Astrometric Microlensing Research Articles

Influence of Black Hole Kick Velocity on Microlensing Distributions

The natal kick velocity distribution for black holes (BHs) is unknown regardless of its importance for understanding the BH formation process. Gravitational microlensing is a unique tool for studying the distribution of BHs in our Galaxy, and the first isolated stellar-mass BH event, OGLE-2011-BLG-0462/MOA-2011-BLG-191 (OB110462), was recently identified by astrometric microlensing. This study investigates how the natal kick velocity for Galactic BHs affects the microlensing event rate distribution. We consider a Maxwell distribution with various average kick velocities, as well as the consequent variation of the spatial distribution of BHs. We find that the event rate for the BH lenses toward the Galactic bulge decreases as v avg increases, mainly due to the scale height inflation. We focus on the unique microlensing parameters measured for OB110462, with microlens parallax π E larger than 0.06 for its long timescale of t E > 200 days. We calculate the expected number of BH events occurring with parameters similar to OB110462 during the OGLE-IV survey by Mróz et al. and compare it with the actual number that occurred, at least one. Our fiducial model predicts 0.52, 0.38, 0.18, 0.042, and 4.0 × 10−3 events occurring for v avg = 25, 50, 100, 200, and 400 km s−1, respectively, which suggests that the average kick velocity is likely to be v avg ≲ 100 km s−1. The expected number smaller than unity even at maximum might indicate our luck in finding OB110462, which can be tested with future surveys by, e.g., the Roman Space Telescope.

Primordial Black Hole Dark Matter Simulations Using PopSyCLE

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 ∼3.6f 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 102 f DM PBH events within the 8 yr OGLE-IV results, and estimate Roman to detect ∼1000f DM PBH microlensing events throughout its planned microlensing survey.

Gaia22dkvLb: A Microlensing Planet Potentially Accessible to Radial-velocity Characterization

We report discovering an exoplanet from following up a microlensing event alerted by Gaia. The event Gaia22dkv is toward a disk source rather than the traditional bulge microlensing fields. Our primary analysis yields a Jovian planet with Mp=0.59−0.05+0.15MJ at a projected orbital separation r⊥=1.4−0.3+0.8 au, and the host is a ∼1.1 M ⊙ turnoff star at ∼1.3 kpc. At r′≈14 , the host is far brighter than any previously discovered microlensing planet host, opening up the opportunity to test the microlensing model with radial velocity (RV) observations. RV data can be used to measure the planet’s orbital period and eccentricity, and they also enable searching for inner planets of the microlensing cold Jupiter, as expected from the “inner–outer correlation” inferred from Kepler and RV discoveries. Furthermore, we show that Gaia astrometric microlensing will not only allow precise measurements of its angular Einstein radius θ E but also directly measure the microlens parallax vector and unambiguously break a geometric light-curve degeneracy, leading to the definitive characterization of the lens system.

Single-epoch and Differential Astrometric Microlensing of Quasars

We propose and discuss a new experimental approach to measure the centroid shift induced by gravitational microlensing in the images of lensed quasars (astrometric microlensing). Our strategy is based on taking the photocenter of a region in the quasar large enough as to be insensitive to microlensing as reference to measure the centroid displacement of the continuum. In this way, single-epoch measurements of astrometric microlensing can be performed. Using numerical simulations, we show that, indeed, the centroid shift monotonically decreases as the size of the emitting region increases, and only for relatively large regions, like the broad line region (BLR), does the centroid shift become negligible. This opens interesting possibilities to study the stratification of the different emitters in the accretion disk and the BLR. We estimate the amplitude of the centroid shifts for 79 gravitationally lensed images and study more thoroughly the special cases Q2237+030 A, RXJ1131-1231 A, PG1115+080 A2, and SDSS J1004+4112 A. We propose to use spectro-astrometry to simultaneously obtain the photocenters of the continuum and of different emission line regions since, with the precision of forthcoming instruments, astrometric microlensing by ∼1 M ⊙ mass microlenses may be detected in many quasar lensed images. When we consider more massive micro/millilenses, M ≳ 10 M ⊙, often proposed as the constituents of dark matter, the BLR becomes sensitive to microlensing and can no longer be used as a positional reference to measure centroid shifts. Differential microlensing between the images of a lensed quasar along several epochs should be used instead.

Astrometric Microlensing by Primordial Black Holes with the Roman Space Telescope

Primordial black holes (PBHs) could explain some fraction of dark matter and shed light on many areas of early-Universe physics. Despite over half a century of research interest, a PBH population has so far eluded detection. The most competitive constraints on the fraction of dark matter comprised of PBHs (f DM) in the (10−9–10)M ⊙ mass ranges come from photometric microlensing and bound f DM ≲ 10−2–10−1. With the advent of the Roman Space Telescope with its submilliarcsecond astrometric capabilities and its planned Galactic Bulge Time Domain Survey (GBTDS), detecting astrometric microlensing signatures will become routine. Compared with photometric microlensing, astrometric microlensing signals are sensitive to different lens masses–distance configurations and contain different information, making it a complimentary lensing probe. At submilliarcsecond astrometric precision, astrometric microlensing signals are typically detectable at larger lens–source separations than photometric signals, suggesting a microlensing detection channel of pure astrometric events. We use a Galactic simulation to predict the number of detectable microlensing events during the GBTDS via this pure astrometric microlensing channel. Assuming an absolute astrometric precision floor for bright stars of 0.1 mas for the GBTDS, we find that the number of detectable events peaks at ≈103 f DM for a population of 1M ⊙ PBHs and tapers to ≈10f DM and ≈100f DM at 10−4 M ⊙ and 103 M ⊙, respectively. Accounting for the distinguishability of PBHs from stellar lenses, we conclude the GBTDS will be sensitive to a PBH population at f DM down to ≈10−1–10−3 for (10−1–102)M ⊙ likely yielding novel PBH constraints.

Prediction of Astrometric and Timing Microlensing Events with Pulsars by ATNF Catalog and Gaia DR3

Determining the mass of neutron stars is crucial for understanding their formation, evolution, and interior structure. Currently, only a few dozen neutron stars have had their masses measured, and most of them belong to binary systems. However, there are a huge number of isolated neutron stars with unknown masses. Microlensing events with neutron stars provide unique opportunities for knowing these compact objects. Astrometric microlensing with a background source lensed by a neutron star might be used to determine the neutron star's mass by measuring the deviation of the motion of the centroid of the images from its unlensed one. We search and predict these recent and future events based on the Australia Telescope National Facility Pulsar Catalog and Gaia DR3. We find 60 candidate astrometric microlensing events caused by neutron stars and the probability distributions of their observables by the Monte Carlo sampling. We also find four candidate “timing microlensing” events with a pulsar lensed by a foreground object that might be detected by timing measurements. While some of these events may be verified by future astrometric missions or pulsar-timing observations, we note that our prediction of these events is significantly restricted by the uncertainties of the available astrometric and timing measurements after assessing and comparing our results with previous works.

Predicting astrometric microlensing events from Gaia Data Release 3

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

Astrometric microlensing of primordial black holes with Gaia

The Gaia space telescope allows for unprecedented accuracy for astrometric measurements of stars in the Galaxy. In this work, we explore the sensitivity of Gaia to detect primordial black hole (PBH) dark matter through the distortions that PBHs would create in the apparent trajectories of background stars, an effect known as astrometric microlensing (AML). We present a novel calculation of the lensing probability, and we combine this with the existing publicly released Gaia eDR3 stellar catalog to predict the expected rate of AML events that Gaia will see. We also compute the expected distribution of a few event observables, which will be useful for reducing backgrounds.Assuming that the astrophysical background rate of AML like events due to other sources is negligible, we then compute the potential exclusion that could be set on the parameter space of PBHs with a monochromatic mass function. We find that Gaia is sensitive to PBHs in the range of 0.4 M ⊙–5 × 107 M ⊙, and has peak sensitivity to PBHs of ∼ 10 M ⊙ for which it can rule out as little as a fraction 3 × 10-4 of dark matter composed of PBHs. With this exquisite sensitivity, Gaia has the potential to rule out a PBH origin for the gravitational wave signals seen at LIGO/Virgo. Our novel calculation of the lensing probability includes for the first time, the effect of intermediate duration lensing events, where the lensing event lasts for a few years, but for a period which is still shorter than the Gaia mission lifetime. The lower end of our predicted mass exclusion is especially sensitive to this class of lensing events. As and when time-series data for Gaia is released, and once we have a better understanding of the astrophysical background rate to AML signals, our prediction of the lensing rate and event observable distributions will be useful to estimate the true exclusion/discovery of the PBH parameter space utilizing this data.

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.

Detecting Isolated Stellar-mass Black Holes with the Roman Telescope

Isolated stellar-mass black holes (ISMBHs) are potentially discernible through microlensing observations, because they are expected to be long-duration microlensing events. In this work, we study the detection and characterization of ISMBHs using Roman observations. We simulate a large ensemble of such events, as they will be seen by Roman, and estimate the errors in the physical parameters of the lens objects, including their masses, distances, and proper motions, by calculating Fisher and covariance matrices. Since the ∼2.3 yr time gap between Roman’s first three observing seasons and its latter three seasons may lower the efficiency of its realization of microlensing events and characterization of ISMBHs, we additionally consider a scenario where we add a small number of additional observations—1 hr of observations, every 10 days, when the Bulge is observable during the large time gap—which is equivalent to a total of an additional day of observations with the Roman telescope. These extra observations increase Roman’s efficiency in terms of characterizing ISMBHs by ∼1%–2%, and, more importantly, they improve the robustness of the results, by avoiding possible degenerate solutions. By considering uniform and power-law mass functions (, α = 2, 1, 0.5) for ISMBHs in the range of [2, 50]M ⊙, we conclude that the Roman telescope will determine the physical parameters of the lenses (the mass, distance, and relative lens–source angular velocity) within <5% uncertainty, with efficiencies of 21% and 16%–18%, respectively. By considering these mass functions, we expect that during its mission the Roman telescope will detect and characterize 3–4, 15–17, and 22–24 ISMBHs through astrometric microlensing, with the relative errors for all physical parameters being less than 1%, 5%, and 10%, respectively. Microlensing events due to ISMBHs with masses ≃10–25M ⊙ that are located close to the observer, with D l ≲ 0.5D s, while the source is inside the Galactic disk, can be characterized with the fewest errors.

First semi-empirical test of the white dwarf mass–radius relationship using a single white dwarf via astrometric microlensing

ABSTRACT In November 2019, the nearby single, isolated DQ-type white dwarf LAWD 37 (WD 1142-645) aligned closely with a distant background source and caused an astrometric microlensing event. Leveraging astrometry from Gaia and followup data from the Hubble Space Telescope, we measure the astrometric deflection of the background source and obtain a gravitational mass for LAWD 37. The main challenge of this analysis is in extracting the lensing signal of the faint background source whilst it is buried in the wings of LAWD 37’s point spread function. Removal of LAWD 37’s point spread function induces a significant amount of correlated noise which we find can mimic the astrometric lensing signal. We find a deflection model, including correlated noise caused by the removal of LAWD 37’s point spread function best explains the data and yields a mass for LAWD 37 of $0.56\pm 0.08\, {\rm M}_{\odot }$. This mass is in agreement with the theoretical mass–radius relationship and cooling tracks expected for CO core white dwarfs. Furthermore, the mass is consistent with no or trace amounts of hydrogen that is expected for objects with helium-rich atmospheres like LAWD 37. We conclude that further astrometric followup data on the source is likely to improve the inference on LAWD 37’s mass at the ≈3 per cent level and definitively rule out purely correlated noise explanations of the data. This work provides the first semi-empirical test of the white dwarf mass–radius relationship using a single, isolated white dwarf and supports current model atmospheres of DQ white dwarfs and white dwarf evolutionary theory.

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

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.

A possible nearby microlensing stellar remnant hiding in Gaia DR3 astrometry

Massive galactic lenses with large Einstein Radii should cause a measurable astrometric microlensing effect, that is, a 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, and therefore significant deviation should cause Gaia’s astrometric parameters to be determined incorrectly. Here we study one of the photometric microlensing events reported in the Gaia Data Release 3, GaiaDR3-ULENS-001, for which a poor goodness of Gaia fit and erroneous parallax could indicate the presence of an astrometric microlensing signal. Based on the photometric microlensing model, we simulated Gaia astrometric time series with the astrometric microlensing effect added. We find that including microlensing with an angular Einstein radius of θE = 2.60−0.24+0.21 mas (2.47−0.24+0.28 mas) assuming a positive (negative) impact parameter, u0, reproduces the astrometric quantities reported by Gaia well. We estimate the mass of the lens to be 1.00−0.18+0.23 M⊙ (0.70−0.13+0.17 M⊙) and its distance 0.90−0.11+0.14 kpc (0.69−0.09+0.13 kpc), proposing the lens could be a nearby isolated white dwarf.

Systematic Errors as a Source of Mass Discrepancy in Black Hole Microlensing Event OGLE-2011-BLG-0462

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 M ⊙ 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 M ⊙). Here, we scrutinize the available photometric and astrometric data and conclude that systematic errors are a cause of the discrepant measurements. We find that the lens is an isolated black hole with a mass of 7.88 ± 0.82 M ⊙ located at a distance of 1.49 ± 0.12 kpc. We also study the impact of blending on the accuracy of astrometric microlensing measurements. We find that low-level blending by source companions is a major, previously unrecognized, challenge to astrometric microlensing measurements of black hole masses.

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 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.

An Isolated Stellar-mass Black Hole Detected through Astrometric Microlensing* *This research is based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

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.

Supplement: “An Isolated Mass-gap Black Hole or Neutron Star Detected with Astrometric Microlensing” (2022, ApJL, 933, L23)

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).

Constraining Black Hole Natal Kicks with Astrometric Microlensing

Multiple pieces of evidence suggest that neutron stars receive large kicks when formed from the remnant of a collapsing star. However, the evidence for whether black holes (BHs) receive natal kicks is less clear, reliant on weak constraints from the analysis of BH X-ray binaries and massive runaway and walkaway stars. Here we show, for the first time, that recent microlensing detections offer a new method for measuring the kicks BHs receive at birth. When a BH is identified through both photometric and astrometric microlensing and when the lensed star has a known distance and proper motion, the mass, distance, and proper motion of the BH can be determined. We study the runaway velocities for components of eccentric binaries disrupted during a supernova (SN), finding the peculiar velocity correlates strongly with the kick a BH received at birth, typically within 20%, even when the natal kick is smaller than the orbital velocity. Therefore, by measuring the peculiar velocity of a BH or other compact object that formed from a binary which disrupted during core collapse, we are in effect measuring the natal kick that object received. We focus on MOA-2011-BLG-191/OGLE-2011-BLG-0462, an isolated, single BH detected by microlensing, and consider a range of possible formation scenarios, including its formation from the disruption of a binary during a SN event. We determine that MOA-2011-BLG-191/OGLE-2011-BLG-0462 has a Milky Way orbit consistent with a thick-disk population, but if it was formed within the kinematic thin disk it received a natal kick ≲100 km s−1.

A public code for astrometric microlensing with contour integration

ABSTRACT We present the first public code for the calculation of the astrometric centroid shift occurring during microlensing events. The computation is based on the contour integration scheme and covers single and binary lensing of finite sources with arbitrary limb darkening profiles. This allows for general detailed investigations of the impact of finite source size in astrometric binary microlensing. The new code is embedded in version 3.0 of vbbinarylensing, which offers a powerful computational tool for extensive studies of microlensing data from current surveys and future space missions.

Completeness of the Gaia-verse – IV. The astrometry spread function of Gaia DR2

ABSTRACT Gaia Data Release 2 (DR2) published positions, parallaxes, and proper motions for an unprecedented 1331 909 727 sources, revolutionizing the field of Galactic dynamics. We complement this data with the astrometry spread function (ASF), the expected uncertainty in the measured positions, proper motions, and parallax for a non-accelerating point source. The ASF is a Gaussian function for which we construct the 5D astrometric covariance matrix as a function of position on the sky and apparent magnitude using the Gaia DR2 scanning law and demonstrate excellent agreement with the observed data. This can be used to answer the question ‘What astrometric covariance would Gaia have published if my star was a non-accelerating point source?’. The ASF will enable characterization of binary systems, exoplanet orbits, astrometric microlensing events, and extended sources that add an excess astrometric noise to the expected astrometry uncertainty. By using the ASF to estimate the unit weight error of Gaia DR2 sources, we demonstrate that the ASF indeed provides a direct probe of the excess source noise. We use the ASF to estimate the contribution to the selection function of the Gaia astrometric sample from a cut on astrometric_sigma5d_max showing high completeness for G &amp;lt; 20 dropping to ${\lt} 1{{\ \rm per\ cent}}$ in underscanned regions of the sky for G = 21. We have added an ASF module to the python package scanninglaw (https://github.com/gaiaverse/scanninglaw) through which users can access the ASF.