A Close Binary Lens Revealed by the Microlensing Event Gaia20bof

Gaia's photometric measurements consist of a wide G band (Jordi et al. 2010) obtained with roughly monthly cadence while Gaia scans the sky. The photometry is publicly available on the GSA web page (Hodgkin et al. 2021). We used the procedure described in Kruszyńska et al. (2022) to obtain the photometric errors of the 163 measurements used in this study.

The OMEGA Key Project is an international collaboration that performs automatic follow-up of microlensing events detected by large-sky surveys. The primary goal is the characterization of cold planets and stellar remnants in the entire sky. Microlensing candidates are first collected from various channels, including from GSA, in the Microlensing Observing Platform (MOP). ²⁵ The MOP system is a Target and Observation Manager, or TOM system, built with the TOM Toolkit package (Street et al. 2018). As soon as data are available, this system automatically fits a single lens model (including microlensing parallax; see, for example, Gould 2004) to all of the data available for each event, using the pyLIMA modeling software (Bachelet et al. 2017). Typically, there are more potential targets at any given time than there are telescope resources to observe them and it is therefore necessary to prioritize targets. MOP incorporates an algorithm that prioritize targets based on their position in the sky and their current status (Hundertmark et al. 2018). For instance, events located toward the Galactic bulge (255° ≤ α ≤ 275° and −36° ≤ δ ≤ –22°) are observed only if they are sufficiently sensitive to planets according to Hundertmark et al. (2018). This is motivated by the fact that this region is regularly monitored by Optical Gravitational Lensing Experiment, Microlensing Observations in Astrophysics, and Korea Microlensing Telescope Network surveys. Otherwise, higher-cadence imaging and spectroscopic observations are requested automatically by the MOP system, tailored to current parameters and phase of the evolution of each event (∼ daily). Most of the observations are collected via the Las Cumbres Observatory (LCO) automatic robotic telescopes network (Brown et al. 2013). The observing strategy consists of regular monitoring of the event in two bands, namely SDSS-g' and SDSS-i' (with the exception of events located toward the Galactic bulge, where the SDSS-g' band is replaced by the SDSS-r' band, due to the higher extinction in these fields), with a cadence depending of the event priority and Einstein ring crossing time t_E. Observing in two bands serves two primary purposes. First, it measures the chromaticity of ongoing events. Indeed, microlensing events are achromatic phenomena (to first order) and therefore the color evolution contributes to exclude astrophysical false-positive detections (such as Be stars) but also helps to distinguish between microlensing models (namely, the double source/double lens scenario; see below). Second, as emphasized by Yoo et al. (2004), observations in (at least) two bands allow the estimation of the angular source radius, a key component in estimating the mass of the lenses. We note that the cadence in the SDSS-i' band is twice that of the other bands in order to increase the sampling of the lightcurve. If at any given time, models predict a high planet sensitivity (during a high magnification event, for example; Hundertmark et al. 2018), a 15 minutes cadence mode is triggered for the next 48 hr to ensure that any potential anomalies are well sampled. If a target is predicted to exceed a brightness threshold of 17 mag, several low-resolution spectra (R ∼ 1000) using the FLOYDS instruments (Brown et al. 2013) are also requested, to help with the source characterization (see, for example, Fukui et al. 2019) as well as to classify contaminants in the alerts stream, such young stellar objects. If the event gets bright enough (i.e., V ≤ 11 mag), high-resolution NRES spectra (R ∼ 55,000) Siverd et al. 2018) can also be triggered to obtain a precise estimation of the source spectral parameters, such as in the event Gaia19bld (Bachelet et al. 2022).

As listed in Table 1, hundreds of images have been collected in the SDSS-g' and SDSS-i' bands, from La Silla in Chile (LSC), Siding Spring in Australia (COJ), and the South African Astronomical Observatory in South Africa (CPT) LCO sites. Some of these images come from precursor observing programs prior to OMEGA. We note that, with the exception of the LSC site that remained closed for a long time, the COVID-19 pandemic only mildly impacted this observing program at LCO.

The target has been followed up photometrically with a network of small telescopes under the umbrella of the OPTICON-RadioNET Pilot program of the European Commission, e.g., Wyrzykowski et al. (2020). For Gaia20bof we used LCO, TRT, and Skynet's PROMPT-MO and PROMPT5 telescopes; the summary of these observations is gathered in Table 1.

TRT stands for Thai Robotic Telescopes, a 0.7 m telescope equipped with Andor iKon-L DW936 BV CCD camera with resolution 08 pixel⁻¹. The telescope is located at 259304 west and 266955 north.

PROMPT-MO is a 0.4 m RC telescope equipped with Apogee USB CCD with resolution 0598 pixel⁻¹. The telescope is located at 243011 west and 31638 south in the Meckering Observatory, Australia.

PROMPT5 is another Skynet Network telescope and is a Ritchey–Chretien 0.41 m telescope operating using Apogee CCD camera at 08 pixel⁻¹ resolution. The telescope is located in CTIO Chile at 708053889 west and 301676389 south.

We collected two spectra during the course of the event: one is from 10 m SALT (Buckley et al. 2006) equipped with the Robert Stobie Spectrograph (Burgh et al. 2003; Kobulnicky et al. 2003), and the second is from the X-Shooter instrument (Vernet et al. 2011) mounted on the ESO 8 m Very Large Telescope (VLT).

The SALT/RSS low-resolution spectrum was obtained on 2020 June 6 (JD ∼ 2459006) at event magnification ∼1.8, ²⁶ with the exposure time 600 s. The longslit mode was used with the slit width 15, grating pg0300. The wavelength range of the obtained spectrum covers 370–930 nm giving the resolving power R ∼ 350 and average signal-to-noise ratio S/N = 160. It has been reduced in a standard way using PySALT ²⁷ software (bias subtraction and flat-field correction; Crawford et al. 2010) and then wavelength and flux calibration was applied using standard IRAF routines thanks to having calibrating data for Ar comparison lamp and spectrophotometric standard star.

The VLT/X-Shooter spectrum was obtained at the baseline of the microlensing event on 2022 January 7 ²⁸ for three wavelength channels: UVB (300–559.5 nm), VIS (559.5–1024 nm) and NIR (1024−2480 nm). We integrated with 191, 220, and 300 s of exposure time for the UVB, VIS, and NIR channel, respectively. The resolution of this spectrum is R ∼ 10000 in UVB part (at slit width 10) and R ∼ 15000 in VIS (at slit width 07) and NIR (at slit width 06) parts, on average. It has been reduced with the dedicated EsoReflex ²⁹ pipeline (v. 2.9.1). For the calibration of UVB, VIS wavelengths, ThAr lamp was used, while for NIR—a set of Ar, Hg, Ne, and Xe lamps. Due to the poor quality of some spectral ranges and low S/N, only the parts between 350–552 nm, 560–745 nm, 780–914 nm and 1133–1350 nm, 1450–1800 nm, 1950–2356 nm were used in further analysis.

The follow-up observations were reduced using the black hole TOM (BHTOM) infrastructure, ³⁰ which utilized CCDPhot suite of image processing and CPCS photometry calibration tools (Zieliński et al. 2019, 2020). The photometry was calibrated to the Gaia Synthetic Photometry catalog Gaia synthetic SDSS magnitudes (Montegriffo et al. 2023). We note that the magnitudes are in the AB system (Oke & Gunn 1983).

As can be seen in Figure 1, the OMEGA follow-up data clearly reveal an anomaly around JD ∼ 2458970. First, we explored the binary lens versus the binary source interpretation (Dominik et al. 2019) and found that the latter can be safely ruled out because of the high χ² value (about 2 times higher than the binary lens solutions). However, the anomaly is mild, with no clear sign of a caustic crossing and looks similar to the approach of a Chang–Refsdal lens (Chang & Refsdal 1979). Such lightcurves are notoriously known for presenting strong degeneracies in terms of lens geometries (see, for instance, Dominik 1999; Han & Gaudi 2008; Shvartzvald et al. 2016; Bozza et al. 2016), implying that several models can reproduce the observations accurately, which is exactly the case here. A binary model is parameterized by the time t₀ of the minimum impact parameters u₀ relative to the center of mass of the binary lens. The angular Einstein ring radius crossing time is defined as ${t}_{{\rm{E}}}=\tfrac{{\theta }_{{\rm{E}}}}{{\mu }_{\mathrm{rel}}}$, where μ_rel is the (geocentric) relative proper motion. We also considered ρ = θ_⋆/θ_E, the normalized source radius where θ_* is the angular source radius, in the models, but this parameter is not constrained in the present case, because the source trajectories are far from the caustic. For this reason, we did not consider limb-darkening effects. The models also include the normalized angular projected separation between the two components of the lens s, and their mass ratio q. Finally, the angle between the lens trajectory and the binary axes is defined by α (counterclockwise). Because of the event duration (t_E ≥ 50 days), we also consider the microlensing parallax vector π _E = (π_EN, π_EE) (Gould 2004) and set the time of reference t_0,par = t₀ for all models. The norm of the parallax vector is directly related to the lens and source distances via

$$\begin{eqnarray}&&| | {{\boldsymbol{\pi }}}_{{\bf{E}}}| | =\displaystyle \frac{{\pi }_{{LS}}}{{\theta }_{E}}\end{eqnarray} \tag{ 1 }$$

with π_LS = 1/D_l − 1/D_s , while the parallax vector is colinear to the lens-source relative proper motion projected in the north–east plane of the sky. The first steps of modeling have been done using the RTModel infrastructure, ³¹ which located eight minima. We refine these solutions with a Monte Carlo Markov Chain (MCMC) exploration on each of them as reported in Table 2. The posterior exploration has been performed with the updated version 2.0 of pyLIMA (Bachelet et al. 2017), which maximizes the total log-likelihood ${ \mathcal L }$:

$$\begin{eqnarray}&&{ \mathcal L }=-0.5\displaystyle \sum _{n=1}^{{N}_{\mathrm{telescopes}}}\displaystyle \sum _{t=1}^{{N}_{\mathrm{data}}}\left[\displaystyle \frac{{\left({f}_{n,t}-{m}_{n,t}\right)}^{2}}{{\sigma }_{n,t}^{2}}+\mathrm{ln}(2\pi {\sigma }_{n,t}^{2})\right],\end{eqnarray} \tag{ 2 }$$

where N_telescopes is the total number of telescopes, N_data is the total number of photometric observations of a given telescope, σ_t are the uncertainties associated with the measured flux f_t at the time t, and m_t is the corresponding microlensing model flux. Version 2.0 of pyLIMA introduces the option of rescaling the flux uncertainties σ_i,t of each telescope i during the MCMC exploration using

$$\begin{eqnarray}&&{\sigma }_{i,t}^{{\prime} }={10}^{{k}_{i}}{\sigma }_{i,t}.\end{eqnarray} \tag{ 3 }$$

A detailed presentation of the new features available with the latest release of pyLIMA will be the subject of a separate paper (E. Bachelet et al. 2024, in preparation). The MCMC exploration is performed with the emcee package (Foreman-Mackey et al. 2013) with a fixed number of 10,000 chains and 32 walkers. The convergence of the chains have been analyzed separately for each model. A summary of the best-fitting models found is displayed in Table 2, and the best model is presented in Figure 1. For each parameter set, the 16, 50 and 84 percentiles of the chains are shown. We note that the reported χ² values for each model are obtained from a gradient fit started at the best MCMC chain position (and includes the rescaled uncertainties obtained from the chains). The Wide+ model (i.e., s ≥ 1) is currently slightly favored and points toward a stellar binary lens interpretation, but the planetary companion scenario remains possible at this time.

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Table 2. Best Models from the Modelling of the Lightcurves

Parameters	Unit	CloseB-	CloseB+	CloseP-	CloseP+	Resonant-	Resonant+	Wide-	Wide+
t0	JD	${2458971.83}_{-0.17}^{+0.16}$	${2458971.90}_{-0.17}^{+0.23}$	${2458969.458}_{-0.075}^{+0.074}$	${2458969.360}_{-0.068}^{+0.068}$	${2458969.427}_{-0.053}^{+0.066}$	${2458969.342}_{-0.065}^{+0.069}$	${2458827.7}_{-59.9}^{+63.5}$	${2458847.2}_{-4.2}^{+9.7}$
u0		$-{0.2744}_{-0.0093}^{+0.0085}$	${0.2552}_{-0.0073}^{+0.0065}$	$-{0.29}_{-0.03}^{+0.03}$	${0.225}_{-0.010}^{+0.012}$	$-{0.306}_{-0.015}^{+0.014}$	${0.254}_{-0.012}^{+0.011}$	$-{0.12}_{-0.02}^{+0.02}$	${1.66}_{-0.10}^{+0.11}$
tE	days	${56.6}_{-1.5}^{+1.2}$	${63.9}_{-1.2}^{+1.6}$	${55.0}_{-2.6}^{+3.0}$	${67.9}_{-2.2}^{+1.8}$	${53.9}_{-1.9}^{+1.9}$	${69.9}_{-2.5}^{+3.2}$	${492.7}_{-98.9}^{+174.5}$	${133.8}_{-3.8}^{+3.7}$
ρ		${0.038}_{-0.026}^{+0.031}$	${0.017}_{-0.014}^{+0.024}$	${0.15}_{-0.08}^{+0.02}$	${0.055}_{-0.024}^{+0.019}$	${0.1808}_{-0.0068}^{+0.0067}$	${0.064}_{-0.030}^{+0.019}$	${0.015}_{-0.014}^{+0.015}$	${0.037}_{-0.020}^{+0.014}$
s		${0.4178}_{-0.0060}^{+0.0075}$	${0.4327}_{-0.0054}^{+0.0065}$	${0.661}_{-0.103}^{+0.047}$	${0.586}_{-0.013}^{+0.017}$	${1.013}_{-0.023}^{+0.029}$	${1.424}_{-0.037}^{+0.033}$	${3.604}_{-0.044}^{+0.043}$	${4.082}_{-0.076}^{+0.075}$
q		${1.05}_{-0.09}^{+0.11}$	${0.84}_{-0.08}^{+0.07}$	${0.025}_{-0.007}^{+0.018}$	${0.0374}_{-0.0031}^{+0.0029}$	${0.0181}_{-0.0017}^{+0.0025}$	${0.0475}_{-0.0032}^{+0.0035}$	${0.770}_{-0.043}^{+0.053}$	${1.40}_{-0.12}^{+0.12}$
α	rad	${0.911}_{-0.020}^{+0.018}$	${5.368}_{-0.024}^{+0.019}$	${1.643}_{-0.005}^{+0.006}$	${4.6527}_{-0.0037}^{+0.0039}$	${1.6452}_{-0.0050}^{+0.0044}$	${4.6517}_{-0.0037}^{+0.0046}$	${0.209}_{-0.099}^{+0.071}$	${5.155}_{-0.012}^{+0.021}$
πEN		${0.368}_{-0.016}^{+0.015}$	${0.227}_{-0.010}^{+0.013}$	${0.333}_{-0.024}^{+0.022}$	${0.25}_{-0.01}^{+0.01}$	${0.341}_{-0.013}^{+0.013}$	${0.243}_{-0.010}^{+0.011}$	${0.059}_{-0.040}^{+0.025}$	${0.082}_{-0.008}^{+0.013}$
πEE		$-{0.346}_{-0.013}^{+0.016}$	$-{0.353}_{-0.012}^{+0.014}$	$-{0.40}_{-0.02}^{+0.02}$	$-{0.320}_{-0.013}^{+0.014}$	$-{0.408}_{-0.020}^{+0.021}$	$-{0.311}_{-0.014}^{+0.015}$	$-{0.2894}_{-0.0095}^{+0.0088}$	$-{0.306}_{-0.011}^{+0.011}$
${ \mathcal L }$		−6048	−6050	–6052	−6056	−6048	−6057	−6062	−6044
χ2/dof		720/692	726/692	707/692	721/692	709/692	707/692	723/692	703/692
GS		${15.905}_{-0.050}^{+0.043}$	${16.005}_{-0.037}^{+0.043}$	${15.87}_{-0.11}^{+0.11}$	${16.152}_{-0.071}^{+0.057}$	${15.821}_{-0.075}^{+0.074}$	${16.156}_{-0.073}^{+0.091}$	${16.095}_{-0.057}^{+0.076}$	${16.052}_{-0.043}^{+0.044}$
GB		${18.18}_{-0.29}^{+0.51}$	${17.60}_{-0.17}^{+0.17}$	${18.1}_{-0.5}^{+1.3}$	${17.1}_{-0.1}^{+0.2}$	${18.8}_{-0.7}^{+1.1}$	${17.1}_{-0.2}^{+0.2}$	${17.29}_{-0.20}^{+0.19}$	${17.44}_{-0.14}^{+0.17}$
gS		${17.055}_{-0.048}^{+0.037}$	${17.129}_{-0.034}^{+0.039}$	${17.02}_{-0.11}^{+0.11}$	${17.265}_{-0.067}^{+0.056}$	${16.960}_{-0.071}^{+0.072}$	${17.267}_{-0.068}^{+0.086}$	${17.237}_{-0.050}^{+0.066}$	${17.209}_{-0.042}^{+0.043}$
gB		${19.22}_{-0.23}^{+0.41}$	${18.80}_{-0.15}^{+0.18}$	${19.3}_{-0.5}^{+1.2}$	${18.4}_{-0.1}^{+0.2}$	${20.0}_{-0.7}^{+1.1}$	${18.4}_{-0.2}^{+0.2}$	${18.36}_{-0.14}^{+0.14}$	${18.51}_{-0.15}^{+0.15}$
iS		${15.435}_{-0.048}^{+0.037}$	${15.510}_{-0.034}^{+0.039}$	${15.40}_{-0.11}^{+0.11}$	${15.645}_{-0.067}^{+0.056}$	${15.340}_{-0.071}^{+0.072}$	${15.648}_{-0.068}^{+0.086}$	${15.616}_{-0.051}^{+0.066}$	${15.589}_{-0.042}^{+0.043}$
iB		${17.25}_{-0.17}^{+0.28}$	${16.93}_{-0.12}^{+0.14}$	${17.41}_{-0.46}^{+0.98}$	${16.56}_{-0.12}^{+0.16}$	${17.89}_{-0.53}^{+0.91}$	${16.56}_{-0.17}^{+0.17}$	${16.58}_{-0.13}^{+0.12}$	${16.70}_{-0.12}^{+0.12}$
θ*	μas	5.5 ± 0.2	5.3 ± 0.2	5.1 ± 0.2	5.4 ± 0.2	5.1 ± 0.2	5.0 ± 0.2	5.5 ± 0.2	5.0 ± 0.2

Notes. The microlensing parameters and errors corresponds to the 16, 50, and 84 percentiles of the MCMC chains. The χ² corresponds to the maximum likelihood and are based on rescaled uncertainties rescaling.

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Based on the low-resolution SALT/RSS spectrum we were able to classified the source as a reddened GK-type star (Ihanec et al. 2020). Data show the stellar spectrum with only absorption lines; therefore, the changes of the brightness of Gaia20bof could be explained by the gravitational microlensing phenomenon. Therefore, we decided to continue with extensive photometric follow-up monitoring of Gaia20bof event.

The high-resolution spectrum from X-Shooter has been used for determining of the atmospheric parameters, i.e., effective temperature T_eff, surface gravity $\mathrm{log}g$ and metallicity [M/H], of the source star. It was possible thanks to a spectral line fitting method by using iSpec ³² package (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019). We used the SPECTRUM ³³ radiative transfer code to generate a set of synthetic spectra based on a grid of MARCS models (Gustafsson et al. 2008), solar abundances taken from Grevesse et al. (2007) and line list with atomic data from Gaia-ESO Survey (GESv6; Heiter et al. 2021). The GESv6 line list covers the wavelength range from 420 to 920 nm so this method uses only UVB and VIS part of the X-Shooter spectrum. The best-matching fit was found for the following parameters: T_eff = (5533 ± 89) K, $\mathrm{log}g\,=(3.54\pm 0.19)$, [M/H] = (–0.51 ± 0.07) dex, and is presented together with the observational X-Shooter data in Figure 2.

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Moreover, both spectra have been modeled with a template matching method using Spyctres, similarly to Bachelet et al. (2022) and Bachelet (2024). The latest version of Spyctres includes an update of the extinction law from Wang & Chen (2019). Briefly, we modeled the two spectra using the stellar template library from Kurucz (1993) as well as the spectral energy distribution at the time of spectra acquisition, including the source magnification A(t). This allows an accurate flux calibration and ultimately the estimation of A_V and the stellar parameters. With this method, the final solution for the source star parameters was found as T_eff = (5297 ± 30) K, $\mathrm{log}g=({3.50}_{-0.25}^{+0.30})$, $[{\rm{M}}/{\rm{H}}]=(\mbox{--}{0.7}_{-0.1}^{+0.3})$ dex, together with the line-of-sight extinction in the V band: ${A}_{V}={1.55}_{-0.04}^{+0.03}$ mag.

Both spectra and the results of template matching are visible in Figure 3 while the modeling results are displayed in Table 3. The results obtained in spectroscopic analysis are in good agreement with the measurements from the GaiaDR3 release, where T_eff = (5434 ± 16) K, $\mathrm{log}g=(3.53\pm 0.02)$, and [M/H] = (–0.520 ± 0.001) dex (GaiaDR3 6054150372473485696; Gaia Collaboration et al. 2016, 2023).

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Table 3. Summary of the Source Properties from the Spectral Analysis and GaiaDR3

Parameter	Template matching	Line fitting	GaiaDR3
AV (mag)	${1.55}_{-0.04}^{+0.03}$	⋯	⋯
Teff (K)	5297 ± 30	5533 ± 89	5434 ± 16
${\rm{log}}\,g$ (cgs)	${3.50}_{-0.25}^{+0.30}$	3.54 ± 0.19	3.53 ± 0.02
[M/H] (dex)	$-{0.7}_{-0.1}^{+0.3}$	−0.51 ± 0.07	−0.520 ± 0.001

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Using the derived parameters and the PARSEC stellar isochrones ³⁴ (Bressan et al. 2012), we found that the source is most likely an old subgiant of G2 spectral type, as can be seen in Figure 4. Combining the source luminosity, the source apparent magnitude in the G band and the extinction law derived from spectral analysis, we found that the source angular radius θ_* = 5.4 ± 0.2 μas is independent of the source age and distance. We note that the angular radius value is also confirmed by the color–radius relation from Boyajian et al. (2014) with θ_* = 5.2 ± 0.2 μas (see Table 2).

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Based on the stellar isochrones, the extinction obtained from the spectra fits and assuming the source magnitude G = (16.00 ± 0.05) mag, we estimated the source distance to be ${D}_{{\rm{S}}}={2.1}_{-0.2}^{+0.5}\,\mathrm{kpc}$, as can be seen in the right panel of Figure 4. We note that using different source magnitude bands (like SDSS-i') and models leads us to similar conclusion.

Moreover, assuming the typical absolute magnitude M_V = (3.0 ± 0.3) mag (Straižys 1992) for metal-poor G2-type subgiant, we also calculated the distance to the source analytically. This way, we obtained the value of D_S =(1.95 ± 0.35) kpc.

These estimates are in excellent agreement with the parallax measurements from Gaia: ${D}_{{\rm{S}}}={2.33}_{-0.02}^{+0.03}\,\mathrm{kpc}$ (distance_gspphot). ³⁵ In addition, the value of the distance inferred for the Gaia20bof parallax published in GaiaDR2 (Bailer-Jones et al. 2018) is ${D}_{{\rm{S}}}={4.32}_{-1.81}^{+2.94}\,\mathrm{kpc}$, while the updated value for the parallax published in GaiaEDR3 assuming geometric and photogeometric approach (Bailer-Jones et al. 2021) is D_S = 2.18 ± 0.15 kpc and ${D}_{{\rm{S}}}={2.14}_{-0.14}^{+0.15}\,\mathrm{kpc}$, respectively. All of these values, except the GaiaDR2 distance, are also in good agreement with the one obtained by us. Therefore, we decided to use the final source distance as ${D}_{{\rm{S}}}={2.1}_{-0.3}^{+0.5}\,\mathrm{kpc}$, from the spectra analysis. We note that at this distance, the galactic coordinates of the source are $(x,y,z)\,=({0.98}_{-0.15}^{+0.29},-{1.74}_{-0.52}^{+0.26},-{0.03}_{-0.00}^{+0.01})$ kpc, which coincides with an overdensity of stars measured by Gaia (Gaia Collaboration et al. 2023).

The next data release from the Gaia Mission (DR4; ∼2025), will include astrometric time series that will help constrain the models. While the photometric lightcurves are almost identical for all of the models, the astrometric microlensing signals (Walker 1995; Dominik & Sahu 2000) can differ significantly. In Figure 5 we show the astrometric microlensing signals as seen by Gaia for the eight models presented, assuming θ_E = 1 mas. It is clear that the exquisite astrometric precision of Gaia will allow the selection of the most plausible model (or, at least, eliminate most of them) as well as measuring θ_E. This has already been done for the event Gaia16aye (Wyrzykowski et al. 2020), ³⁶ which is similar in brightness to Gaia20bof, but presents more caustic crossing features. In the case of Gaia16aye, the early access to the astrometric time series confirmed both the microlensing model and the angular Einstein ring radius measurement of ∼3 mas.

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By directly measuring the lens fluxes and/or the relative proper motions, high-resolution imagers have been able to place strong constraints on microlensing systems; see, for example, Beaulieu (2018), Bhattacharya et al. (2018), and Vandorou et al. (2020). In the case of Gaia20bof, high-resolution imaging will also bring new constraints. First, the models predict different blend magnitudes in different bands, as listed in Table 2. A direct measurement of the lens flux, as well as a better analysis of the blend, will limit the number of possible scenarios. Moreover, the lens/source relative proper motions are significantly different between the models. Indeed, given that π _E = π_E μ_LS the (geocentric) relative proper motion can be written as (Gould 2004)

$$\begin{eqnarray}&&\displaystyle \frac{{{\boldsymbol{\mu }}}_{{\bf{LS}}}}{{\theta }_{{\rm{E}}}}=\displaystyle \frac{1}{{t}_{E}}\displaystyle \frac{{{\boldsymbol{\pi }}}_{{\bf{E}}}}{{\pi }_{E}}.\end{eqnarray} \tag{ 4 }$$

All models predict different timescales t_E and parallax vectors π _E (especially the Wide models). Therefore, observations of the lens and the source at different epochs will discriminate between models and ultimately provide a measurement of θ_E (Vandorou et al. 2020). Assuming a typical value of θ_E ∼ 1 mas, high-resolution observations could start in about 5 yr, with a lens and source separation δ ≥ 10 mas for all models except Wide-.

As soon as the lens and source separate, it will be possible to conduct radial-velocity follow-up of the host that should lead to the full characterization of the system in combination with the two methods described previously. The radial-velocity monitoring of microlensing lenses is challenging, due to the faintness of the host. However, it has been done in the past on at least two occasions. Yee et al. (2016) used the Keck High-resolution Echelle Spectrometer (Vogt et al. 1994) and the Magellan Inamori Kyocera Echelle spectrometer (Bernstein et al. 2003) to measure the radial-velocity signal of the host of the microlensing event OGLE-2009-BLG-020 (Skowron et al. 2011). Their data confirms and refine the stellar binary parameters from the original publication. A second radial-velocity test has been made by Boisse et al. (2015) on the microlensing predictions of OGLE-2011-BLG-0417 (Shin et al. 2012). In this case, Boisse et al. (2015) did not measure any modulations in the radial velocity of the host, indicating strong tensions with the microlensing models later confirmed by high-resolution imaging (Santerne et al. 2016). Ultimately, Bachelet et al. (2018) identified a competitive microlensing model that explains the lack of modulations. In the case of Gaia20bof, radial-velocity observations will be challenging, as the lens cannot be brighter than the measured blend (ib ≤ 18 mag). However, it could be done with the most recent spectrographs, such as ESO ESPRESSO (Pepe et al. 2021).