OGLE-2019-BLG-1180Lb: Discovery of a Wide-orbit Jupiter-mass Planet around a Late-type Star

As of 2023 April 10, 5332 ¹³ exoplanets have been detected by various detection methods including transit, radial velocity, microlensing, and imaging. Out of them, 95% have been detected by transit and radial velocity methods, in which their host stars are mostly Sun-like stars and they are almost all located inside the snow line of the stars, which represents the distance where the water can form ice grains in the protoplanetary disk (Kennedy & Kenyon 2008). This is because the two methods depend on the brightness of stars and are advantageous in detecting close-in planets of the stars. By contrast, microlensing is sensitive to planets around faint low-mass objects such as M dwarfs and brown dwarfs. This is because the microlensing relies on the mass of objects, not their brightness. As a result, microlensing exoplanets are almost all located beyond the snow line of their host stars and about 70% ¹⁴ of the host stars are faint M-dwarf stars. Recently, Shin et al. (2023a) showed that M-dwarf host stars with M < 0.3 M_⊙ detected by microlensing commonly have massive planets with >0.3 M_J, whereas for transit and radial velocity such massive planets are sparse in spite of high detection efficiency (see Figure 12 of Shin et al. 2023a), which suggests that the formation of massive planets around low-mass M dwarfs is not challenging. Therefore microlensing samples are very crucial to constrain planet formation theories, including core accretion and disk instability, which were constructed based on our solar system and modified by observed exoplanetary systems. In addition, microlensing exoplanets are distributed in a wide range of distances from the Sun, ∼0.4–8.8 kpc, thus making it possible to investigate the census of all kinds of planets in the Galaxy.

The Korea Micorolensing Telescope Network (KMTNet; Kim et al. 2016) has detected 124 (66%) of the 187¹⁴ microlensing exoplanets discovered so far. These results were achieved within about 7 yr after the start of the official observations of KMTNet in 2016, whereas the other 34% of detections were achieved over about 25 yr. This is due to 24 hr, high-cadence observations for a wide field of about 100 deg² toward the Galactic bulge (Shin et al. 2016). Chung et al. (2022) reported that KMTNet has detected about 50% of microlensing planets, as of 2022 April. Compared with this, the planet discovery rate of KMTNet has increased by 16% a year. This is mainly because the results of KMTNet's systematic AnomalyFinder (AF; Zang et al. 2021) applied to the 2018–2019 prime fields (Gould et al. 2022; Zang et al. 2022) and 2018 subprime fields (Jung et al. 2022) have been published and they reported that 18 exoplanets have been newly discovered by the AF, which was initiated in order to find buried planetary signals. Since the systematic AF searches of the 2019 subprime (Jung et al. 2023) and 2016 prime fields ((Shin et al. 2023b) were already done and other remaining seasons will be conducted soon, we expect that the KMTNet planet discovery rate will increase at a similar rate for the next few years. In addition, thanks to the 24 hr, high-cadence observations, KMTNet is readily detecting very-low-mass-ratio events of q < 10⁻⁴ by eye and via AF (Jung et al. 2023; Zang et al. 2023), which were rarely detected before KMTNet observations. Moreover, KMTNet is often detecting planetary events caused by planetary caustics, which are more difficult to detect because planetary caustic anomalies are unpredictable.

In this paper, we analyze the microlensing event OGLE-2019-BLG-1180 and report a newly discovered wide-orbit giant planet around an M dwarf with KMTNet. The paper is organized as follows. In Section 2, we present the observations of OGLE-2019-BLG-1180, and we describe the analysis of the light curve in Section 3. We characterize the source star from its color and magnitude in Section 4, and we estimate the physical lens parameters from a Bayesian analysis in Section 5. In Section 6, we review wide-orbit planetary lensing events and present a general investigation into prospects for further expanding the sample of wide-orbit planets. Finally, we conclude in Section 7.

The microlensing event OGLE-2019-BLG-1180 occurred at equatorial coordinates (R.A., decl.) = (17:56:59.17, −27:58:31.6), corresponding to the Galactic coordinates (l, b) = (210, −166). The event was first alerted by the Optical Gravitational Lensing Experiment (OGLE; Udalski 2003). OGLE uses a 1.3 m telescope with a 1.4 deg² field of view (FOV) at Las Campanas Observatory in Chile. The event lies in the OGLE IV field BLG504, which is observed with a cadence of Γ ≃ 0.4 hr⁻¹. The OGLE data partially covered the anomalies induced by the wide planetary caustic, but they were not enough to find the best solution. In addition, the peak was almost not covered by OGLE.

KMTNet also detected this event, and it was designated as KMT-2019-BLG-1912. KMTNet uses 1.6 m telescopes with 4 deg² FOV cameras at three different southern sites: the Cerro Tololo Inter-American Observatory in Chile (KMTC), the South African Astronomical Observatory (KMTS), and the Siding Spring Observatory in Australia (KMTA). The event lies in the KMT main field BLG02 with a cadence of Γ ≃ 2 hr⁻¹. With this high cadence, the peak and anomalies were well covered. For the measurement of the color of the source star, KMTNet data were mainly taken in the I band, and some data were taken in the V band. The KMTNet data were reduced using pySIS based on the difference imaging method (Alard & Lupton 1998; Albrow et al. 2009). For the characterization of the source color and construction of the color–magnitude diagram (CMD) of stars around the source, KMTC I- and V-band images were reduced using the pyDIA code (Albrow 2017). However, all KMT V-band images for the three sites were affected by bleeding. We thus could not construct the KMTC CMD of the event. On the other hand, for the KMTC I-band images, the bleeding was located away from the source by 3 pixels (12), but it was weak so that there was no problem for identifying the source. For the I-band images of KMTA and KMTS, the bleeding was located away from the source by 7 pixels (28), and thus the source was isolated enough. Therefore, there was no problem to use the KMT I-band data for modeling. For the source color and CMD, we used the OGLE I- and V-band data sets, which will be discussed in detail in Section 4. The OGLE data were reduced by the difference imaging pipeline developed by Woźniak (2000).

3.1. Standard Model

3.2. High-order Effects

3.2.1. Parallax+Orbital Model

The microlens parallax is usually well measured for events with a long timescale (t_E > yr/2π; Yoo et al. 2004), because it is caused by the orbital motion of the Earth. The timescale of this event is t_E = 28 days, which is relatively short to be affected by the microlens parallax. However, the event has both cusp-passing and caustic-crossing anomalies induced by the wide planetary caustic and the anomalies were well covered. In this case, it is possible to measure the microlens parallax. Since the lens orbital motion effect can mimic the parallax effect (Batista et al. 2011; Skowron et al. 2011), we conduct the parallax modeling together with the orbital motion effect. The microlens parallax is described by π _E = (π_E,N, π_E,E), while the lens orbital motion is described by (ds/dt, d α/dt), which are the instantaneous changes of the binary separation and the orientation angle of the binary axis, respectively. Here we note that the orbital parameters are not well constrained, and thus we consider only lens systems with a ratio of the projected kinetic to the potential energy limited to β < 0.8. The ratio β is defined as

$$\begin{eqnarray}&&\beta \equiv {\left(\displaystyle \frac{\mathrm{KE}}{\mathrm{PE}}\right)}_{\perp }=\displaystyle \frac{{(s{\theta }_{{\rm{E}}}{D}_{{\rm{L}}}/\mathrm{au})}^{3}({\gamma }^{2}\ {\mathrm{yr}}^{2})}{M/{M}_{\odot }},\end{eqnarray} \tag{ 1 }$$

where $\gamma ={[{({ds}/{dt}/s)}^{2}+{(d\alpha /{dt})}^{2}]}^{1/2}$. As a result, we find that the whole data set is well fitted by the parallax+orbital model, especially in the region with anomalies, and its χ² is improved by 255 compared to the standard model. The best-fit light curve of the parallax+orbital model is presented in Figure 1, and Figure 2 shows a close-up view of the region with anomalies. The best-fit lensing parameters are presented in Table 1 and the geometry of the best-fit model is shown in Figure 3.

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Table 1. Lensing Parameters of OGLE-2019-BLG-1180

	Standard		Parallax		Parallax+Orbital
Parameter	u0 > 0	u0 < 0	u0 > 0	u0 < 0	u0 > 0	u0 < 0
χ2	8005.74	8005.94	7751.45	7752.74	7750.80	7752.08
t0 (HJD')	8705.7077	8705.7005	8705.7673	8705.7610	8705.7619	8705.7931
	(0.0420)	(0.0420)	(0.0580)	(0.0582)	(0.0648)	(0.0612)
u0	0.2614	−0.2612	0.2880	−0.2891	0.2876	−0.2876
	(0.0013)	(0.0013)	(0.0024)	(0.0025)	(0.0027)	(0.0027)
tE (days)	27.8869	27.8715	28.1782	28.0997	28.1627	28.0510
	(0.1362)	(0.1389)	(0.1779)	(0.1731)	(0.1902)	(0.2051)
s	1.8936	1.8943	1.8656	1.8645	1.8642	1.8706
	(0.0051)	(0.0052)	(0.0070)	(0.0075)	(0.0079)	(0.0076)
q(10−3)	4.7969	4.8275	3.5516	3.5075	2.8209	3.3405
	(0.1139)	(0.1165)	(0.2154)	(0.2233)	(0.5583)	(0.4776)
α (radians)	0.2021	−0.2018	0.2772	−0.2771	0.2818	−0.2414
	(0.0013)	(0.0013)	(0.0051)	(0.0049)	(0.0188)	(0.0183)
ρ	0.0024	0.0024	0.0023	0.0023	0.0021	0.0023
	(0.0001)	(0.0001)	(0.0001)	(0.0001)	(0.0002)	(0.0001)
πE,N	...	...	0.3616	−0.3757	0.4076	−0.1208
	...	...	(0.0198)	(0.0201)	(0.1421)	(0.1411)
πE,E	...	...	−0.2896	−0.2894	−0.2891	−0.1804
	...	...	(0.0874)	(0.0901)	(0.0911)	(0.0921)
ds/dt (yr−1)	...	...	...	...	1.0686	0.5397
	...	...	...	...	(0.6235)	(0.5575)
d α/dt (radians yr−1)	...	...	...	...	−0.0902	0.4517
	...	...	...	...	(0.2244)	(0.2216)
fs,ogle	0.1482	0.1483	0.1612	0.1619	0.1610	0.1611
	(0.0007)	(0.0007)	(0.0013)	(0.0013)	(0.0014)	(0.0014)
fb,ogle	0.2194	0.2194	0.2056	0.2050	0.2059	0.2058
	(0.0007)	(0.0007)	(0.0013)	(0.0013)	(0.0014)	(0.0014)

Note. HJD' = HJD –2450000. The value in parantheses represents 1σ error of each parameter.

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In order to find the source of the χ² improvement, we construct the cumulative distribution of Δχ² between the standard and the parallax+orbital models as a function of time. As shown in Figure 4, only the KMTC and KMTS data have improvements in the range of HJD'$=\mathrm{HJD}-2450000\,\lt 8686$, while for OGLE and KMTA, there is no improvement. However, we could not find noticeable improvements of the light curve in the range of HJD$^{\prime} \lt 8686$ for KMTC and KMTS. This trend is the same as the event OGLE-2018-BLG-1428 (Kim et al. 2021). As mentioned in Kim et al. (2021), the improvements of KMTC and KMTS are likely due to correlated noise. On the other hand, for the range of HJD$^{\prime} \geqslant 8686$, the improvement of KMTC and KMTS looks reasonable. This is because the improvement of KMTC follows OGLE at the same time zone, but having better improvements due to better coverage (especially the anomaly range) relative to OGLE, while for KMTS it is similar to KMTC due to the similar coverage. As shown in Figure 2, the anomalies were almost covered by KMTC and KMTS. Hence, we carry out parallax+orbital remodeling with partial data sets for KMTC and KMTS and full data sets for OGLE and KMTA. For KMTC and KMTS, we use only the data sets in the range HJD$^{\prime} \geqslant 8686$. Figure 5 shows the χ² distributions of the best-fit parallax and orbital parameters. From Figure 5, we find that the parallax (π_E = 0.46 ± 0.14) has relatively large errors, while the orbital parameters were very poorly constrained. The best-fit lensing parameters for the partial data sets are presented in Table 2.

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Table 2. Lensing Parameters for the Parallax-only and Parallax+Orbital model with the Partial KMTC and KMTS Data Sets and the Full OGLE and KMTA Data Sets

	Parallax		Parallax+Orbital
Parameter	u0 > 0	u0 < 0	u0 > 0	u0 < 0
χ2	4980.49	4980.96	4979.85	4980.20
t0 (HJD')	8705.7512 ± 0.0658	8705.7693 ± 0.0620	8705.7423 ± 0.0676	8705.7945 ± 0.0659
u0	0.2863 ± 0.0030	−0.2868 ± 0.0026	0.2877 ± 0.0032	−0.2862 ± 0.0032
tE (days)	27.7722 ± 0.1938	27.7904 ± 0.1870	27.8479 ± 0.2206	27.8238 ± 0.2016
s	1.8739 ± 0.0103	1.8735 ± 0.0089	1.8673 ± 0.0100	1.8741 ± 0.0107
q(10−3)	3.6282 ± 0.3231	3.6693 ± 0.2684	3.3079 ± 0.5456	3.4273 ± 0.4966
α (radians)	0.2709 ± 0.0070	−0.2698 ± 0.0056	0.2699 ± 0.0221	−0.2567 ± 0.0131
ρ	0.0024 ± 0.0001	0.0023 ± 0.0001	0.0021 ± 0.0002	0.0023 ± 0.0001
πE,N	0.3390 ± 0.0237	−0.3528 ± 0.0222	0.3170 ± 0.1641	−0.2572 ± 0.0964
πE,E	−0.3331 ± 0.1181	−0.2965 ± 0.1038	−0.3378 ± 0.1172	−0.2456 ± 0.1225
ds/dt (yr−1)	...	...	0.7098 ± 0.5537	0.3941 ± 0.5153
d α/dt (radians yr−1)	...	...	−0.1498 ± 0.2403	0.2086 ± 0.1644
fs,ogle	0.1614 ± 0.0015	0.1615 ± 0.0014	0.1615 ± 0.0017	0.1610 ± 0.0017
fb,ogle	0.2057 ± 0.0015	0.2056 ± 0.0014	0.2056 ± 0.0016	0.2061 ± 0.0017

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3.2.2. Parallax-only Model

In order to check why the parallax and orbital parameters are not well constrained, in spite of the well-covered anomalies, we conduct parallax-only modeling. The resulting best-fit parameters for the full data sets and partial data sets are presented in Tables 1 and 2, respectively. Figure 6 shows the χ² distribution of the best-fit parallax-only model for the partial data sets. As shown in the figure, we find that π_E,N is much better constrained relative to the parallax+orbital model and the Δχ² between the parallax-only and parallax+orbital models is very small by Δχ² = 0.6, while π_E,E is similarly constrained to that of the parallax+orbital model. The big improvement of the π_E,N error indicates that the parallax parameters are strongly correlated with the orbital parameters. We plot the χ² of the parallax and orbital parameters to check their correlation in Figure 7. From Figure 7, we find a strong correlation between π_E,N and d α/dt, while π_E,N is barely correlated with ds/dt. Hence, even though the orbital parameters are not well constrained, it is clear that they are important because including them changes the parallax constraints; i.e., part of the reason the orbital parameters are poorly constrained is because of the degeneracy with the parallax parameters. We also mark four different models in Figure 7 and their parameters are presented in Table 3. As shown in Table 3, each model has different parallax and orbital parameters, but the Δχ² among the four models is small (Δχ² < 4) and the physical parameters of the models are similar. This result is similar to the results of Batista et al. (2011) and Skowron et al. (2011), where there is a strong degeneracy between π_E,N and d α/dt, and shows that it is very important to consider simultaneously the parallax and orbital parameters, even in the cases where the orbital parameters are poorly constrained.

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Table 3. Degenerate Models

Model	1	2	3	4
χ2	4980.05	4982.07	4982.37	4983.93
πE,N	0.45	−0.07	0.18	0.52
πE,E	−0.40	−0.20	−0.30	−0.35
ds/dt	0.92	−0.23	−0.56	−0.78
d α/dt	0.01	−0.54	−0.11	0.41
Mh (M⊙)	0.10	0.15	0.14	0.07
Mp (MJ)	0.28	0.99	0.59	0.33
DL (kpc)	2.42	3.83	3.73	2.69

Note. The physical parameters were estimated with (θ_E, π_E), where θ_E is described in Section 4.

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3.2.3. Xallarap Model

The parallax signal could come from the xallarap effect because of the orbital motion of the binary source. We thus conduct xallarap modeling. In the modeling, we assume that the binary source is in a circular orbit. The xallarap modeling requires five additional parameters from the standard model: the orbital period of the binary source P, the counterparts of the parallax parameters ξ_E = (ξ_E,N, ξ_E,E), and the phase λ and inclination i of the binary source's orbital motion. If the parallax measurement is real, the xallarap period should converge to the Earth orbital motion of 1 yr. This is because the parallax effect is caused by the orbital motion of the Earth, as mentioned in Section 3.2.1. Figure 8 shows the χ² distributions for the best-fit xallarap solutions as a function of fixed orbital period for the binary source P. As shown in the figure, the best-fit xallarap solution appears at P = 1 yr. The χ² difference between the xallarap and the parallax models is Δχ² = 0.5, indicating that they are almost the same. These suggest that the parallax measurement is real.

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We then check that the best-fit xallarap solution is physically reasonable. With P and (ξ_E,N, ξ_E,E), we can check the reasonability of the xallarap solution. ξ_E is defined as

$$\begin{eqnarray}&&{\xi }_{{\rm{E}}}=\displaystyle \frac{{a}_{{\rm{s}}}}{{\hat{r}}_{{\rm{E}}}},\,\displaystyle \frac{{\hat{r}}_{{\rm{E}}}}{{\rm{au}}}={\theta }_{{\rm{E}}}{D}_{{\rm{S}}},\end{eqnarray} \tag{ 2 }$$

where a_s is the semimajor axis of the binary source, ${\hat{r}}_{{\rm{E}}}$ is the Einstein radius projected on the source plane, and D_S is the distance to the source. We adopt D_S = 7.73 kpc from Nataf et al. (2013). The source is a late G dwarf star in the bulge, and thus θ_E = 0.46 mas (see Section 4). Hence, the mass of the source is ∼1.0 M_⊙ and ${\hat{r}}_{{\rm{E}}}=3.54\,\mathrm{au}$. We then apply Kepler's third law

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{tot}}}{{M}_{\odot }}{\left(\displaystyle \frac{P}{\mathrm{yr}}\right)}^{2}={\left(\displaystyle \frac{{a}_{\mathrm{tot}}}{\mathrm{au}}\right)}^{3},\end{eqnarray} \tag{ 3 }$$

where M_tot = M_s + M_comp and a_s/a_tot = M_comp/M_tot (Dong et al. 2009; Kim et al. 2021). Here M_s and M_comp are the masses of the source and its companion, respectively. As mentioned in Kim et al. (2021), Equation (3) can be described as a cubic equation

$$\begin{eqnarray}&&\displaystyle \frac{{(1+Q)}^{2}}{{Q}^{3}}=\displaystyle \frac{{M}_{{\rm{s}}}}{{M}_{\odot }}\displaystyle \frac{{(P/\mathrm{yr})}^{2}}{{a}_{{\rm{s}}}^{3}};\quad Q=\displaystyle \frac{{M}_{\mathrm{comp}}}{{M}_{{\rm{s}}}}.\end{eqnarray} \tag{ 4 }$$

If 0.1 < Q < 1.0, the solution is physically reasonable, which means that the companion will be a typical main-sequence star. For the best-fit xallarap solution, the orbital period of the source is P = 1 yr and ξ_E = 0.47, and thus Q = 6.1. We can also estimate the minimum mass of the source companion with ${\theta }_{{\rm{E}},\min }$, which is defined as ${M}_{{\rm{c}},\min }={({\xi }_{{\rm{E}}}{\hat{r}}_{{\rm{E}},\min }/\mathrm{au})}^{3}/{({\rm{P}}/\mathrm{yr})}^{2}$. Adopting ${\theta }_{{\rm{E}},\ \min }\simeq 0.41\,\mathrm{mas}$ from Section 4, the minimum mass of the source companion is ${M}_{{\rm{c}},\min }\simeq 3.2\,{M}_{\odot }$. These indicate that the companion would be a black hole, thus and thus it is not physically reasonable. Therefore, we can rule out the xallarap interpretation.

3.2.4. Point-source Point-lens Model with Parallax

In order to test the impact of the planetary anomaly on the parallax, we conduct the following test. After removing data from the planetary anomaly, i.e., $8725\lt \mathrm{HJD}^{\prime} \lt 8755$, we fit point-source point-lens (PSPL) models to the remaining light curve including the parallax effect. This PSPL+parallax modeling is carried out by almost the same method with the standard modeling, which performs a grid search in the parallax parameter space (π_E,N, π_E,E) and then additional modeling using local solutions. From the grid search, we find only one local solution (π_E,N, π_E,E) = (0.31, −0.67). The modeling result shows that the point-lens part of the light curve gives the usual 1D parallax constraint (see black and gray contours in Figure 9). We also add the result of the parallax+orbital model (colored contours) in Figure 9. This figure shows that the point-lens parallax constraint is almost consistent with the constraint from fitting the full light curve including orbital motion within 3σ, but shows that the planetary anomaly provides more precise information about parallax.

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As mentioned in Section 2, all KMT V-band data for the three sites were affected by bleeding. We thus use the OGLE data sets for the source color and CMD. From the OGLE CMD, we find that the color and magnitude of the clump are (V − I, I)_cl = (3.32, 16.71). The brightness of the source is I_s = 19.98 ± 0.01, which is obtained from the source flux of the best-fit model. OGLE has three well-magnified V-band data points, but it turned out that they are not enough to get a precise source color. We thus estimate the source color by combining the OGLE CMD and a CMD constructed from Hubble Space Telescope (HST) observations of Baade's window (Holtzman et al. 1998). We note that the two CMDs are combined by calibrating the clump positions on each CMD, in which the the color and magnitude of the clump on the HST CMD (V − I, I)_HST,cl = (1.62, 15.15) is used from Bennett et al. (2008). We then extract HST stars that have similar magnitudes to the source star, in which they are in the ranges of 17.63 ≤ I₀ ≤ 17.65. We estimate the mean color of the HST stars and the standard deviation of the color and then take them as the source color and its uncertainty, respectively. From this, it is found that the source color is (V − I)_HST,s = 1.33 ± 0.08. The angular source radius is estimated from the intrinsic color and magnitude of the source, which are determined from

$$\begin{eqnarray}&&{(V-I,I)}_{{\rm{s}},0}={(V-I,I)}_{\mathrm{cl},0}+{\rm{\Delta }}(V-I,I),\end{eqnarray} \tag{ 5 }$$

where ${\rm{\Delta }}{(V-I)={(V-I)}_{HST,{\rm{s}}}-(V-I)}_{HST,\mathrm{cl}}$ and ΔI = I_s − I_cl. We adopt the intrinsic color and magnitude of the clump (V − I)_cl,0 = 1.06 and I_cl,0 = 14.37 from Bensby et al. (2011) and Nataf et al. (2013), respectively. Hence, we find that the intrinsic color and magnitude of the source are (V − I, I)_s,0 = (0.77 ± 0.08, 17.64 ± 0.01), indicating that the source is a late G dwarf. The combined CMD is presented in Figure 10. By adopting the VIK color–color relation of Bessell & Brett (1988) and the color-surface brightness of Kervella et al. (2004), we determine an angular source radius of θ_⋆ = 0.98 ± 0.09μas. From the determined θ_⋆ and ρ, we measure the angular Einstein radius

$$\begin{eqnarray}\begin{array}{c}{\theta }_{{\rm{E}}}=\displaystyle \frac{{\theta }_{\star }}{\rho }=\left\{\begin{array}{cc}0.458\pm 0.044\,{\rm{mas}} & ({u}_{0}\gt 0),\\ 0.443\pm 0.042\,{\rm{mas}} & ({u}_{0}\lt 0).\end{array}\right.\end{array}\end{eqnarray} \tag{ 6 }$$

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Then the relative lens–source proper motion is estimated as

$$\begin{eqnarray}\begin{array}{c}{\mu }_{{\rm{rel}}}=\displaystyle \frac{{\theta }_{{\rm{E}}}}{{t}_{{\rm{E}}}}=\left\{\begin{array}{cc}6.01\pm 0.58\,{\rm{mas}}\,{{\rm{yr}}}^{-1} & ({u}_{0}\gt 0),\\ 5.86\pm 0.55\,{\rm{mas}}\,{{\rm{yr}}}^{-1} & ({u}_{0}\lt 0).\end{array}\right.\end{array}\end{eqnarray} \tag{ 7 }$$

As mentioned in Section 1, the physical lens parameters including the lens mass and distance to the lens are directly determined by two observables, θ_E and π_E, which are defined as

$$\begin{eqnarray}&&{M}_{{\rm{L}}}=\displaystyle \frac{{\theta }_{{\rm{E}}}}{\kappa {\pi }_{{\rm{E}}}};\quad {D}_{{\rm{L}}}=\displaystyle \frac{\mathrm{au}}{{\pi }_{{\rm{E}}}{\theta }_{{\rm{E}}}+{\pi }_{{\rm{S}}}},\end{eqnarray} \tag{ 8 }$$

where κ ≡ 4G/(c²au) ≈ 8.14 mas M_⊙ ^–1 and π_S = au D_S ^–1 denotes the parallax of the source. We adopt D_S = 7.73 kpc and π_S = 0.13 mas in this work. For OGLE-2019-BLG-1180, π_E and θ_E were measured, but π_E was not constrained well. We thus estimate the physical lens parameters by conducting a Bayesian analysis with the measured three observables of (t_E, θ_E, π_E) and the Galactic model of Jung et al. (2021). The Bayesian analysis assumes that all stars have an equal probability to host a planet with the observed mass ratio. For the Bayesian analysis, we first randomly generate 2 × 10⁷ artificial microlensing events. We then calculate the probability distributions of the physical lens parameters for events with (t_E, θ_E, π_E) located within the uncertainties of the three observables.

In order to estimate the lens brightness, we consider the extinction at a given lens distance. According to Bennett et al. (2020), the extinction to the lens, A_i,L, is computed by

$$\begin{eqnarray}&&{A}_{i,{\rm{L}}}=\displaystyle \frac{1-{e}^{-| {D}_{{\rm{L}}}(\sin \ b)/{h}_{\mathrm{dust}}| }}{1-{e}^{-| {D}_{{\rm{S}}}(\sin \ b)/{h}_{\mathrm{dust}}| }}\ {A}_{i},\end{eqnarray} \tag{ 9 }$$

where the index i denotes the passband: V, I, H, or K; the dust scale height is h_dust = 120 pc, and A_i is the extinction to the source. Using the information on the color and magnitude of the clump discussed in Section 4, we find A_I = 2.34 and A_V = 4.61. For the extinctions in the H and K bands, we adopt A_H = 0.87 and A_K = 0.53, respectively, using the extinction law of Cardelli et al. (1989) for R_V = 3.1, i.e., A_H = 0.190 A_V and A_K = 0.114 A_V .

Figure 11 shows the probability distributions of the physical lens parameters estimated from the Bayesian analysis. The physical lens parameters and their uncertainties represent the median values and 68% confidence intervals of each distribution. The mass and distance of the host star are estimated as

$$\begin{eqnarray}&&{M}_{{\rm{h}}}={0.549}_{-0.260}^{+0.272}\,{M}_{\odot },\quad {D}_{{\rm{L}}}={6.07}_{-1.32}^{+0.87}\,\mathrm{kpc}.\end{eqnarray} \tag{ 10 }$$

Then, the planet mass is determined as

$$\begin{eqnarray}&&{M}_{{\rm{p}}}={{qM}}_{{\rm{h}}}={1.747}_{-0.507}^{+0.527}\,{M}_{{\rm{J}}}.\end{eqnarray} \tag{ 11 }$$

The projected star–planet separation is ${a}_{\perp }={5.19}_{-1.23}^{+0.90}\,\mathrm{au}$. According to a_snow = 2.7 M/M_⊙ (Kennedy & Kenyon 2008), the snow line of the host is ${a}_{\mathrm{snow}}={1.48}_{-0.70}^{+0.74}\,\mathrm{au}$, indicating that the planet is orbiting beyond the snow line of the M-dwarf star. However, the host star could be also a K or a G dwarf star.

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The probability distributions of the brightness of the lens star are shown in the bottom panel of Figure 11. The brightness of the lens star is ${I}_{{\rm{L}}}={23.75}_{-2.11}^{+1.01}$, ${H}_{{\rm{L}}}={20.55}_{-1.45}^{+0.89}$, and ${K}_{{\rm{L}}}={20.05}_{-1.35}^{+0.84}$. The lens is 32 times fainter than the G dwarf source star of I = 19.98, implying that it is possible to resolve them by follow-up observations. Considering the relative lens–source proper motion μ_rel = 6 mas yr⁻¹, the lens will be separated from the source by 60 mas in 2029. The separation 60 mas is about 4 times the FWHM at 1.6 μm for a next-generation 30 m telescope, e.g., the Giant Magellan Telescope (GMT; McGregor et al. 2012) that will be operated in ∼2029, thus the lens can be easily resolved with a 30 m telescope.

In addition, Vandorou et al. (2023) have very recently reported the results of follow-up observations using Keck for OGLE-2016-BLG-1195. The results show a star with K 20, which is about 15 times fainter than the nearby star of K = 17.0 at a separation of 56.4 mas, can be resolved with Keck. For this event, the brightnesses of the lens and source stars are K_L = 20.1 and K = 17.3 and their separation is 60 mas, thus their results suggest that this lens star can be detected with Keck. If the lens flux could be detected, one can measure more precise lens properties, and then the orbital motion of the wide lens system can be better constrained.

OGLE-2019-BLG-1180Lb is striking because it is a clear wide-separation planet detection with s ∼ 2. By contrast, the core of microlensing's sensitivity to planets is s ∼ (0.62, 1.62). This may be calculated by assuming that in a typical planetary lensing event, the source position offset from the lens star is u_anom ≤ 1 (Hwang et al. 2022) and using the equation for the location of the planetary caustic

$$\begin{eqnarray}&&{u}_{{\rm{anom}}}=s-1/s,\end{eqnarray} \tag{ 12 }$$

from Han (2006). By contrast, OGLE-2019-BLG-1180 has u_anom = 1.36, giving it a value of s outside the standard "lensing zone."

To place OGLE-2019-BLG-1180Lb in context with known microlensing planets, we consider two samples of wide-orbit planets. First, we consider the microlensing planet discoveries from the systematic AF search of the 2018 and 2019 KMTNet seasons from which OGLE-2019-BLG-1180 is drawn (Gould et al. 2022; Jung et al. 2022, 2023; Zang et al. 2022). Second, we consider microlensing planets in the literature discovered in data prior to KMTNet (i.e., prior to 2015) taken from the NASA Exoplanet Archive (accessed 2023 May 1). We limit this sample to planets with light-curve solutions that have s > 1.5 and q < 0.03 and only consider solutions with Δχ² < 10 of the best fit. These planets are summarized in Table 5. Figure 12 shows u_anom versus s for these two samples of planets.

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Table 4. Physical Lens Parameters

Parameter
Mh (M⊙)	${0.545}_{-0.260}^{+0.272}$
Mp (MJ)	${1.747}_{-0.507}^{+0.527}$
DL (kpc)	${6.07}_{-1.32}^{+0.87}$
a⊥ (au)	${5.19}_{-1.23}^{+0.90}$
IL (mag)	${23.75}_{-2.11}^{+1.01}$
HL (mag)	${20.55}_{-1.45}^{+0.89}$
KL (mag)	${20.05}_{-1.35}^{+0.84}$
θE (mas)	0.46 ± 0.04
μrel (mas yr−1)	6.01 ± 0.58

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Table 5. Wide-orbit Planets

Name	$\mathrm{log}q$	s	uanom	Reference(s)
Literature (pre-2015):
MOA-2007-BLG-400Lb	−2.64	2.72	0.005	Dong et al. (2009); Bhattacharya et al. (2021)
MOA-2011-BLG-028Lb	−3.90	1.69	1.098	Skowron et al. (2016)
MOA-2011-BLG-028Lb	−2.28	1.83	0.004	Yee et al. (2012)
MOA-2011-BLG-322Lb	−1.55	1.82	0.126	Shvartzvald et al. (2014)
MOA-2012-BLG-006Lb	−1.78	4.41	4.170	Poleski et al. (2017)
MOA-2012-BLG-006Lb	−3.42	2.41	1.866	Sumi et al. (2016)
MOA-bin-1Lb	−2.34	2.13	1.610	Bennett et al. (2012)
MOA-bin-29b	−2.21	1.75	0.089	Kondo et al. (2019)
OGLE-2005-BLG-390Lb	−4.12	1.61	0.981	Beaulieu et al. (2006)
OGLE-2008-BLG-092Lb	−3.62	5.26	5.064	Poleski et al. (2014)
OGLE-2011-BLG-0173Lb	−3.34	4.66	4.403	Poleski et al. (2018)
OGLE-2012-BLG-0563Lb	−2.96	2.42	0.002	Fukui et al. (2015)
OGLE-2012-BLG-0838Lb	−3.40	2.15	1.696	Poleski et al. (2020)
KMTNet (2018–2019):
KMT-2018-BLG-0030Lb	−2.56	1.58	1.231	Jung et al. (2022)
OGLE-2018-BLG-1367Lb	−2.48	1.70	0.026	Gould et al. (2022)
OGLE-2018-BLG-0383Lb	−3.67	2.45	2.062	Wang et al. (2022)
OGLE-2018-BLG-0567Lb	−2.91	1.81	1.257	Jung et al. (2021)
KMT-2019-BLG-0414Lb	−2.26	2.80	0.005	Han et al. (2022)
KMT-2019-BLG-1953Lb	−2.71	2.51	0.002	Han et al. (2020)
OGLE-2019-BLG-1180Lb	−2.57	1.87	1.359	This work
KMT-2019-BLG-0298Lb	−2.53	1.85	1.520	Jung et al. (2023)
OGLE-2019-BLG-0249Lb	−2.11	1.78	0.046	Jung et al. (2023)
OGLE-2019-BLG-0679Lb	−2.41	2.17	1.630	Jung et al. (2023)

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The first feature of Figure 12 is that the planets are clearly delineated by u_anom. The first group of planets are the planetary caustic anomalies, which have u_anom > 0.83, which is what we would expect from Equation (12) given our limit s > 1.5. These planets all fall very close to the expected u_anom relation with some small scatter because the source trajectory does not always pass through the exact center of the caustic. All but one of these planets has an unambiguous wide-orbit planet. The one exception is OGLE-2011-BLG-0173Lb (Poleski et al. 2018), which has an alternate, planetary caustic solution with s < 1 and a completely different value of q.

In contrast to the planetary caustic events, the planets with u_anom ∼ 0 all (or likely all) suffer from close-wide degeneracy (Griest & Safizadeh 1998) due to being central caustic anomalies. MOA-2011-BLG-322Lb (Shvartzvald et al. 2014) is the one possible exception. It has only an s > 1 solution in the literature, but the s^† analysis described in Hwang et al. (2022) and Ryu et al. (2022) reveals that in the corresponding s < 1 solution, the angle of the source trajectory is such that it passes near or through the planetary caustic, creating an extra signal that would nominally exclude such models. However, Shvartzvald et al. (2014) only considered static models; it seems likely that adding the parallax or orbital motion of the planet would allow for a plausible s < 1 solution that avoids the planetary caustic.

For planets with 1.5 < s < 3, KMTNet has a significant advantage over early microlensing detections: six out of 10 detections are planetary caustic detections. By contrast, the early microlensing detections had a much higher proportion of central caustic events (50%). Most likely, this is due to the need for follow-up observations (Gould & Loeb 1992) and the subsequent bias toward high-magnification events (Udalski et al. 2005). Hence, KMTNet is fulfilling its promise to detect a larger number of planetary caustic events. This is essential for studying the dependence of planet occurrence on separation (Poleski et al. 2021) because, as shown above, these are the events with a clear measurement of the host–planet separation.

However, the early microlensing detections also show a class of planets with s > 4 that have no KMTNet counterparts to date. They are OGLE-2008-BLG-092 (Poleski et al. 2014), OGLE-2011-BLG-0173 (Poleski et al. 2018), and MOA-2012-BLG-006 (Poleski et al. 2017). In these cases, the planetary anomalies all occurred near the beginning or end of the observing season, with a separation from the peak that was, respectively, 67%, 52%, and 28% of the total duration of the observing season. Hence, it is possible that similar anomalies occur for KMTNet events, but they might fall during gaps between the observing seasons or even in other seasons entirely, e.g., if the peak of the stellar event is shifted with respect to the midpoint of the season.

To explore further the possibility of missed planets with KMTNet, we consider the expected ratios of central caustic to planetary caustic events. The probability that a planet is detected through a caustic crossing is proportional to the size of that caustic. Chung et al. (2005) and Han (2006) give approximations for the sizes of the central and planetary caustics, respectively

$$\begin{eqnarray}&&{\rm{\Delta }}{\xi }_{\mathrm{cent}}\sim \displaystyle \frac{4q}{{(s-1/s)}^{2}};\quad {\rm{\Delta }}{\xi }_{\mathrm{pl}}\sim \left(\displaystyle \frac{4\sqrt{q}}{{s}^{2}}\right)\left(1+\displaystyle \frac{1}{2{s}^{2}}\right).\end{eqnarray} \tag{ 13 }$$

Hence, the ratio Δξ_pl/Δξ_cent scales as q^−1/2 and, in the limit s ≫ 1, reduces to q^−1/2. So, for $\mathrm{log}q=-2.5$, we expect ∼18 planetary caustic-type events for every central caustic event as $s\to \inf$.

For the KMTNet sample, $\mathrm{log}q=-2.5$ and s = 2 are typical values. This suggests that there should be ∼11 planetary caustic events (either with or without host star detections) for every central caustic event. This is much larger than our observed ratio 6:4. Of course, this does not take into account several factors. First, not all planetary caustic events will have a detectable host star. Some of the 11 might manifest as free-floating planet candidates, and so might be excluded from the AF search. Alternatively, some of the hosts may not manifest as a separate peak, but only as a distortion to the planetary event, such as in MOA-bin-1 (Bennett et al. 2012), and there may be separate detection effects for distorted, short-timescale events. This simple calculation also does not take into account any observability criteria such as observing window (as discussed above) or signal-to-noise ratio (which creates a bias toward central caustic perturbations because of their higher magnifications). Finally, some or all of the central caustic events could be due to planets with a separation of s⁻¹; disentangling this contribution would require knowledge of the underlying separation distribution of planets. However, given that there are s > 4 planets from the literature that so far have no counterparts in KMTNet data, it would be worthwhile to consider more carefully whether additional wide-orbit planets might be missing from the KMTNet sample. In particular, a search for planetary anomalies in data from observing seasons adjacent to the main stellar event could yield additional planets.

We analyzed the planetary lensing event OGLE-2019-BLG-1180, which has remarkable anomalies near the baseline after the peak of the light curve. We estimated the physical lens parameters by conducting a Bayesian analysis using the measured observables of (t_E, θ_E, π_E). From the Bayesian analysis, it was found that the lens system is composed of a late-type star of ${0.55}_{-0.26}^{+0.27}\,{M}_{\odot }$ and a super-Jupiter-mass planet of ${1.75}_{-0.51}^{+0.53}\,{M}_{{\rm{J}}}$ at a distance ${D}_{{\rm{L}}}={6.1}_{-1.3}^{+0.9}\,\mathrm{kpc}$. The projected star–planet separation is ${a}_{\perp }={5.2}_{-1.2}^{+0.9}\,\mathrm{au}$, which indicates that the planet lies beyond the snow line of the host star. Considering μ_rel = 6 mas yr⁻¹, the lens flux can be resolved by adaptive optics of Keck or a next-generation 30 m class telescope in the future.

The work by S.-J.C. was supported by the Korea Astronomy and Space Science Institute under the R&D program (project No. 2023-1-832-03) supervised by the Ministry of Science and ICT. J.C.Y., I.-G.S., and S.-J.C. acknowledge support from N.S.F grant No. AST-2108414. The work by C.H. was supported by the grants of National Research Foundation of Korea (2020R1A4A2002885 and 2019R1A2C2085965). This research has made use of the KMTNet system operated by the KASI and the data were obtained at three sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia. Data transfer from the host site to KASI was supported by the Korea Research Environment Open NETwork (KREONET).