# Cross-Matching of OGLE, GAIA, and Hubble Catalogs: Evaluating the
Probability of Resolving Lens Stars in Microlensing Events

S. Mozaheb,1 S. Rahvar,1,2
1Department of Physics, Sharif University of Technology, Azadi Ave, Tehran
11365-9161-Iran
2Research Center for High Energy Physics, Sharif University of Technology,
Tehran, Iran E-mail:saeed.mozaheb<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

This study commenced by cross-matching data from the GAIA and OGLE telescopes
with the aim of resolving the source star, long after microlensing is
finished. The aim is breaking degeneracy between parameters of the
microlensing equation, and ultimately calculating the mass of lens. We have
examined different catalogs and found no evidence.
Subsequently, employing the Monte Carlo method and guided by sensible
assumptions, we embarked a simulation to discern the distribution of angular
separation and to probe the feasibility of detecting this phenomenon. The
results revealed that a mere $0.029\%$ of gravitational microlensing events
exhibited separations exceeding $50$ milliarcseconds. Consequently, the
likelihood of observing this phenomenon utilizing the OGLE and GAIA telescopes
appears exceedingly far available. However, it is worth noting that
instruments with very high angular resolution in the range of several tens of
milliarcseconds present a viable avenue for such observations. Finally, we
proposed $60$ microlensing events for which the observation of separation is
more probable based on the measured proper velocity.

###### keywords:

Gravitational Lensing: Micro – Methods: Data Analysis – Techniques: High
Angular Resolution – Software: Simulations

††pubyear: 2023††pagerange: Cross-Matching of OGLE, GAIA, and Hubble Catalogs:
Evaluating the Probability of Resolving Lens Stars in Microlensing Events–A

##  1 INTRODUCTION

General relativity introduced by Albert Einstein Where gravitational lensing
was one of predictions of this theory (Einstein, 1936). This phenomena, was
observed by Eddington and strongly supported the theory’s validity (Eddington,
1919). Gravitational lensing is categorized into three types: strong, weak,
and microlensing. Microlensing events are characterized by the inability to
resolve the lensed image. These events are identified through the analysis of
their light curves and the observable effect of amplification. (Schneider et
al., 2006; Paczynski, 1986). This work focuses on observing the separation
between the lens and source stars in gravitational microlensing.
Calculating the mass of various objects is a challenging problem in
astrophysics. Natural phenomena like gravitational lensing are crucial for
mass calculation specially for dark objects and also, investigating the
distribution of dark matter in galaxies (Paczynski, 1986). While the notion of
MACHOs serving as potential dark matter candidates has been ruled out,
gravitational microlensing has subsequently been employed as a versatile
astrophysical technique to investigate distant stars (Rahvar, 2015; Paczynski,
1986) and detect exoplanets orbiting the lensed stars (Gaudi, 2010).
(Wyrzykowski et al., 2016) identified $13$ microlensing events which are
consistent with having dark lens.
Determining mass solely through the light curve of microlensing events is not
possible due to degeneracy in terms of Einstein crossing time. Therefore,
various observational disturbances such as the parallax effect (Gould, 1994;
Rahvar et al., 2003), finite size effect (Mróz et al., 2020), frequency shift
effect (Rahvar, 2020) and source separation are utilized to break degeneracy
and calculate mass (Gould & Yee, 2014; Rahvar, 2015). This idea needs high
precision telescopes to resolve the lens and source after a long time ending
microlensing event. The relative proper motion may provide possibility to
resolve them as two objects.
Initially, due to recent research on simulations that calculate probability of
observation of source-lens separation (Dehghani & Rahvar, 2022), this work
aims to observe the separation of microlensing events by cross-match data from
the GAIA and OGLE telescopes. Also, Hubble Space Telescope data is used for
higher resolution observations. Despite creating a comprehensive database of
microlensing events, the source-lens separation was not observed in any of the
data. To determine the probability of observing separation, simulations using
the Monte Carlo method is performed. The probability of observing separation
was investigated for various telescopes and projects, including Hubble and
ALMA. The final conclusion indicates that a resolution of at least $50$ mas is
necessary to separate the source and the lens. Ground telescopes that use
adaptive optics can be very effective for investigating this separation. This
observation was made once by (Bennett et al., 2020) using Keck telescope which
helped calculating the mass of the central star in a planetary system.
Required resolution exceeds the capabilities of the GAIA and OGLE telescopes,
making it practically impossible to observe the lens and the source in the
images captured by these telescopes.
Considering the different conditions required for separation visibility, the
number of visible events for different observational instruments is examined.
As a result, the Hubble telescope and the ALMA radio telescope were identified
as the best choices for future separation observations.
In Section (2), we address the degeneracy problem and the calculation of lens
mass. Additionally, we explore the consideration of perturbations, which aids
in breaking the degeneracy. Moving to Section (3), we present the cross-match
method that we implemented to identify the source-lens separation. Section (4)
delves into the simulations conducted to estimate the probability of resolving
the desired separation, taking into account the observational capabilities of
available telescopes. conclusion is given in (5).

##  2 GRAVITATIONAL MICROLENSING AND DEGENERACY PROBLEM

The amount of light deviation causes by a point mass is $\alpha=4GM/bc^{2}$
which can be calculated by solving geodesic in Schwarzschild metric. Here, the
mass of the lens is $M$, $c$ is speed of light and the light impact parameter
is $b$.

Figure 1: Illustration of the parameters involved in a gravitational lensing
event. Here, $D_{d}$ represents the distance between the lens and the
observer, while $D_{s}$ represents the distance between the source and the
observer. (Bartelmann & Schneider, 2001)

For gravitational lensing events, the Einstein angle is defined as the
characteristic angle of the lens, which is determined by the mass of the lens
$M$, the source distance $D_{s}$, and the ratio of the lens distance to the
source distance $x$, these parameters are represented in Figure (1). The
Einstein angle is represented by the parameter $\theta_{E}$:

$\theta_{E}=0.901(\frac{M}{M_{\odot}})^{1/2}(\frac{D_{s}}{10kpc})^{-1/2}(\frac{1-x}{x})^{1/2}mas$
(1)

The Earth’s movement, along with the source and the lens, causes the lensed
light to appear to move from the perspective of the observer on Earth. This
relative tangential velocity parameter is significant in determining Einstein
crossing time. The relative angular velocity is:

$\mu=\frac{V_{S\perp}-V_{E\perp}}{D_{s}}-\frac{V_{L\perp}-V_{E\perp}}{D_{d}}$
(2)

Einstein crossing time is the specific time parameter of this event, defined
as $t_{E}=\theta_{E}/\mu$. So finally, we can write Einstein crossing time:

$\begin{split}t_{E}&=45.6day(\frac{D_{s}}{8.5kpc})^{1/2}(\frac{M}{0.5M_{\odot}})^{1/2}(\frac{1-x}{x})^{1/2}\\\
&\times(|V_{S\perp}-V_{E\perp}-\frac{1}{x}(V_{L\perp}-V_{E\perp})|\frac{1}{220km/s})^{-1}\\\
\end{split}$ (3)

The relationship here clearly explains how mass is related to five other
factors: By means that Einstein time $t_{E}$, as the observable parameter
depends on source distance $D_{s}$, distance ratio $x$, source tangential
velocity $V_{S\perp}$ , and lens tangential velocity $V_{L\perp}$. In
gravitational microlensing events, light curve diagrams can only be used to
calculate Einstein’s time out of these parameters. To accurately determine the
mass of the lens, it is essential to account for the interdependence among the
known parameters referred to as degeneracy. Several methods can be employed to
tackle this issue effectively. In specific instances of gravitational
microlensing events, discrete disturbances such as parallax effect (Waagaard,
2017), Xallarap (Rahvar & Dominik, 2008), and finite-source effect manifest
(Choi et al., 2012; Golchin & Rahvar, 2020). By meticulously observing the
effects of these perturbations, an additional equation can be derived that
establishes a connection between the pertinent parameters, thereby
facilitating a more straightforward analytical solution. Consequently, through
the meticulous assessment of the fluctuations in the said parameters, a
reliable estimation of the lens mass can be achieved (Alcock et al., 1995;
Waagaard, 2017).

###  2.1 Lens-Source Separation Detection

The methodology employed in this research to address the degeneracy problem
entailed the observation of the separation between the lens and the source. By
examining the location of this event several years after the occurrence of the
gravitational microlensing event and being able to detect the source and the
lens as distinct entities, it becomes feasible to compute the astrometric and
astrophysical parameters for each of them individually. This approach
facilitates a more precise estimation of the parameters associated with
degeneracy and enables a more accurate calculation of the mass involved as
investigated in (Bennett, 2008) and implemented in (Bennett et al., 2020).

In previous computer simulation studies (Dehghani & Rahvar, 2022), extensive
investigations have been conducted to explore the feasibility of observing the
separation phenomenon. The research anticipated that a substantial number of
separations could be detected by cross-match the microlensing observed through
the OGLE ground telescope with the GAIA space telescope. Building upon this
premise, the mass calculation was performed.

Based on these findings, the present study commenced by cross-match two
catalogs. Subsequently, a meticulous search was conducted within these
comparison to identify the desire separation, which will be elaborated upon in
the following section in detail

##  3 OGLE, GAIA and Hubble Cross-match

In this research, the data from OGLE and GAIA were utilized. By cross-matching
the light sources identified by the OGLE telescope as gravitational
microlenses with the light sources in the GAIA catalog, access to all the
recorded data from both projects was obtained. Figure (2) shows an example of
the created cross-match.

Figure 2: An example of cross-matched images: The background image is an OGLE
image with its sources marked by green circles. The foreground image consists
of GAIA-generated data, where each source is depicted with a velocity vector
for illustration tangential proper motion, scaled up by a factor of $10$. The
source which indicated with black arrows represents gravitational microlensing
event. The source marked with faded red arrows is used for coordinate
calibration.

The search to determine the separation was conducted by analyzing each
individual image. For the OGLE-related images, Gaussian point-spread function
was applied using the DAOstarfinder programming function to identify the light
sources and determine their exact locations. Additionally, vectors
representing the specific velocities in the direction of Right ascension and
Declination were plotted for each light source in the GAIA images. As the OGLE
telescope images were not astrometrically calibrated and only prepared for
photometric measurements, the star with the least specific motion was chosen
as a guide for alignment. This star is indicated in red in the matching
images. Subsequently, each matching image was examined to identify a pattern
similar to Figure (3). The OGLE project recorded a total of about $21000$
gravitational microlensing events between $2002$ and $2022$. In the matching
done by us, $14000$ events were matched successfully.
The OGLE images were expected to show a single light source due to the
separation, but the GAIA images captured several years later revealed two
light sources moving away from each other. These two observed light sources
can be identified as candidates for the source and the lens. Taking into
account that the GAIA telescope had calculated the velocities of both sources,
it became possible to calculate the mass.

Figure 3: What is expected to be observed in image matching is for it to be
considered as separation of lens and lens.

This process was repeated for every event in the OGLE project. However, in
some events where the observation magnitude was over $20$, the matching was
not performed accurately. Ultimately, the collation achieved a $91\%$ accuracy
rate, meaning that $91$ out of $100$ events were correctly matched.
Nonetheless, no separation was observed in the investigation of these events.
Consequently, the data from OGLE is cross-matched with the Hubble data.

After this analyzing GAIA data, we turned to Hubble Space Telescope data in an
attempt to observe the separation between lens and sourve. Given its
exceptional resolution and the availability of its raw data to the public, the
Hubble Space Telescope was a compelling choice for this endeavor. However, due
to its limited field of view, mainly targeting non-stellar light sources, the
telescope observed very few gravitational microlensing events initially
recorded by OGLE in later years.

Observing gravitational microlensing in a single Hubble image does not allow
for direct mass calculation. Instead, it necessitates multiple images captured
in different years to analyze the movement of objects within them and estimate
relative velocities. Consequently, we were able to identify only two
gravitational microlensing events ($OGLE-2014-BLG-0265$ and
$OGLE-2011-BLG-0123$) that Hubble had imaged over different years. A time
series of images related to one of these events is presented in Figure (4).

Figure 4:  This is a time series of images taken by the Hubble Space Telescope
of $OGLE-2014-BLG-0265$. The event reached its maximum brightness on March
$19$, $2014$, with $12$ images captured before the event and $3$ taken after.
However, despite our efforts, we did not identify any significant movement
indicative of the desired separation and there is no other images from this
field of view in Hubble archive.

After examining the Hubble data, we doubted the results of the previous
simulations and decided to do this simulation again to get more accurate
results.

##  4 Lens-Source Simulation

To assess the likelihood of separation visibility in gravitational
microlensing events, given the multitude of kinematic and astrophysical
factors influencing this measurement, we employ the Monte Carlo method to
calculate this probability. This method necessitates deriving the variances of
the various parameters involved and subsequently generating random
gravitational microlensing events based on these parameters.

In our simulation, we assume that gravitational microlensing is initiated by
one source and one lens star. It’s important to note that other celestial
objects, such as black holes, can also play a role in the occurrence of these
events. We further assume the source star’s location in the central bulge of
the Milky Way galaxy, while the lens star is positioned in the galactic disk.

For sampling, we select an area with a 4-degree arc diameter around the bulge
at the galaxy’s center, based on the distribution of observed gravitational
microlensing event coordinates from the OGLE telescope.

Figure 5: A schematic diagram depicting the positions of the three primary
members of this event, along with an explanation of the cylindrical coordinate
system employed.

Subsequently, using GAIA data, we collect information on the distances between
the stars within this region. The spatial distribution of stars in this field
of view obtained from (Moniez et al., 2017). Following this, we apply the
kinematic parameters, the definitions of which are elucidated in Figure (5).
We formulate both a global tangential and a dispersion set of sentences for
these parameters, encompassing the sun, the source star, and the lens star:
$\vec{V}=\vec{V}_{global}+\vec{V}_{dispersion}$.
For the Sun, the global term pertains to $220km/s$ , accompanied by the
dispersion term, representing the Sun’s motion at the speed of $16.5km/s$
towards coordinates defined by $l_{0}=25^{\circ}$ and $b_{0}=53^{\circ}$.
Concerning the lens star located within the galactic disc, the general term
relates to the star’s distance from the galaxy’s center, measured at
$V_{L,\theta}=V_{R_{0},\theta}(\frac{r}{R_{0}})^{\beta}$ with
$V_{R_{0},\theta}=220km/s$ and $R_{0}=8kpc$ distance of sun from center of
galaxy. The dispersion velocities in various directions for lens star located
in galactic disk are as follows:

$\begin{split}&\bar{\sigma}_{r}=39.4\pm 0.3km/s\\\
&\bar{\sigma}_{\theta}=25.21\pm 0.3km/s\\\ &\bar{\sigma}_{z}=21.1\pm
0.2km/s\\\ \end{split}$ (4)

For the source star situated in the galactic bulge, the general velocity is
$V_{S,\theta}=-19km/s$, and the dispersion velocity in all directions remains
consistent at:

$\bar{\sigma}_{r,\theta,z}=104\pm 10km/s\\\ $ (5)

Also, the time interval between the observations of two telescopes was
considered based on the time interval of OGLE and GAIA observations with an
average of $10$ years and a dispersion of $3$ years.

This process led to the computation of equation (2) for each simulated event,
which subsequently facilitated the determination of event separation rates.
Refer to Figure (6) for an illustrative depiction of the separation results
obtained through these simulations.

Figure 6: Normalized distribution of the separation parameter from 1 million
simulation replications

To calculate the probability of observing the separation, various parameters
come into play, including the likelihood of detecting a gravitational
microlensing event and the received brightness from this event.

As outlined by (Alcock et al., 2001), microlensing detection efficiency is
related to Einstein crossing time of the event (i.e $E=E(t_{E})$). To
incorporate this into our simulation, it becomes imperative to assign a
corresponding value related to the mass of the lens stars. We accomplished
this by utilizing Bosanson simulation, and the outcome for disc stars is
depicted in Figure (7).

Figure 7: Stellar mass distribution in galaxy disk based on Besançon Model of
the Galaxy(Robin et al., 2012)

Another important factor in determining the visibility of a gravitational
microlensing event is the apparent brightness of star. Drawing upon the
luminosity of the light sources found in the GAIA catalog and considering
their distances calculated from parallax data, we were able to construct
absolute magnitude for stars in both the galactic disc and bulge.
Consequently, we allocated a brightness proportional to each of the light
sources. The brightness distributions for the source and lens stars are
represented in Figure (8).

Figure 8: Source and Lens brightness magnitude based on absolute magnitude of
stars and distribution of stars distances from observer

##  5 Conclusion

Based on the simulation results (figure(6)), it is evident that a mere
$0.029\%$ of gravitational microlensing events produce a separation exceeding
$50$ milli arc seconds. Out of this fraction, only $24\%$ exhibit a magnitude
below $20$ and can be observed with a reasonable probability from Earth. This
calculation is based on the distribution of event detection interval by OGLE
and data recording of GAIA(average of 10 years with dispersion of 3 years).
Meanwhile, after $5$ years this proportion increase considerably. Events with
over $50$ mac separation will account for $1.18\%$ and over $30.23\%$ of such
events would be visible due to brightness limitation. These values will be
$3.16\%$ and $30.67\%$ for the next $5$ years ($20$ years after microlensing
detection). The corresponding comparison is shown in figure (9) . This implies
that in the coming years, cross-matching the latest observational data with
the OGLE catalog could make it more likely to detect separation between source
and lens. However, with the current data, detection of this phenomenon is very
unlikely. The threshold of $50$ milliseconds of arc, which is just slightly
below the highest resolution of the Hubble Space Telescope, underscores the
considerable challenge in detecting the separation phenomenon, more so than
previously anticipated. This leads to the primary conclusion that the odds of
observing this separation, by combining OGLE and GAIA datasets, appear
exceedingly unlikely. This conclusion is corroborated by the absence of
separations found in the data matching process.

Figure 9: Comparison of separation parameter for 10, 15 and 20 years time
intervals

Similar results were obtained in other research (Bennett et al., 2020). This
study utilized the resolution of a source-lens event to calculate the mass of
the lens, which, in this case, was a star with a Neptunian planet. The
researchers derived the mass ratio from light curves, allowing them to
estimate the mass of both the star and the planet. In their investigation, an
image was captured using the Keck telescope $14$ years after the microlensing
event, revealing a $55$ milliarcsecond separation between the lens and the
star in the final images.

(Delplancke et al., 2001) explored the possibility of observing gravitational
microlensing with VLTI, it becomes evident that the current prospects for
observing the separation phenomenon are predominantly confined to data with
exceptionally high resolutions, such as VLTI and ALMA. It is worth noting that
the observation of separations in radio wavelengths is restricted to cases
where both the source and lens exhibit substantial radio radiation. While
stars like Mira and T-Tauri within the galaxy emit notable radio radiation,
their population remains relatively limited. Previously (Karami et al., 2016)
has studied gravitational microlensing for these objects.

Considering a constant velocity for stars in the Milky way within our
observation time-scale, it is anticipated that observations with extended time
intervals (in the range of $15$ to $20$ years between two observations) in the
upcoming years will significantly elevate the likelihood of observing the
separation phenomenon.
Ultimately, we recommend $60$ events identified as potential candidates for
resolving in gravitational microlensing events in tables 1 and 2. These
selections stem from cross-matching data between GAIA and OGLE, with proper
motion serving as the decisive parameter. we choose $15$ events from OGLEIII
and $45$ from OGLEIV.

## DATA AVAILABILITY

The data underlying this article and cross-match results are available in
Microlensing Separation Detection Repository, at
https://github.com/saeedmozaheb

## References

  * Alcock et al. (1995) Alcock C., et al., 1995, The Astrophysical Journal, 454, L125
  * Alcock et al. (2001) Alcock C., et al., 2001, The Astrophysical Journal Supplement Series, 136, 439
  * Bartelmann & Schneider (2001) Bartelmann M., Schneider P., 2001, Physics Reports, 340, 291
  * Bennett (2008) Bennett D. P., 2008, Exoplanets: Detection, Formation, Properties, Habitability, pp 47–88
  * Bennett et al. (2020) Bennett D. P., et al., 2020, The Astronomical Journal, 159, 68
  * Brown et al. (2021) Brown A. G., et al., 2021, Astronomy & Astrophysics, 649, A1
  * Choi et al. (2012) Choi J.-Y., et al., 2012, The Astrophysical Journal, 751, 41
  * Dehghani & Rahvar (2022) Dehghani A., Rahvar S., 2022, International Journal of Modern Physics D, 31, 2250051
  * Delplancke et al. (2001) Delplancke F., Górski K., Richichi A., 2001, Astronomy & Astrophysics, 375, 701
  * Eddington (1919) Eddington A. S., 1919, The Observatory, Vol. 42, p. 119-122 (1919), 42, 119
  * Einstein (1936) Einstein A., 1936, Science, 84, 506
  * Gaudi (2010) Gaudi B. S., 2010, Exoplanetary Microlensing (arXiv:1002.0332)
  * Golchin & Rahvar (2020) Golchin L., Rahvar S., 2020, Monthly Notices of the Royal Astronomical Society, 494, 584
  * Gould (1994) Gould A., 1994, Arxiv preprint astro-ph/9408032
  * Gould & Yee (2014) Gould A., Yee J. C., 2014, The Astrophysical Journal, 784, 64
  * Karami et al. (2016) Karami M., Broderick A. E., Rahvar S., Reid M., 2016, The Astrophysical Journal, 833, 169
  * Moniez et al. (2017) Moniez M., Sajadian S., Karami M., Rahvar S., Ansari R., 2017, Astronomy & Astrophysics, 604, A124
  * Mróz et al. (2020) Mróz P., et al., 2020, The Astronomical Journal, 159, 262
  * Paczynski (1986) Paczynski B., 1986, The Astrophysical Journal, 304, 1
  * Rahvar (2015) Rahvar S., 2015, International Journal of Modern Physics D, 24, 1530020
  * Rahvar (2020) Rahvar S., 2020, Phys. Rev. D, 101, 024015
  * Rahvar & Dominik (2008) Rahvar S., Dominik M., 2008, in Manchester Microlensing Conference. p. 37
  * Rahvar et al. (2003) Rahvar S., Moniez M., Ansari R., Perdereau O., 2003, Astronomy & Astrophysics, 412, 81
  * Robin et al. (2012) Robin A. C., Reylé C., Marshall D. J., Schultheis M., 2012, in Miglio A., Montalbán J., Noels A., eds, Red Giants as Probes of the Structure and Evolution of the Milky Way. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 171–180
  * Schneider et al. (2006) Schneider P., Kochanek C., Wambsganss J., 2006, Gravitational lensing: strong, weak and micro: Saas-Fee advanced course 33. Vol. 33, Springer Science & Business Media
  * Waagaard (2017) Waagaard E., 2017
  * Wyrzykowski et al. (2016) Wyrzykowski Ł., et al., 2016, Monthly Notices of the Royal Astronomical Society, 458, 3012

##  Appendix A Introducing Candidates

In this section, we introduce gravitational microlensing events in which
separation is more likely to be observed. Based on the cross-match between
GAIA and OGLE catalogs, the proper motion of the events were determined and
the events with proper velocities greater than $mean+3\sigma$ were introduced.

Table 1: Top candidates of resolving in OGLEIII based on proper motion detected by GAIA space telescope. OGLE Name | GAIA ID | $Ra_{deg}$ | $Dec_{deg}$ | $\mu_{(mas/yr)}$ | G Mag a | $t_{E(day)}$
---|---|---|---|---|---|---
2004-BLG-161 | $4062741369288060800$ | $269.62878$ | $-28.180710$ | $36.48\pm 2.30$ | $20.10$ | $5.89\pm 0.47$
2002-BLG-063 | $4067963985105597824$ | $265.62533$ | $-25.159622$ | $24.35\pm 2.61$ | $20.38$ | $13.56\pm 1.29$
2006-BLG-224 | $4062826860616038784$ | $271.58647$ | $-28.195817$ | $22.87\pm 1.21$ | $19.36$ | $1.49\pm 0.03$
2009-BLG-091 | $4056521535135350400$ | $269.14828$ | $-29.388038$ | $20.18\pm 1.34$ | $18.94$ | $39.00\pm 0.64$
2009-BLG-113 | $4044141205918658176$ | $270.40029$ | $-30.722650$ | $20.01\pm 0.46$ | $15.61$ | $14.32\pm 0.46$
2003-BLG-350 | $4068114961855612032$ | $266.09246$ | $-24.571951$ | $19.20\pm 1.08$ | $19.72$ | $14.00\pm 0.44$
2008-BLG-242 | $4062651450009511424$ | $269.47422$ | $-28.131145$ | $18.87\pm 1.03$ | $19.21$ | $13.44\pm 0.07$
2002-BLG-350 | $4041646208000844160$ | $267.68555$ | $-34.087184$ | $17.71\pm 1.25$ | $19.90$ | $24.68\pm 3.64$
2002-BLG-337 | $4042496645812141184$ | $269.33007$ | $-33.511307$ | $17.63\pm 0.59$ | $18.80$ | $12.25\pm 0.23$
2007-BLG-590 | $4043225828379478016$ | $268.67603$ | $-33.162788$ | $17.30\pm 1.75$ | $19.90$ | $10.34\pm 0.50$
2005-BLG-305 | $4056287579617814912$ | $268.67116$ | $-30.072743$ | $17.16\pm 0.77$ | $18.32$ | $13.39\pm 2.84$
2008-BLG-408 | $4062484118116292608$ | $270.16814$ | $-28.506867$ | $17.08\pm 1.43$ | $19.14$ | $70.21\pm 11.41$
2008-BLG-613 | $4062615788792334464$ | $269.13666$ | $-28.519895$ | $17.01\pm 0.66$ | $18.75$ | $45.45\pm 1.18$
2007-BLG-552 | $4050406983474790400$ | $271.58890$ | $-28.839279$ | $16.94\pm 1.06$ | $19.00$ | $11.37\pm 0.23$
2002-BLG-272 | $4118048698256676736$ | $264.69169$ | $-21.111670$ | $16.92\pm 1.45$ | $19.38$ | $2.53\pm 0.18$
a: G-band: Gaia’s white light magnitude (330 - 1050nm) (Brown et al., 2021)
Table 2: Top candidates of resolving in OGLEIV based on proper motion detected by GAIA space telescope. OGLE Name | GAIA ID | $Ra_{deg}$ | $Dec_{deg}$ | $\mu_{(mas/yr)}$ | G Mag a | $t_{E(day)}$
---|---|---|---|---|---|---
2011-BLG-0061 | $4044073173675897472$ | $269.4517017$ | $-30.95517821$ | $112.89\pm 0.17$ | $17.00$ | $882979.269$
2012-BLG-1027 | $5980774811978506624$ | $258.7892033$ | $-30.20803266$ | $37.09\pm 1.06$ | $20.13$ | $2.93\pm 0.082$
2013-BLG-0004 | $4068223121980873600$ | $265.4639788$ | $-24.45023805$ | $34.05\pm 0.62$ | $18.99$ | $15.26\pm 0.386$
2012-BLG-1213 | $4056294455913437696$ | $268.996156$ | $-29.87321965$ | $29.37\pm 0.56$ | $19.14$ | $16.44\pm 0.143$
2013-BLG-0005 | $4041751181184034944$ | $266.9550319$ | $-34.14068047$ | $29.30\pm 1.64$ | $20.35$ | $27.54\pm 0.718$
2012-BLG-0853 | $4057401178708838016$ | $267.7557356$ | $-28.70658233$ | $29.22\pm 0.05$ | $15.97$ | $0.78\pm 0.015$
2017-BLG-1044 | $4044201683435491200$ | $269.9074331$ | $-30.59145968$ | $26.69\pm 0.36$ | $18.44$ | $0.88\pm 0.029$
2014-BLG-1679 | $4062577851300138240$ | $269.6969118$ | $-28.65232268$ | $25.28\pm 1.72$ | $19.43$ | $9.87\pm 0.374$
2018-BLG-1730 | $4063532472163597568$ | $269.0610067$ | $-27.70846212$ | $24.24\pm 0.88$ | $20.00$ | $4.33\pm 0.274$
2016-BLG-0282 | $4041419055751492224$ | $267.168099$ | $-35.57943674$ | $24.20\pm 0.96$ | $18.63$ | $18.86\pm 0.074$
2013-BLG-0006 | $4062593935921180416$ | $269.7644697$ | $-28.4206839$ | $24.14\pm 0.68$ | $16.67$ | $32.54\pm 0.146$
2015-BLG-0620 | $4043398936841900544$ | $268.0827489$ | $-33.17631868$ | $23.57\pm 1.53$ | $19.65$ | $24.639\pm 0.84$
2011-BLG-0473 | $4062777619010136448$ | $270.1510563$ | $-27.77020718$ | $23.56\pm 1.49$ | $19.50$ | $6.809\pm 0.048$
2017-BLG-0381 | $4041474374998087040$ | $267.4616912$ | $-34.92498384$ | $23.35\pm 2.11$ | $19.80$ | $72.284\pm 3.16$
2015-BLG-1024 | $4043382199512780160$ | $269.4345185$ | $-32.26154717$ | $23.18\pm 1.37$ | $19.79$ | $23.833\pm 1.614$
2022-BLG-0060 | $4056327162008855680$ | $269.2863419$ | $-29.63845511$ | $21.87\pm 0.08$ | $16.24$ | $16.371\pm 0.56$
2017-BLG-0318 | $4043712052876957824$ | $270.4078286$ | $-32.17890951$ | $21.62\pm 1.22$ | $19.80$ | $3.962\pm 0.144$
2022-BLG-0260 | $4061103547960320512$ | $265.6300101$ | $-26.40105123$ | $20.91\pm 2.16$ | $20.43$ | $44.253\pm 1.486$
2017-BLG-1537 | $4041936857013164800$ | $266.8620549$ | $-33.46353572$ | $20.88\pm 0.43$ | $19.05$ | $11.104\pm 0.201$
2019-BLG-0239 | $4056491680794776704$ | $268.6880389$ | $-29.61538108$ | $20.35\pm 1.06$ | $18.93$ | $24.769\pm 0.225$
2014-BLG-1739 | $4043201673345585664$ | $268.1079637$ | $-33.45638128$ | $20.09\pm 1.66$ | $19.67$ | $9.78\pm 0.103$
2012-BLG-1393 | $4063554462406705536$ | $269.492422$ | $-27.45635038$ | $19.93\pm 1.00$ | $18.30$ | $23.934\pm 0.745$
2013-BLG-0008 | $4050954089398508672$ | $272.758165$ | $-27.86918009$ | $19.82\pm 0.68$ | $18.59$ | $9.195\pm 0.185$
2016-BLG-0542 | $4064909507432758272$ | $271.8802831$ | $-25.57526051$ | $19.75\pm 0.97$ | $19.33$ | $12.965\pm 0.668$
2016-BLG-1651 | $4060489161450409600$ | $263.9847059$ | $-28.19889371$ | $19.73\pm 1.42$ | $19.83$ | $30.632\pm 1.46$
2013-BLG-0010 | $4041939915021368576$ | $266.9596781$ | $-33.31566796$ | $19.55\pm 0.99$ | $19.54$ | $20.842\pm 0.762$
2011-BLG-0362 | $4062745531088556288$ | $269.5724639$ | $-28.0996355$ | $19.35\pm 0.78$ | $17.87$ | $22.542\pm 0.449$
2011-BLG-0945 | $4062675059292894464$ | $269.8576718$ | $-28.43470195$ | $19.28\pm 0.20$ | $17.73$ | $8.58\pm 0.115$
2017-BLG-1525 | $4065693802815477888$ | $271.8022592$ | $-24.99892613$ | $19.03\pm 0.40$ | $18.89$ | $6.637\pm 0.414$
2018-BLG-0810 | $4062612833786281088$ | $269.0584278$ | $-28.62470256$ | $18.89\pm 0.49$ | $17.56$ | $0.661\pm 0.015$
2018-BLG-1740 | $4055765139815537792$ | $267.945982$ | $-30.92866272$ | $18.84\pm 1.38$ | $19.51$ | $21.816\pm 0.403$
2014-BLG-2015 | $4041389682454535168$ | $265.8254412$ | $-34.72022203$ | $18.47\pm 2.14$ | $20.24$ | $46.945\pm 7.705$
2012-BLG-0054 | $4063305178372953088$ | $271.1995579$ | $-26.79606505$ | $18.38\pm 1.10$ | $18.77$ | $17.928\pm 0.086$
2019-BLG-1117 | $4056219100786930816$ | $269.0217936$ | $-30.30468202$ | $18.31\pm 0.36$ | $18.30$ | $22.201\pm 0.17$
2012-BLG-0790 | $4056616372275423360$ | $268.5480385$ | $-28.72121258$ | $18.28\pm 0.60$ | $17.98$ | $8.752\pm 0.168$
2018-BLG-0603 | $4061951855541710080$ | $265.0064516$ | $-25.56900354$ | $18.28\pm 0.70$ | $19.40$ | $7.902\pm 0.582$
2014-BLG-0095 | $4062332286515948928$ | $269.7500704$ | $-29.27495509$ | $18.26\pm 1.00$ | $18.68$ | $11.246\pm 0.214$
2016-BLG-0728 | $4061874443077112320$ | $265.4572736$ | $-25.94042816$ | $18.25\pm 0.61$ | $18.38$ | $9.225\pm 0.095$
2015-BLG-1362 | $4041546225426345088$ | $266.9678953$ | $-34.58893805$ | $18.05\pm 1.44$ | $19.66$ | $121.285\pm 22.763$
2013-BLG-0011 | $4117984960891575424$ | $264.2843569$ | $-21.85027407$ | $18.05\pm 2.25$ | $20.21$ | $55.929\pm 2.105$
2012-BLG-0390 | $4062800193314792832$ | $269.7567579$ | $-27.53970982$ | $17.86\pm 0.41$ | $18.82$ | $19.24\pm 0.518$
2015-BLG-0198 | $4067954330017995008$ | $265.4848581$ | $-25.34528433$ | $17.62\pm 0.18$ | $17.74$ | $96.649\pm 5.95$
2019-BLG-0672 | $4050420860487572352$ | $271.2847121$ | $-28.84668324$ | $17.60\pm 1.17$ | $18.98$ | $12.122\pm 0.112$
2011-BLG-0882 | $4041466128651375744$ | $267.6340073$ | $-35.02864029$ | $17.42\pm 1.88$ | $19.79$ | $9.651\pm 0.657$
2013-BLG-0013 | $4056250544149378944$ | $269.5584665$ | $-30.0362847$ | $17.41\pm 1.86$ | $19.61$ | $3.156\pm 0.063$
a: G-band: Gaia’s white light magnitude (330 - 1050nm) (Brown et al., 2021)