajectories in the Galaxy and track the origins of black hole and neutron star X-ray binaries that are of topical interest in astrophysics. We find three distinct classes of black hole and neutron star X-ray binaries: (1) low mass X-ray binaries that move at high velocities on galactocentric orbits similar to the most ancient stars born in the Galactic bulge and the halo, (2) those that move in the Galactic disk along paths that resemble the circular orbits of massive stars formed in the disk, and (3) high and intermediate mass X-ray binaries running away from their parent regions of star formation. Here we discuss some of the cases studied. The large transverse motions of neutron stars (NS's) in the plane of the sky are believed to result from kicks imparted in natal supernova (SN) explosions. SN explosions are usually invoked in models of the core collapse of massive stars onto black holes (BH's), but until present there have been few observations that can constrain the models of the physical processes by which stellar-mass black holes are formed. The velocity in three dimensions and the galactocentric orbit can be used to gain insight into this issue, tracking the compact object back to its birth place and constraining the energy of any putative natal kick. Compact microquasar jets are ubiquitous among accreting black holes and neutron stars, and their motion in the plane of the sky can be followed with high precision by astrometry at radio wavelengths with Very Long Baseline Interferometry (VLBI). The proper motion can also be determined by astrometry of the donor star at optical wavelengths. Optical and IR spectroscopy of the companion star provides the line of sight velocity of the system. Knowing the distance either from VLBI or from the properties of the donor star, the Galactic orbit of the X-ray binary can be computed using a Galactic potential model. Here we summarize the results of a series of papers on individual objects, on which we search for some new constrains to the physical models that describe the formation of stellar-mass black holes and neutron stars.

There is now strong evidence that the close binary fraction (P &lt; 104 days; a &lt; 10 au) of solar-type stars (M 1 ≈ 0.6–1.5 ) decreases significantly with metallicity. Although early surveys showed that the observed spectroscopic binary (SB) fractions in the galactic disk and halo are similar (e.g., Carney–Latham sample), these studies did not correct for incompleteness. In this study, we examine five different surveys and thoroughly account for their underlying selection biases to measure the intrinsic occurrence rate of close solar-type binaries. We reanalyze (1) a volume-limited sample of solar-type stars, (2) the Carney-Latham SB survey of high proper motion stars, (3) various SB samples of metal-poor giants, (4) the APOGEE survey of radial velocity (RV) variables, and (5) eclipsing binaries (EBs) discovered by Kepler. The observed APOGEE RV variability fraction and Kepler EB fraction both decrease by a factor of ≈4 across −1.0 &lt; [Fe/H] &lt; 0.5 at the 22σ and 9σ confidence levels, respectively. After correcting for incompleteness, all five samples/methods exhibit a quantitatively consistent anticorrelation between the intrinsic close binary fraction (a &lt; 10 au) and metallicity: F close = 53% ± 12%, 40% ± 6%, 24% ± 4%, and 10% ± 3% at [Fe/H] = −3.0, −1.0, −0.2 (mean field metallicity), and +0.5, respectively. We present simple fragmentation models that explain why the close binary fraction of solar-type stars strongly decreases with metallicity while the wide binary fraction, close binary fraction of OB stars, and initial mass function are all relatively constant across −1.5 ≲ [Fe/H] &lt; 0.5. The majority of solar-type stars with [Fe/H] ≲ −1.0 will interact with a stellar companion, which has profound implications for binary evolution in old and metal-poor environments such as the galactic halo, bulge, thick disk, globular clusters, dwarf galaxies, and high-redshift universe.

This supplement provides supporting material for Lam et al. We briefly summarize past gravitational microlensing searches for black holes (BHs) and present details of the observations, analysis, and modeling of five BH candidates observed with both ground-based photometric microlensing surveys and Hubble Space Telescope astrometry and photometry. We present detailed results for four of the five candidates that show no or low probability for the lens to be a BH. In these cases, the lens masses are <2 M ⊙, and two of the four are likely white dwarfs or neutron stars. We also present detailed methods for comparing the full sample of five candidates to theoretical expectations of the number of BHs in the Milky Way (∼108).