Systematic KMTNet Planetary Anomaly Search. X. Complete Sample of 2017 Prime-field Planets

With one exception that is explicitly noted below, we reproduce here Section 3.1 of Jung et al. (2022), which describes the common features of the light-curve analysis. We do so (rather than simply referencing that paper) to provide easy access to the formulae and variable names used throughout this paper. The reader who is interested in more details should consult Section 3.1 of Gould et al. (2022a). Readers who are already familiar with these previous works can skip this section, after first reviewing the paragraph containing Equation (9) below.

All of the events can be initially approximated by 1L1S models, which are specified by three Paczyński (1986) parameters, (t₀, u₀, t_E), that is, the time of lens-source closest approach, the impact parameter in units of θ_E, and the Einstein timescale,

$$\begin{eqnarray}&&{t}_{{\rm{E}}}=\displaystyle \frac{{\theta }_{{\rm{E}}}}{{\mu }_{\mathrm{rel}}};\ {\theta }_{{\rm{E}}}=\sqrt{\kappa M{\pi }_{\mathrm{rel}}};\ \kappa \equiv \displaystyle \frac{4\,G}{{c}^{2}\,\mathrm{au}}\simeq 8.14\,\displaystyle \frac{\mathrm{mas}}{{M}_{\odot }},\end{eqnarray} \tag{ 1 }$$

where M is the lens mass, π_rel and μ _rel are the lens-source relative parallax and proper motion, respectively, and μ_rel ≡ ∣ μ _rel∣. The notation "nLmS" means n lenses and m sources. In addition, to these three nonlinear parameters, there are two flux parameters, (f_S , f_B ), that are required for each observatory, representing the source flux and the blended flux.

We then search for "static" 2L1S solutions, which generally require four additional parameters (s, q, α, ρ), that is, the planet-host separation in units of θ_E, the planet-host mass ratio, the angle of the source trajectory relative to the binary axis, and the angular source size normalized to θ_E, that is, ρ = θ_ast/θ_E.

We first conduct a grid search with (s, q) held fixed at a grid of values and the remaining five parameters allowed to vary in a Markov Chain Monte Carlo (MCMC). After we identify one or more local minima, we refine these by allowing all seven parameters to vary.

We often make use of the heuristic analysis introduced by Hwang et al. (2022) and modified by Ryu et al. (2022) based on further investigation in Gould et al. (2022a). If a brief anomaly at t_anom is treated as due to the source crossing the planet-host axis, then one can estimate two relevant parameters:

$$\begin{eqnarray}&&{s}_{\pm }^{\dagger }=\displaystyle \frac{\sqrt{4+{u}_{\mathrm{anom}}^{2}}\pm {u}_{\mathrm{anom}}}{2};\quad \tan \alpha =\displaystyle \frac{{u}_{0}}{{\tau }_{\mathrm{anom}}},\end{eqnarray} \tag{ 2 }$$

where ${u}_{\mathrm{anom}}^{2}={\tau }_{\mathrm{anom}}^{2}+{u}_{0}^{2}$ and τ_anom = (t_anom − t₀)/t_E. Usually, ${s}_{+}^{\dagger }\gt 1$ corresponds to anomalous bumps and ${s}_{-}^{\dagger }\lt 1$ corresponds to anomalous dips. This formalism predicts that if there are two degenerate solutions, s_±, then they both have the same α and there exists a ${\rm{\Delta }}\mathrm{ln}s$ such that

$$\begin{eqnarray}&&{s}_{\pm }={s}^{\dagger }\exp (\pm {\rm{\Delta }}\mathrm{ln}s),\end{eqnarray} \tag{ 3 }$$

where α and s^† are given by Equation (2). To test this prediction in individual cases, we can compare the purely empirical quantity ${s}^{\dagger }\equiv \sqrt{{s}_{+}{s}_{-}}$ with the prediction from Equation (2), which we always label with a subscript, that is, either ${s}_{+}^{\dagger }$ or ${s}_{-}^{\dagger }$. This formalism can also be used to find "missing solutions" that have been missed in the grid search, as was done, for example, for the case of KMT-2021-BLG-1391 (Ryu et al. 2022).

For cases in which the anomaly is a dip, the mass ratio q can be estimated,

$$\begin{eqnarray}&&q={\left(\displaystyle \frac{{\rm{\Delta }}{t}_{\mathrm{dip}}}{4\,{t}_{{\rm{E}}}}\right)}^{2}\displaystyle \frac{{s}^{\dagger }}{| {u}_{0}| }| {\sin }^{3}\alpha | ,\end{eqnarray} \tag{ 4 }$$

where Δt_dip is the full duration of the dip. In some cases, we investigate whether the microlens parallax vector,

$$\begin{eqnarray}&&{{\boldsymbol{\pi }}}_{{\rm{E}}}\equiv \displaystyle \frac{{\pi }_{\mathrm{rel}}}{{\theta }_{{\rm{E}}}}\,\displaystyle \frac{{{\boldsymbol{\mu }}}_{\mathrm{rel}}}{{\mu }_{\mathrm{rel}}},\end{eqnarray} \tag{ 5 }$$

can be constrained by the data. When both π_E and θ_E are measured, they can be combined to yield

$$\begin{eqnarray}&&M=\displaystyle \frac{{\theta }_{{\rm{E}}}}{\kappa {\pi }_{{\rm{E}}}};\qquad {D}_{L}=\displaystyle \frac{\mathrm{au}}{{\theta }_{{\rm{E}}}{\pi }_{{\rm{E}}}+{\pi }_{S}},\end{eqnarray} \tag{ 6 }$$

where D_L is the distance to the lens and π_S is the parallax of the source.

To model the parallax effects due to Earth's orbital motion, we add two parameters (π_E,N , π_E,E ), which are the components of π _E in equatorial coordinates. We also add (at least initially) two parameters γ = [(ds/dt)/s, d α/dt], where s γ are the first derivatives of projected lens-orbital position at t₀, that is, parallel and perpendicular to the projected separation of the planet at that time, respectively. In order to eliminate unphysical solutions, we impose a constraint on the ratio of the transverse kinetic to potential energy,

$$\begin{eqnarray}&&\beta \equiv {\left|\displaystyle \frac{\mathrm{KE}}{\mathrm{PE}}\right|}_{\perp }=\displaystyle \frac{\kappa {M}_{\odot }\,{\mathrm{yr}}^{2}}{8{\pi }^{2}}\,\displaystyle \frac{{\pi }_{{\rm{E}}}}{{\theta }_{{\rm{E}}}}{\gamma }^{2}{\left(\displaystyle \frac{s}{{\pi }_{{\rm{E}}}+{\pi }_{S}/{\theta }_{{\rm{E}}}}\right)}^{3}\lt 0.8.\end{eqnarray} \tag{ 7 }$$

It often happens that γ is neither significantly constrained nor significantly correlated with π _E. In these cases, we suppress these 2 dof.

Particularly if there are no sharp caustic-crossing features in the light curve, 2L1S events can be mimicked by 1L2S events. Where relevant, we test for such solutions by adding at least three parameters (t_0,2, u_0,2, q_F ) to the 1L1S models. These are the time of closest approach and impact parameter of the second source and the ratio of the second to the first source flux in the I band. If either lens-source approach can be interpreted as exhibiting finite source effects, then we must add one or two further parameters, that is, ρ₁ and/or ρ₂. And, if the two sources are projected closely enough on the sky, one must also consider source orbital motion.

In a few cases, we make kinematic arguments that solutions are unlikely because their inferred proper motions μ_rel are too small. If planetary events (or, more generally, anomalous events with planet-like signatures) traced the overall population of microlensing events, then the fraction with proper motions less than a given μ_rel ≪ σ_μ would be

$$\begin{eqnarray}&&p(\leqslant {\mu }_{\mathrm{rel}})=\displaystyle \frac{{\left({\mu }_{\mathrm{rel}}/{\sigma }_{\mu }\right)}^{3}}{6\sqrt{\pi }}\to 4\times {10}^{-3}{\left(\displaystyle \frac{{\mu }_{\mathrm{rel}}}{1\,\mathrm{mas}\,{\mathrm{yr}}^{-1}}\right)}^{3}\ (\mathrm{old}),\end{eqnarray} \tag{ 8 }$$

where (following Gould et al. 2021) the bulge proper motions are approximated as an isotropic Gaussian with dispersion σ_μ = 2.9 mas yr⁻¹.

However, subsequent to the work of Gould et al. (2022a) and Jung et al. (2022), Gould (2022) showed that the proper-motion distribution of observed planetary microlensing events scales $\propto d{\mu }_{\mathrm{rel}}{(\mu /{\sigma }_{\mu })}^{\nu }$, where σ_μ = 3.06 ± 0.29 mas yr⁻¹ and ν = 1.02 ± 0.29. Hence, in place of Equation (8), we adopt

$$\begin{eqnarray}\begin{array}{rcl}p(\leqslant {\mu }_{\mathrm{rel}}) & = & \displaystyle \frac{{\left({\mu }_{\mathrm{rel}}/2{\sigma }_{\mu }\right)}^{\nu +1}}{[(\nu +1)/2]!}\to \displaystyle \frac{{\mu }_{\mathrm{rel}}^{2}}{4{\sigma }_{\mu }^{2}}\\ & \to & \ 2.8\times {10}^{-2}{\left(\displaystyle \frac{{\mu }_{\mathrm{rel}}}{1\,\mathrm{mas}\,{\mathrm{yr}}^{-1}}\right)}^{2},\end{array}\end{eqnarray} \tag{ 9 }$$

where we have evaluated at σ_μ = 3.0 mas yr⁻¹ and ν = 1. For example, p( ≤ 0.5 mas yr⁻¹) = 0.7% and p( ≤ 0.1 mas yr⁻¹) = 0.03%.

Figure 1 shows a relatively low-amplitude 1L1S microlensing event punctuated by a dip just Δt_anom ≃ − 0.3 day before peak, with a full width, Δt_dip ≃ 3.0 days. A Paczyński (1986) fit (with the dip excised) yields t_E = 13.3 days and u₀ = 0.40. Using the formulae from Section 3.1, we obtain τ_anom = − 0.02, u_anom = 0.40, α = 273°, ${s}_{-}^{\dagger }=0.82$, and q = 6.5 × 10⁻³.

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The grid search yields three minima, two of which (when refined) form a classic "inner/outer" degenerate pair, whose parameters are in excellent agreement with the heuristic predictions for α and ${s}^{\dagger }=\sqrt{{s}_{\mathrm{inner}}{s}_{\mathrm{outer}}}$, and in qualitative agreement for q. See Table 2. Note that, as is often the case (Yee et al. 2021), the source passes outside the planetary wing of a resonant caustic in the "outer" model and inside the planetary caustics in the "inner" model.

Table 2. Ground-only Parameters for OGLE-2017-BLG-1275

Parameters	Inner	Outer	Wide
χ2/dof	9823.68/9824	9823.67/9824	9858.66/9824
t0 − 2457940	9.962 ± 0.017	9.950 ± 0.017	9.918 ± 0.017
u0	0.395 ± 0.020	0.389 ± 0.019	0.399 ± 0.017
tE (days)	13.41 ± 0.42	13.51 ± 0.42	13.00 ± 0.34
s	0.631 ± 0.014	1.092 ± 0.040	1.254 ± 0.009
q (10−3)	8.25 ± 1.31	9.13 ± 1.69	1.30 ± 0.23
log q (mean)	−2.084 ± 0.069	−2.041 ± 0.080	−2.889 ± 0.076
α (rad)	4.758 ± 0.014	4.755 ± 0.013	1.718 ± 0.005
ρ (10−2)	${3.4}_{-2.1}^{+2.7}$	${3.9}_{-2.5}^{+3.2}$	${0.17}_{-0.11}^{+0.17}$
IS [OGLE]	19.358 ± 0.074	19.373 ± 0.074	19.277 ± 0.061
IB [OGLE]	${21.09}_{-0.31}^{+0.46}$	${21.02}_{-0.28}^{+0.42}$	${21.62}_{-0.42}^{+0.73}$

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Somewhat surprisingly, it also yields a third solution characterized by a caustic-crossing ("wide") major-image perturbation. In this solution, the dip is produced by the declining magnification just outside of the caustic walls, while the violent caustic crossing itself is finessed by a 0.4 day gap in the data. In addition to being somewhat implausible, this fit is substantially worse, with Δχ² = 35, so we do not further consider it.

While dip-type anomalies are rarely well-fit by 1L2S models, this can happen. Therefore, as a matter of due diligence, we check such models but find that they are excluded by Δχ² = 95.

3.2.1. OGLE-2017-BLG-1275: A Spitzer Planet

3.2.2. Test of Color Constraints

A key point is that, in contrast to most Spitzer microlensing planets, the case of OGLE-2017-BLG-1275 permits an independent check from the so-called color–color flux constraint. To briefly review, when Refsdal (1966) first advocated microlens parallax observations from solar orbit, he implicitly assumed that the peak and (at least one) wing of the event would be observed from space. Then, the times of peak (t_0,⊕, t_0,sat) and normalized impact parameters (u_0,⊕, u_0,sat) could be directly extracted from both light curves. The microlens parallax (in modern notation) could then be "read off"

$$\begin{eqnarray}\begin{array}{rcl}{{\boldsymbol{\pi }}}_{{\rm{E}}} & = & \displaystyle \frac{\mathrm{au}}{{D}_{\perp }}({\rm{\Delta }}\tau ,{\rm{\Delta }}\beta );\ {\rm{\Delta }}\tau \equiv \displaystyle \frac{{t}_{0,\mathrm{sat}}-{t}_{0,\oplus }}{{t}_{{\rm{E}}}},\\ {\rm{\Delta }}\beta & \equiv & {u}_{0,\mathrm{sat}}-{u}_{0,\oplus },\end{array}\end{eqnarray} \tag{ 10 }$$

where ${D}_{\perp }=| {D}_{\perp }|$, $| {{\bf{D}}}_{\perp }|$ is the Earth–satellite vector offset projected on the sky and the two components are, respectively, parallel and perpendicular to this vector. As Refsdal (1966) already recognized, but is better illustrated in Figure 1 from Gould (1994), there is a four-fold degeneracy because u₀ is a signed quantity, but only its amplitude can normally be extracted from a single-observatory light curve. However, while some Spitzer microlensing light curves do essentially meet the conditions implicitly assumed by Refsdal (1966; see Yee et al. 2015b for a spectacular example that looks eerily similar to Figure 1 from Gould 1994), the great majority do not. The main reason for this is that operational constraints imposed a 3–10 days' delay from the time that the event was recognized until Spitzer observations could begin. A secondary reason is that for disk (although not bulge) lenses, typically π_E,E > 0, while Spitzer was in an Earth-trailing orbit, that is, west of Earth, and so these events typically peaked earlier as seen from Spitzer.

It is well-known that for rising events, one cannot accurately predict either t₀ or (especially) u₀ at times t such that (t₀ − t) ≫ t_eff ≡ u₀ t_E. By the same token, it is equally impossible to recover t_0,sat and u_0,sat for satellite data that begin well after peak. However, these difficulties can be greatly ameliorated if the source flux of the space observatory (3.6 μm, i.e., L band, in the present case) can be strongly constrained by VIL or IHL color–color relations. The π _E contours then take the form of circular arcs (Gould 2019), which are more or less extended according to the size of (t_start − t₀)/t_eff, where t_start marks the commencement of the space observations. See Zang et al. (2020) for an extreme example.

In the present case, one could take the orientation that color–color relations are superfluous because the peak is covered. But this also means that color–color relations can provide an external check on systematics: if the unconstrained fits yield Spitzer fluxes that are in strong conflict with the constraint, this would be strong evidence that these fits are dominated by systematics, whereas the contrary result would be evidence that they are not.

3.2.3. Spitzer Analysis

We begin by undertaking a Spitzer-"only" analysis, in which the seven standard 2L1S parameters are held fixed at the values given in Table 2 and the 17 Spitzer data points are fit to four parameters (π_E,N , π_E,E , f_S,sat, f_B,sat). We consider the "inner" and "outer" solutions separately. We do not employ a flux constraint. In this initial test, we consider only the u_0,⊕ > 0 solutions, in the expectation (confirmed below) that the u_0,⊕ < 0 solutions will be essentially symmetric in π_E,N . To ensure that we completely cover the relevant parameter space, we conduct this modeling by a dense grid in (π_E,N , π_E,E ), fully covering π_E < 1.

The main result of this test is that for each of the inner/outer pair of solutions, and even without a flux constraint, there is a single, well-localized minimum. These are at (π_E,N , π_E,E ) ≃ ( − 0.08, + 0.02) and (−0.06, + 0.03), for the outer and inner solutions, respectively, with the first favored by Δχ² ∼ 7. See Table 3. ¹⁹ That is, there is no ±u_0,sat degeneracy, such as was predicted by Refsdal (1966) for 1L1S events. The physical reason for this is that the single minima have u_0,sat = + 0.025 and +0.03, respectively, that is, both passing on the same minor-image side of the caustic as is seen from Earth. In the alternate solutions (for 1L1S), these would have u_0,sat = − 0.025 and −0.03, that is, passing on the major-image side of the caustic. Once the planet is included this would have a completely different structure, with a bump instead of a dip. Indeed, for the outer solution case, this impact parameter would have the source passing directly over the caustic. For many Spitzer planets, this 1L1S degeneracy survives because the source does not pass close to any caustics as seen from Spitzer. However, as in the case of the first Spitzer planet, OGLE-2014-BLG-0124 (Udalski et al. 2015), this degeneracy is broken here.

Table 3. Spitzer-"only" Parameters for OGLE-2017-BLG-1275

Parameters	Inner (+, +)	Outer (+, +)	Inner (−, −)	Outer (−, −)
χ2/dof	19.71/13	13.00/13	19.75/13	13.34/13
πE,N	−0.059 ± 0.029	−0.084 ± 0.022	0.062 ± 0.028	0.089 ± 0.022
πE,E	0.027 ± 0.015	0.022 ± 0.009	0.022 ± 0.017	0.013 ± 0.011
LS [Spitzer]	17.17 ± 0.20	17.30 ± 0.16	17.17 ± 0.20	17.33 ± 0.17
LB [Spitzer]	${16.60}_{-0.14}^{+0.20}$	${16.52}_{-0.11}^{+0.14}$	${16.60}_{-0.13}^{+0.20}$	${16.50}_{-0.10}^{+0.14}$

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We refine this test by seeding an MCMC at each of the minima derived from the grid. This approach allows us to evaluate the (I − L) color and its uncertainty (in the absence of a constraint), (I − L)_outer = 2.05 ± 0.16 and (I − L)_inner = 2.14 ± 0.20. These can be compared with the constraint, which is derived in Section 4.1, (I − L)_constraint = 2.43 ± 0.08. These are therefore in 2.1σ and 1.3σ tension, respectively. Of course, only one of these solutions can be correct, so one might infer that the overall tension is at 1.3σ, which would be hardly notable. However, we should keep in mind that it is the outer solution that is overall preferred by Δχ² ∼ 7 (for the Spitzer-"only" data) that is in greater tension. We conclude that the constraint-free measurement and the constraint are in qualitative agreement, but we await investigation of the full fits to make a final assessment.

Next we conduct full fits by seeding an MCMC, fitting both the ground and Spitzer data, and then allowing 11 parameters (t₀, u₀, t_E, ρ, s, q, α, π_E,N , π_E,E , f_S,sat, f_B,sat) to vary, while determining the ground observatory flux parameters by a standard linear fit. We seed eight different models, that is, four for each of the outer and inner solutions. In each case, the first seed is the model just described, which we label (++) because u_0,⊕ > 0 and u_0,sat > 0. We seed the (− − ) model by reversing the signs of (u₀, α, π_E,N ). Although based on the π _E grid search we do not expect to find (+ − ) and (− + ) solutions, as a matter of due diligence we seed them according to the prescription of Refsdal (1966). However, we find that indeed these do not converge.

For the four solutions that do converge, that is, (outer and inner) × ((++) and (− − )), we repeat the fit with and without the flux constraint. The results, shown in Tables 4 and 5, confirm the preliminary assessment based on the Spitzer-"only" analysis. For the inner (++) solution, imposing the constraint increases χ² by Δχ² = 4.3 for 1 dof, while for the outer solution, Δχ² = 7.2. The numbers are similar for the (− − ) solution. While these results are broadly consistent with statistical fluctuations, they could reflect low-level systematics. However, even if so, these are no more severe than is typical for ground-based data in microlensing events. Hence, we accept the constrained fits from Tables 4 and 5 at face value. Note also that the seven standard parameters are hardly affected by the addition of Spitzer data relative to what was derived in Table 2 based on the ground-only fits.

Table 4. OGLE-2017-BLG-1275 (+, +) Parameters for Ground+Spitzer Data

Parameters	Inner (+, +)	Outer (+, +)	Inner-FREE (+, +)	Outer-FREE (+, +)
χ2/dof	9847.41/9838	9844.09/9838	9843.13/9837	9836.90/9837
t0 − 2457940	9.962 ± 0.017	9.951 ± 0.017	9.961 ± 0.018	9.949 ± 0.017
u0	0.395 ± 0.020	0.390 ± 0.019	0.397 ± 0.020	0.392 ± 0.020
tE (days)	13.41 ± 0.42	13.50 ± 0.42	13.38 ± 0.42	13.44 ± 0.42
s	0.630 ± 0.013	1.089 ± 0.040	0.630 ± 0.013	1.089 ± 0.039
q (10−3)	8.36 ± 1.34	9.11 ± 1.63	8.35 ± 1.28	9.08 ± 1.60
log q (mean)	−2.079 ± 0.069	−2.041 ± 0.078	−2.080 ± 0.067	−2.043 ± 0.077
α (rad)	4.755 ± 0.014	4.753 ± 0.013	4.756 ± 0.013	4.754 ± 0.013
ρ (10−2)	${3.0}_{-1.9}^{+2.7}$	${3.8}_{-2.4}^{+3.3}$	${2.7}_{-1.8}^{+2.5}$	${3.4}_{-2.1}^{+2.9}$
πE,N	−0.025 ± 0.015	−0.032 ± 0.016	−0.054 ± 0.032	−0.083 ± 0.024
πE,E	0.036 ± 0.017	0.032 ± 0.014	0.029 ± 0.017	0.023 ± 0.011
LS [Spitzer]	16.92 ± 0.11	16.96 ± 0.11	17.11 ± 0.23	17.31 ± 0.19
LB [Spitzer]	16.84 ± 0.12	16.81 ± 0.12	${16.64}_{-0.16}^{+0.23}$	${16.51}_{-0.12}^{+0.15}$
IS [OGLE]	19.359 ± 0.074	19.371 ± 0.073	19.352 ± 0.076	19.362 ± 0.074
IB [OGLE]	${21.08}_{-0.30}^{+0.46}$	${21.03}_{-0.28}^{+0.42}$	${21.12}_{-0.32}^{+0.48}$	${21.07}_{-0.29}^{+0.45}$

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Table 5. OGLE-2017-BLG-1275 (−, − ) Parameters for Ground+Spitzer Data

Parameters	Inner (−, − )	Outer (−, − )	Inner-FREE (−, − )	Outer-FREE (−, − )
χ2/dof	9847.18/9838	9845.24/9838	9843.58/9837	9836.81/9837
t0 − 2457940	9.963 ± 0.018	9.951 ± 0.017	9.962 ± 0.018	9.950 ± 0.017
u0	−0.396 ± 0.021	−0.390 ± 0.020	−0.397 ± 0.020	−0.392 ± 0.020
tE (days)	13.38 ± 0.42	13.48 ± 0.42	13.37 ± 0.41	13.44 ± 0.42
s	0.631 ± 0.014	1.089 ± 0.039	0.630 ± 0.013	1.089 ± 0.038
q (10−3)	8.29 ± 1.30	9.12 ± 1.60	8.29 ± 1.27	9.08 ± 1.58
log q (mean)	−2.082 ± 0.068	−2.041 ± 0.076	−2.082 ± 0.067	−2.043 ± 0.076
α (rad)	−4.755 ± 0.013	−4.752 ± 0.013	−4.756 ± 0.013	−4.754 ± 0.013
ρ (10−2)	${3.3}_{-2.1}^{+2.7}$	${3.8}_{-2.4}^{+3.2}$	${2.9}_{-1.8}^{+2.6}$	${3.5}_{-2.2}^{+2.8}$
πE,N	0.027 ± 0.015	0.034 ± 0.016	0.060 ± 0.030	0.087 ± 0.024
πE,E	0.034 ± 0.017	0.029 ± 0.015	0.022 ± 0.018	0.014 ± 0.012
LS [Spitzer]	16.91 ± 0.11	16.95 ± 0.11	17.14 ± 0.22	17.31 ± 0.19
LB [Spitzer]	16.85 ± 0.13	16.82 ± 0.12	${16.63}_{-0.15}^{+0.23}$	${16.51}_{-0.12}^{+0.15}$
IS [OGLE]	19.354 ± 0.075	19.369 ± 0.074	19.352 ± 0.073	19.361 ± 0.074
IB [OGLE]	${21.11}_{-0.31}^{+0.48}$	${21.04}_{-0.29}^{+0.43}$	${21.12}_{-0.31}^{+0.48}$	${21.07}_{-0.30}^{+0.45}$

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In Figure 2, we show the π _E contours for the three different fits (Spitzer-"only", ground+Spitzer without color constraint, and ground+Spitzer with color constraint) ²⁰ for each of the four geometries. Figure 2 shows that the color constraint has three effects. First, it reduces the error bars, primarily in the north direction. It is expected from Equation (10) that the main impact will be on the north direction because the Earth–satellite separation is mainly east–west, so that π_E,E is mainly constrained by the location of t_0,sat, which is directly fit from the light curve and does not depend on the source flux. Second, the best-fit parallax amplitude, π_E, is driven to lower values, by factors of about 1.4 and 1.9 for the inner and outer solutions, respectively. For the inner solutions, this change is within the error bar, while for the outer solution, it is in mild tension. Third, the parallax amplitude, π_E, is brought into closer agreement among the four solutions.

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The very small parallax amplitudes, π_E ∼ 0.045 ± 0.015, imply that the host lies in or very near the Galactic bulge. That is, the projected velocities are $\tilde{v}\equiv \mathrm{au}/{\pi }_{{\rm{E}}}{t}_{{\rm{E}}}\sim 2900\,\mathrm{km}\,{{\rm{s}}}^{-1}$, which is typical of bulge lenses. By comparison, for disk lenses moving according to an idealized flat rotation curve with v_rot ≃ 220 km s⁻¹ (and for typical bulge sources), ${\pi }_{\mathrm{rel}}\,=\mathrm{au}\,{\mu }_{\mathrm{rel}}/\tilde{v}\to {\pi }_{S}({v}_{\mathrm{rot}}/\tilde{v})\sim 0.01\,\mathrm{mas}$, that is, indicating a lens location where the bulge strongly dominates over the disk. We present a full Bayesian analysis in Section 5.1.

Figure 3 shows a relatively short, relatively low-amplitude 1L1S event, peaking at t₀ ≃ 7888.0 and punctuated by a dip at t_anom ≃ 7894.5 with full width Δt_dip ≃ 5.5 days. Although the baseline I_base ∼ 19.5 appears faint, the KMT tabulated extinction is unusually high, A_I = 4.69, implying that the source is likely to be a giant, in which case the blending is likely to be small. Under this assumption a 1L1S fit to the event with the anomaly excised yields u₀ = 0.64 and t_E = 15 days. Then τ_anom = 0.43 and u_anom = 0.77, implying (from Equations (2) and (4)) that α = 236°, ${s}_{-}^{\dagger }=0.69$, and q = 5.2 × 10⁻³.

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The grid search returns only one competitive local minimum, whose refined parameters are given in Table 6 and which has an inner geometry, as illustrated in Figure 3. The heuristic predictions for α and q are confirmed, while the fit value s_inner suggests that there may be another solution at ${s}_{\mathrm{outer}}={({s}_{-}^{\dagger })}^{2}/{s}_{\mathrm{inner}}=0.78$. In fact, the grid search has a minimum with this topology, but it was too strongly disfavored to warrant refinement. As a matter of due diligence, we seed an MCMC with this prediction for s_outer but find that it is excluded by Δχ² = 227. The fundamental reason for this is that the inner/outer degeneracy is much less severe when (as in the present case), α is far from ±90° (Zhang et al. 2022). In particular, for OGLE-2017-BLG-0640, the inner trajectory passes close to the second caustic, which generates a weak bump at the end of the dip, whereas the outer trajectory would generate such a weak bump at the beginning of the dip.

Table 6. Microlens Parameters for OGLE-2017-BLG-0640

Parameters	2L1S
χ2/dof	10845.18/10845
t0 − 2457880	7.917 ± 0.030
u0	0.651 ± 0.028
tE (days)	14.47 ± 0.40
s	0.610 ± 0.008
q (10−3)	4.87 ± 0.27
log q (mean)	−2.313 ± 0.024
α (rad)	4.133 ± 0.009
ρ (10−2)	${2.0}_{-1.3}^{+1.6}$
IS [OGLE]	19.637 ± 0.078
IB [OGLE]	${21.92}_{-0.511}^{+0.913}$

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OGLE-2017-BLG-1237 shows a clear caustic exit peaking at HJD${}^{{\prime} }=7935.70$, followed by a caustic entrance peaking at HJD${}^{{\prime} }=7937.63$, with a low-amplitude bump between these at HJD${}^{{\prime} }=7936.0$. Because of the time ordering of these two clear caustic features, there must be an additional entrance before the first (which was, in fact, observed at HJD${}^{{\prime} }=7933.8$) and an additional exit after the second (which occurred during a gap in the data). The bump is then almost certainly due to an approach to the cusp associated with the more massive component of the binary lens. That is, the geometry of the caustic system can be inferred by eye. A systematic grid search confirms that there is only one minimum, whose refinement is illustrated in Figure 4 and whose parameters are given in Table 7.

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Table 7. Microlens Parameters for OGLE-2017-BLG-1237

Parameters	2L1S
χ2/dof	6616.58/6617
t0 − 2457930	5.888 ± 0.004
u0 (10−2)	${1.766}_{-0.108}^{+0.075}$
tE (days)	${27.94}_{-1.13}^{+1.74}$
s	1.041 ± 0.001
q (10−3)	${7.93}_{-0.46}^{+0.35}$
log q (mean)	−2.105 ± 0.024
α (rad)	4.075 ± 0.005
ρ (10−4)	${7.66}_{-0.47}^{+0.35}$
IS [OGLE]	${21.865}_{-0.046}^{+0.068}$
IB [OGLE]	15.958 ± 0.001
t* (hours)	0.514 ± 0.007

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In general, it would be unusual for such an obvious and well-constrained planetary event to escape publication for 6 yr following its occurrence. However, in this case, there is a nearby bright star, I = 15.88, that lies 14 from the lens, which is a double-mode pulsator. The two closely spaced modes have periods P = 2.9 days, with a beat period of 41 days and some additional long-term structure as well. This star lies on the foreground main sequence (see Section 4.3), and it has a Gaia parallax π = 0.60 ± 0.14 mas, seemingly confirming that it is a nearby disk star. While the full amplitude of its variations is only ΔI ∼ 0.06 mag, relative to its own baseline flux, this amplitude is about 15 times larger than the unmagnified flux of the source star. Thus, the variable created significant difficulties for the light-curve analysis. By chance, the caustic features of the light curve occur near the minimum of the 41 day beat period, so contamination by the variable does not have a major impact on their interpretation. However, the effect, particularly the fractional effect, on the wings of the light curve is much larger, which directly impacts the measurement of t_E and thus would indirectly impact ρ, q, and other parameters.

To remove this impact, we first carried out photometry of the nearby variable over 2 yr, restricted to KMTC and KMTS, which are both high cadence and high quality. We then fit the resulting light curve (excluding the portion during the microlensing event) to the sum of nine sine waves, each characterized by three parameters (amplitude, period, and phase). When fitting the microlensing light curve, we added a term consisting of a free parameter multiplied by the mathematical representation of the variable light curve. We expect that the amount of contamination from the variable may be a function of seeing, and therefore we tried to find more complicated models that would include both seeing variations and the variable star function. However, these efforts did not lead to significant improvement.

OGLE-2017-BLG-1777 was early recognized as a potentially 2L1S planetary event by C. Han based on his combined analysis of OGLE and KMT data. However, he judged that the light curve could in principle also have been generated by a 1L2S binary-source event. Because of this complication (and the difficulty of ultimately resolving it), detailed analysis was deferred.

Such a detailed analysis was initiated by us as part of the AnomalyFinder series of papers. The orientation of these papers is to thoroughly analyze all events that are identified by the KMT AnomalyFinder (Zang et al. 2021) and that have competitive planetary solutions, regardless of whether the events are unambiguously planetary. For example, for 2018, Gould et al. (2022a) and Jung et al. (2022) analyzed (or cataloged from earlier AnomalyFinder papers) not only a total of 17 clear planets but also six other events for which the interpretation of the anomaly was ambiguous.

However, even in this context, OGLE-2017-BLG-1777 is unusually complex. Its light curve is best explained by the lens and source both having companions, with the former being a Jovian mass-ratio planet and the latter being a very low mass (VLM) star or brown dwarf (BD). The event has a number of peculiar features, such as an exceptionally small Einstein radius, θ_E, and an exceptionally small lens-source relative proper motion, μ_rel. As these two parameters derive from completely independent physical characteristics but could in principle be generated by an incorrect estimate of the normalized source radius, ρ, their confluence invites caution. If the θ_E measurement is correct, then the lens host is (like the source companion) a VLM star or BD. Much, but not all, of the evidence for the planetary companion comes from a single discrepant data point, which was the last one taken by OGLE during 2017. In fact, there are additional issues related to the long-term behavior of the OGLE data that required careful investigation. Hence, it is not a simple matter to properly address all of these issues within the context of a paper that systematically analyzes many planetary (and possibly planetary) events.

Nevertheless, because the goal of the AnomalyFinder papers is to present comprehensive analyses of all planetary and possibly planetary events, we must address all of these issues. We do so by putting the main thread of the light-curve analysis in this section, while deferring complex technical and semitechnical points to appendices.

The first point is that the light curve is affected in two different ways by a neighbor that lies ∼800 mas to the west of the source and is brighter than it by ∼4.3 mag. We analyze these effects and correct the light curve for them, as we discuss in Appendix A.

Next, contrary to the usual practice, we begin by introducing all the parameters that are required to describe our final model, rather than recapitulating the history of their gradual introduction as simpler models failed, one by one. This will allow us to comprehensively present the relationship between the final model and these simpler models. The final models as well as several intermediate models are illustrated in Figure 5, while their parameters are given in Tables 8 and 9.

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Table 8. Intermediate-model Parameters for OGLE-2017-BLG-1777

	2L1S	2L1S	1L1S	2L1S
Parameters	Static	Parallax	Xallarap	Xallarap
χ2/dof	12777.22/11900	12453.50/11898	11922.83/11896	11901.61/11893
t0 − 2458040	1.184 ± 0.002	1.169 ± 0.002	1.352 ± 0.003	${1.255}_{-0.025}^{+0.013}$
u0 (10−2)	1.016 ± 0.002	1.987 ± 0.046	0.814 ± 0.025	0.714 ± 0.023
tE (days)	60.40 ± 0.91	31.74 ± 0.53	81.36 ± 2.40	85.89 ± 3.03
s	0.796 ± 0.004	0.801 ± 0.003	⋯	${0.744}_{-0.056}^{+0.041}$
q (10−3)	6.08 ± 0.14	11.93 ± 0.29	⋯	${0.86}_{-0.20}^{+0.38}$
log q (mean)	−2.216 ± 0.010	−1.923 ± 0.010	⋯	−3.045 ± 0.129
α (rad)	2.983 ± 0.001	2.949 ± 0.003	⋯	3.003 ± 0.025
ρ (10−3)	13.33 ± 0.21	24.63 ± 0.37	8.24 ± 0.27	5.78 ± 032
πE,N	⋯	1.371 ± 0.060	⋯	⋯
πE,E	⋯	1.835 ± 0.078	⋯	⋯
ξN (10−2)	⋯	−	−0.829 ± 0.151	$-{0.267}_{-0.191}^{+0.289}$
ξE (10−2)	⋯	−	1.348 ± 0.045	1.098 ± 0.065
αS	⋯	−	305.0 ± 23.66	${334.5}_{-25.1}^{+14.8}$
δS	⋯	−	$-{15.4}_{-7.2}^{+5.4}$	${6.1}_{-11.6}^{+4.9}$
Ellipticity	⋯	−	0.055 ± 0.026	${0.114}_{-0.040}^{+0.050}$
Phase	⋯	−	0.400 ± 0.071	${0.367}_{-0.041}^{+0.073}$
Period (days)	⋯	−	12.75 ± 0.14	12.62 ± 0.16
IS [OGLE]	20.390 ± 0.018	19.674 ± 0.021	20.665 ± 0.032	${20.695}_{-0.031}^{+0.033}$
t* (hours)	19.32 ± 0.10	18.77 ± 0.13	16.06 ± 0.21	11.93 ± 0.42

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Table 9. Final-model Parameters for OGLE-2017-BLG-1777

Parameters	2L1S (Local 1)	2L1S (Local 2)
χ2/dof	11886.17/11889	11886.25/11889
t0 − 2458040	${1.251}_{-0.022}^{+0.015}$	1.224 ± 0.018
u0 (10−2)	0.945 ± 0.077	0.924 ± 0.072
tE (days)	65.3 ± 5.0	68.0 ± 5.3
s	0.732 ± 0.031	0.704 ± 0.030
q (10−3)	${1.17}_{-0.27}^{+0.40}$	1.63 ± 0.44
$\mathrm{log}q$ (mean)	−2.93 ± 0.12	−2.79 ± 0.12
α (rad)	3.015 ± 0.017	3.008 ± 0.014
ρ (10−3)	7.67 ± 0.63	6.97 ± 0.62
πE,N	0.09 ± 0.29	0.02 ± 0.25
πE,E	${0.246}_{-0.080}^{+0.120}$	0.230 ± 0.090
ds/dt (yr−1)	${3.15}_{-0.46}^{+0.35}$	${3.63}_{-0.67}^{+0.50}$
d α/dt (yr−1)	0.45 ± 0.57	$-{1.20}_{-0.56}^{+0.38}$
ξN (10−2)	$-{0.259}_{-0.132}^{+0.205}$	−0.074 ± 0.199
ξE (10−2)	1.395 ± 0.092	1.416 ± 0.096
αS	324.0 ± 21.6	336.0 ± 11.6
δS	$-{4.5}_{-6.7}^{+8.3}$	${7.2}_{-6.1}^{+3.8}$
Ellipticity	0.112 ± 0.038	${0.098}_{-0.032}^{+0.039}$
Phase	0.386 ± 0.056	0.363 ± 0.032
Period (days)	12.55 ± 0.15	12.58 ± 0.16
IS [OGLE-IV]	20.394 ± 0.090	20.407 ± 0.086
t* (hours)	12.00 ± 0.51	11.40 ± 0.48
β	${0.35}_{-0.11}^{+0.14}$	${0.51}_{-0.20}^{+0.16}$

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The final model is described by 18 parameters. Seven of these are the standard parameters that are always required to analyze 2L1S events, including all of the other events in this paper, (t₀, u₀, t_E, s, q, α, ρ). Four of the parameters are the microlens parallax vector π _E and the linearized transverse lens-orbital motion, γ , as described in Section 3.1. Finally, seven parameters are required to describe the Kepler orbit of the source around the center of mass of itself and its dark companion, that is, the "xallarap effect."

From a microlensing standpoint, xallarap is the inverse of parallax: light-curve distortions are induced by the orbital motion of the source rather than the observer. Hence, in principle, an annual parallax signal can always be imitated by xallarap, provided that the source orbital motion mimics that of Earth. Because of this, standard xallarap parameterization is set so that the measured xallarap parameters will mimic the corresponding parallax parameters for the case that the apparent xallarap is caused by parallax. Thus, while the microlens xallarap parameters are closely related to standard Kepler parameters, they are expressed somewhat differently.

The amplitude and orientation of the source motion (scaled by θ_E) is ξ ≡ (ξ_N , ξ_E ). As with the parallax, π _E, the direction is expressed with respect to the lens-source relative motion at t₀. The phase and inclination of the orbit are expressed as (α_S , δ_S ), so that in the case that the apparent xallarap is due to parallax, these will be exactly equal to the ecliptic coordinates of the event. Note in particular that edge-on orbits have δ_S = 0°, whereas in standard Kepler parameterization, the inclination would be i = 90°. The period P and eccentricity e are exactly the same as in the standard Kepler parameterization. Finally the "phase" of the periastron is measured relative to t₀. See Appendix B for more details about xallarap.

We briefly summarize how we were led to such a complex model. We began with a standard 2L1S model, which provided a reasonable first approximation to the data but (1) failed to match the final OGLE point and (2) left an oscillatory residual with a period of order 13 days near the peak. See the magenta curve and the bottom panel of residuals in Figure 5. As single-point discrepancies are quite common in microlensing, and this data point was taken at high air mass and in twilight, we initially suppressed the final OGLE point at HJD' = 8056.4965. We then added xallarap to the 2L1S fit and found substantial improvement (red curve and third panel of Figure 5). We then investigated whether a second lens was really required to explain the light curve or whether the entire light-curve distortion could be explained just by 1L1S plus xallarap (black curve and fourth panel). We found Δχ² = χ²(1L1S + xallarap) − χ²(2L1S + xallarap) = 21 for 3 dof, which would imply a marginal detection of a planet. However, we noticed that the 2L1S+xallarap model predicted a caustic crossing within a few days of the final OGLE data point (which we had previously suppressed). Hence, we carefully examined this point at the image level. Although the observing conditions were not optimal, there proved to be no indicators that artifacts of nonastronomical origin were corrupting the measurement. We then reincluded this point and added lens-orbital motion and parallax to the fit, thereby finding two different models, in each of which the final OGLE data point was explained by the source passing through the planetary caustic.

The two 18-parameter 2L1S models have an improvement over the 1L1S+xallarap model of Δχ² = 36 for 7 dof. Formally (for Gaussian statistics), this would imply a false-alarm probability of p ∼ 10⁻⁵. However, there are many reasons for caution. First, microlensing data are known to be non-Gaussian, although it is rare that Δχ² = 36 differences between competing models would be questioned. Second, much of this Δχ² is due to a single data point that was taken under somewhat difficult conditions. While we have closely vetted this point at the image level, the possibility that we have missed something about it cannot be absolutely ignored. Third, there are several features of the solution, which we summarize in the next two paragraphs, that are very unusual. While unusual things do happen, it is worrisome that they occur in an event for which the planetary interpretation relies on somewhat uncertain evidence. While the AnomalyFinder papers do not aim to make final decisions about including any particular event in subsequent statistical analyses, they do attempt to provide comprehensive accounts of all the information that is required to make such decisions. We therefore alert the reader to the nature of these issues in the next two paragraphs, while providing systematic accounts in the appendices.

The first issue is that both θ_E and μ_rel are unusually small. We will show in Section 4.4 that θ_ast ≃ 0.5 μas, which implies θ_E ≃ 70 μas and μ_rel ≃ 0.4 mas yr⁻¹. These are both rare for planetary microlensing events. The first depends only on the lens mass and the distances to the lens and source, while the second depends only on the proper motions of the lens and source. Because these are physically independent, but both depend on the same ρ measurement, they could be a warning sign of a major error in the model. We address this issue in Appendix C.

The second issue is that, as we show in Appendix B, BD and VLM star companions to the source can only be detected via xallarap if both θ_E and μ_rel are unusually small. Therefore, given that we report the detection of such a xallarap companion, it is not a further surprise that θ_E and μ_rel are small. On the other hand, it is the case that the presence of such objects in close-in orbits is rare. In particular, the probability of transit for companions in P = 12.5 day orbits about Sun-like stars is ∼4.5%. Such transits would give rise to strong signals in the great majority of stars observed by Kepler and would appear as Jovian-planet-sized companions, which would certainly be investigated. Hence, their low observed frequency shows they are intrinsically rare.

On the other hand, the fact that these two major questions about the event are both entangled with the prediction of the models that the source has a BD or VLM star companion (i.e., M_comp ∼ 0.075 M_⊙, see Appendix B) implies that confirmation of this companion would greatly increase confidence in the solution. We note that the predicted semiamplitude of radial velocity (RV) variations of the source star is $v\sin i\sim 6.5\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (see Appendix B), which should be measurable on large telescopes despite the faintness of the source, I_S ∼ 20.3.

Finally, there is one further test that we can make regarding the reality and/or plausibility of this unusually complex lens-source system. One can see from the top two caustic diagrams of Figure 5 (i.e., orbital-motion models) that the planetary caustics moved a substantial distance (0.2 or 0.4 Einstein radii) between t₀ (gray triangles) and the time of the final OGLE point (black contours), a motion that is determined directly by the data (in particular, the time of the final "discrepant" OGLE data point) but that is interpreted as being caused by physical motion of the planet within the context of these models. If the point were spurious, which is the main concern about the reality of these models, then most likely the inferred planetary motion would be either too large to be consistent with Kepler's laws or would be so small that it would require an improbable projection on the plane of the sky to be consistent with Kepler's laws. This test can be made in terms of the ratio of the transverse kinetic-to-potential energy parameters, β, which is defined in Equation (7). For face-on circular orbits, β = 0.5, and for a typical range of random projections, 0.1 ≲ β ≲ 0.5. Figure 6 shows the distributions of β based on the MCMCs for the two solutions. In both cases, we see that the peaks of these distributions are both relatively compact and overlap the expected range. Logically, this test would only require that this be true of at least one of these solutions, but in any case, it is true of both. The fact that the inferred orbital motion is consistent with expectations from Kepler's laws adds to the credibility of these planetary solutions but does not prove that they are correct.

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Figure 7 shows a relatively short, low-amplitude 1L1S event that is punctuated by a short bump at t_anom = 7873.5, that is, Δt_anom = + 2.5 days after the peak at t₀ = 7871. Taking account of the KMT tabulated extinction, A_I = 2.24, the baseline object has I_0,base ∼ 15.1, corresponding to a giant. Assuming, as is likely, it is unblended or only weakly blended, u₀ = 1.25 and t_E = 12 days. Then τ_anom = 0.21, u_anom = 1.27, α = 805, and ${s}_{+}^{\dagger }=1.82$.

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The grid search returns two local minima. We find (as is common for such low-amplitude events) that the division of the baseline flux into source and blend fluxes is poorly constrained, and so we set f_B = 0, which (as mentioned above) is plausible. The resulting parameters are shown in Table 10. The heuristic predictions for α are correct to within ∼2°. The prediction ${s}_{+}^{\dagger }=1.82$ is in excellent agreement with ${s}^{\dagger }\equiv \sqrt{{s}_{\mathrm{outer}}{s}_{\mathrm{inner}}}=1.82$.

Table 10. Microlens Parameters for OGLE-2017-BLG-0543

Parameters	Outer	Inner	1L2S
χ2/dof	8614.517/8615	8631.408/8615	8617.388/8614
t0 − 2457870	0.882 ± 0.050	1.040 ± 0.042	0.791 ± 0.057
u0	1.251 ± 0.003	1.242 ± 0.003	${1.276}_{-0.006}^{+0.007}$
tE (days)	12.080 ± 0.061	12.083 ± 0.061	12.104 ± 0.077
s	1.518 ± 0.027	2.185 ± 0.037	⋯
q (10−3)	4.250 ± 0.727	4.430 ± 0.672	⋯
log q (mean)	−2.373 ± 0.074	−2.354 ± 0.066	⋯
α (rad)	1.373 ± 0.007	1.389 ± 0.006	⋯
ρ	0.079 ± 0.052	${0.061}_{-0.038}^{+0.049}$	${0.114}_{-0.072}^{+0.093}$
t0,2 − 2457870	⋯	⋯	3.802 ± 0.080
u0,2	⋯	⋯	${0.093}_{-0.024}^{+0.018}$
ρ2	⋯	⋯	${0.086}_{-0.054}^{+0.044}$
qF (10−3)	⋯	⋯	3.656 ± 0.643
IS [KMTC]	17.336 ± 0.001	17.336 ± 0.001	17.336 ± 0.001
IB [KMTC]	⋯	⋯	⋯
IS,2 [KMTC]	⋯	⋯	23.433 ± 0.192

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As for any smooth-bump anomaly, we must check for alternative 1L2S solutions. After applying the same f_B = 0 constraint, we indeed find such a solution, which is illustrated in Figure 7 and summarized in Table 10. This solution is disfavored by only Δχ² = 2.9, which is well below the level needed to securely claim the detection of a planet. In some cases there can be additional arguments that could be made against the 1L2S solution. For example, it might predict an implausibly low proper motion, μ_rel = θ_ast/t_ast. In Section 4.5, we will show that θ_ast ≃ 5 μas. From Equation (9), we would have to be able to constrain μ_rel ≲ 1 mas yr⁻¹ to contribute significantly to such an argument, which would in turn require a restriction t_ast > 44 hr. However, this value is nearly within the 1σ range for both t_ast and t_ast,2. Hence, no such argument can be made.

Another possible argument could be made if the 1L2S model predicted a substantially different color than the one measured from the light curve. However, first, the second source is predicted to lie $-2.5\mathrm{log}{q}_{F}=6.0$ mag below the primary. Because the primary is a giant in or just below the clump, such a secondary would have a similar color to the primary, so even a precise color measurement could not distinguish between the 2L1S and 1L2S predictions. Second, the V-band signal from the secondary (assuming that the 1L2S model is correct) is too weak to measure its color.

Therefore, while it is possible that the anomaly in OGLE-2017-BLG-0543 is due to a planet, the 1L2S model also provides a plausible solution, and it certainly cannot be confidently excluded. Hence, this event should not be cataloged as planetary.

Figure 8 shows an approximately 1L1S event with a weak anomaly near peak, plausibly a postpeak bump. The underlying 1L1S curve is itself somewhat ambiguous because it is consistent with a range of timescales, t_E, or (because t_eff = u₀ t_E and f_S t_E are approximate invariants), equivalently, a range of f_S or u₀. Because both the 1L1S event and the anomaly are ambiguous, we dispense with a heuristic analysis and proceed directly to the grid search. This yields nine different solutions that are within Δχ² < 10 of the minimum, plus some additional ones that are somewhat worse. Two of these, with (s, q) = (0.637, 0.023) and (1.926, 0.019), form a close-wide pair of a major-image perturbation and are planetary in nature. A third is also planetary, but with a resonant caustic geometry and (s, q) = (1.16, 0.0016). See Table 11. For this reason, the event is included in the present paper as a "possible planet." However, another two, with (s, q) = (0.492, 0.051) and (1.892, 0.062), form a close-wide pair of a minor-image perturbation and are in the BD regime. See Table 12. And the remaining four are clearly in the stellar regime. See Table 13. Finally, in Table 11, we show one other planetary model that is just beyond our Δχ² < 10 threshold. The residuals of all these models are shown in Figure 8. As there is no way to distinguish among them, the event cannot be cataloged as planetary. Moreover, we find that there is a 1L2S solution whose χ² is similar to (actually slightly better than) those of the 2L1S solutions. See Table 14. This reinforces the ambiguous character of this event.

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Table 11. Planet Models for OGLE-2017-BLG-1694

Parameters	Close	Wide	Resonant 1	Resonant 2
χ2/dof	10193.24/10193	10194.72/10193	10193.56/10193	10215.75/10193
t0 − 2458000	3.349 ± 0.032	3.359 ± 0.039	3.390 ± 0.031	3.286 ± 0.069
u0	0.193 ± 0.016	0.204 ± 0.017	0.222 ± 0.014	0.322 ± 0.028
tE (days)	15.77 ± 0.74	15.65 ± 0.80	14.93 ± 0.62	13.07 ± 0.65
s	0.637 ± 0.077	1.926 ± 0.169	1.164 ± 0.017	1.104 ± 0.040
q (10−2)	${2.321}_{-0.909}^{+1.625}$	${1.915}_{-0.624}^{+1.000}$	${0.156}_{0.036}^{+0.049}$	3.409 ± 0.715
log q (mean)	−1.63 ± 0.23	−1.71 ± 0.19	−2.80 ± 0.12	−1.47 ± 0.09
α (rad)	0.965 ± 0.052	1.022 ± 0.037	1.095 ± 0.019	3.548 ± 0.045
ρ	0.035 ± 0.022	${0.025}_{-0.016}^{+0.019}$	0.068 ± 0.006	${0.088}_{-0.036}^{+0.024}$
IS [KMTC]	20.429 ± 0.096	20.363 ± 0.097	20.293 ± 0.079	19.877 ± 0.118
IB [KMTC]	19.678 ± 0.047	19.712 ± 0.053	19.753 ± 0.047	${20.114}_{-0.127}^{+0.171}$

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Table 12. Brown Dwarf Models for OGLE-2017-BLG-1694

Parameters	Close	Wide
χ2/dof	10201.45/10193	10201.27/10193
t0 − 2458000	3.410 ± 0.031	3.386 ± 0.032
u0	0.134 ± 0.009	0.136 ± 0.010
tE (days)	18.80 ± 0.87	19.24 ± 0.92
s	0.492 ± 0.016	1.892 ± 0.076
q (10−2)	5.05 ± 0.84	6.20 ± 1.12
log q (mean)	−1.300 ± 0.074	−1.209 ± 0.081
α (rad)	4.897 ± 0.019	4.920 ± 0.025
ρ	${0.021}_{-0.013}^{+0.018}$	${0.023}_{-0.015}^{+0.019}$
IS [KMTC]	20.820 ± 0.079	20.785 ± 0.084
IB [KMTC]	19.526 ± 0.024	19.536 ± 0.026

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Table 13. Star Models for OGLE-2017-BLG-1694

Parameters	Close 1	Wide 1	Close 2	Wide 2
χ2/dof	10198.91/10193	10196.59/10193	10194.32/10193	10198.98/10193
t0 − 2458000	3.596 ± 0.039	3.226 ± 0.033	3.063 ± 0.062	3.667 ± 0.036
u0	0.163 ± 0.011	0.130 ± 0.014	0.203 ± 0.015	0.117 ± 0.014
tE (days)	17.02 ± 0.78	${21.50}_{-1.84}^{+2.66}$	15.80 ± 0.79	${26.62}_{-2.54}^{+3.39}$
s	0.329 ± 0.012	4.228 ± 0.652	0.389 ± 0.021	4.397 ± 0.324
q (10−2)	${46.5}_{-9.0}^{+13.2}$	${43.1}_{-21.1}^{+41.2}$	${36.1}_{-4.8}^{+8.6}$	${170.2}_{-50.2}^{+77.1}$
log q (mean)	−0.326 ± 0.100	−0.356 ± 0.303	−0.426 ± 0.087	0.236 ± 0.156
α (rad)	0.895 ± 0.033	0.848 ± 0.025	${5.416}_{-0.049}^{+0.065}$	5.613 ± 0.039
ρ	${0.040}_{-0.025}^{+0.032}$	${0.015}_{-0.010}^{+0.015}$	${0.026}_{-0.017}^{+0.026}$	${0.020}_{-0.013}^{+0.016}$
IS [KMTC]	20.622 ± 0.079	20.669 ± 0.078	20.392 ± 0.092	20.450 ± 0.075
IB [KMTC]	19.593 ± 0.030	19.576 ± 0.028	19.697 ± 0.048	19.668 ± 0.037

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Table 14. 1L2S Parameters for OGLE-2017-BLG-1694

Parameters	1L2S
χ2/dof	10191.42/10192
t0 − 2458000	${3.00}_{-0.20}^{+0.16}$
u0	0.218 ± 0.021
tE (days)	15.811 ± 0.923
ρ	0.098 ± 0.064
t0,2 − 2458000	5.112 ± 0.071
u0,2	0.070 ± 0.022
ρ2	${0.073}_{-0.041}^{+0.028}$
qF	${0.084}_{-0.043}^{+0.071}$
IS [KMTC]	20.425 ± 0.120
IB [KMTC]	19.893 ± 0.073
IS,2 [KMTC]	${23.210}_{-0.517}^{+0.663}$

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For OGLE-2017-BLG-1275, we start by analyzing the source color primarily using I/H data (as opposed to V/I data). We do so for two reasons. First, the source is very reddened, which leads to substantially smaller error bars on individual H-band observations compared with those in the V band. Second, contrary to most of the AnomalyFinder planets, this event has Spitzer data, for which we require a color–color relation. These are overall both easier to determine and more reliable in IHL than VIL because the former is based on a shorter extrapolation.

Toward this end, we construct an I versus I − H CMD by matching field star photometry from UKIRT and OGLE-III, which are both calibrated. See Figure 9.

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The H-band light curve is already on the same scale as the field stars. We align the KMTC02 pySIS photometry (used in the fits) to KMTC02 pyDIA by regression and then to OGLE-III based on field stars. The comparison yields an offset Δ(I − H) = − 0.60 ± 0.05 of the source relative to the clump. Adopting (I − H)_0,cl = 1.29 from Bensby et al. (2013) and Bessell & Brett (1988), this implies (I − H)_0,S = 0.69 ± 0.05. From its I-band magnitude, ΔI = + 2.10 mag below the clump, the source is a turnoff star or subgiant. In terms of surface gravity, these are much closer to dwarfs than giants. Therefore, we estimate the corresponding (V − I) color using the dwarf star color–color relations of Bessell & Brett (1988), finding (V − I)_0,S = 0.65 ± 0.05. This is certainly possible, particularly within the errors, but it is relatively blue for a star of this magnitude.

Therefore, we conduct an independent assessment using V/I photometry. Because of severe extinction, our normal procedure of evaluating (V − I)_0,S from a single observatory-field combination yields statistical errors of σ(V − I)_s ∼ 0.14 mag, which is too large to obtain a useful check. We therefore combine four such measurements from KMTC02, KMTC42, KMTS02, and KMTS42, finding Δ(V − I) (relative to the clump) of (−0.22 ± 0.13), (−0.17 ± 0.14), (−0.41 ± 0.16), and (−0.24 ± 0.14), respectively, As these are are mutually consistent (χ² = 1.4 for 3 dof), we combine them to obtain Δ(V − I) = − 0.25 ± 0.07, which is substantially redder than the H-band-based determination. To proceed further, we convert this to (I − H)_0,S = 0.91 ± 0.09 using the dwarf star tables from Bessell & Brett (1988). Hence the two determinations are separated by 2.1σ and are therefore in mild tension. To reflect this tension, we adopt their weighted average, (I − H)_0,S = 0.74, but also adopt a larger error than the standard error of the mean (0.046 mag), namely, σ(I − H)_0,S = 0.07. For purposes of homogeneous reporting in Table 15, we note that this is equivalent to (V − I)_0,S = 0.69 ± 0.05.

We now apply this (I − H)_0,S color measurement to determine the (I − L)_S color constraint by applying an empirical IHL color–color relation derived by matching field stars from OGLE-III, UKIRT, and Spitzer. However, the only stars bright enough to enter an empirical determination based on field stars are giants, so we must take account of the fact that the IHL color–color relation is different for giants and dwarfs (including the object of interest, i.e., the microlensed source). This process is illustrated in Figure 10. In the main panel, the IHL relations from Bessell & Brett (1988) are shown for dwarfs and giants, in red and black, respectively. The green line segment shows the slope (1.24) of the empirical color–color relation derived by matching field stars from OGLE-III, UKIRT, and Spitzer. The length of this segment represents the range of colors of the stars that entered the determination. Its height is set to match its center to the black curve. The key point is that the slopes of the black curve and the green line are the same in this region. If this were not the case, it would mean that Bessell & Brett (1988) had made a serious error, that there was some problem with one of the three data sets that we are using, or that the IHL relation of bulge giants was substantially different from local giants. The magenta line extrapolates the linear relation represented by the green segment to bluer colors. The inset shows the offset of the dwarf IHL relation from this extrapolation, while the blue vertical line indicates the color of the microlensed source.

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The empirical IHL relation from field stars is (I − L) = 1.24[Δ(I − H)] + 3.146, where Δ(I − H) is the offset from the observed clump centroid (I − H)_cl = 3.58 or (I − H)_0,cl = 1.29. Finally, the color constraints must be applied to light-curve photometry, for example, I_KMTC02,pysis, which is offset from calibrated OGLE-III CMD photometry by I_KMTC02,pysis − I = − 0.08. Combining all these terms,

$$\begin{eqnarray}&&\begin{array}{l}({I}_{\mathrm{KMTC}02,\mathrm{pysis}}-L)=1.24[{\rm{\Delta }}(I-H)]+3.146\\ \quad +\,({I}_{\mathrm{KMTC}02,\mathrm{pySIS}}-I)+{\rm{\Delta }}(I-L),\end{array}\end{eqnarray} \tag{ 12 }$$

where the last term is given by the inset in Figure 10. This yields (I_KMTC02,pysis − L) = 2.43 ± 0.08.

We also place constraints on the blended light. In the light-curve fits, only about 16% of the baseline light is attributed to the blend. Nevertheless, this may be partly due to the difficulty of carrying out point-spread function (PSF) photometry of the baseline object in crowded bulge fields. Therefore, we more conservatively adopt I_B > 20.5, which constrains the lens flux, I_L ≥ I_B > 20.5. We expect this to provide only a very weak constraint because the π _E measurement already confines the lens to be in or near the bulge, so this limit only implies M_I,L > I_B − I_cl + M_I,cl > 3.1, which, among stars that are in or near the bulge, would only rule out those that have already evolved off the main sequence. Moreover, to be ruled out, such stars would need proper motions μ_rel ≡ θ_E/t_E =κ M π_E/t_E ≳ 10 mas yr⁻¹, which are themselves relatively rare. Nevertheless, for completeness, we will include this constraint in the Bayesian analysis of Section 5.1. Note that the blend is not displayed in Figure 9 because its color is not known.

Because this field is highly extincted and the source is intrinsically red, (V − I)_S cannot be measured from the KMT data. Fortunately, this event lies within the UKIRT Microlensing Survey (Shvartzvald et al. 2017), so we are able to determine θ_ast from an I/H CMD. See Figure 9. Although the CMD is based on a relatively small ($1^{\prime}$) circle centered on the event, there is strong differential extinction. That is, without extinction, the mean I-band magnitude of clump stars would be approximately independent of color, while the CMD shows that the bluer clump stars are, on average, substantially brighter than the redder ones. If this effect were due to a pure gradient in extinction across the field. The clump center at the location of the event would simply be the center of this tilted structure. We have investigated the CMD on smaller angular scales and find no evidence against the gradient hypothesis. We therefore adopt the center of the structure for the position of the clump (red dot). The source is Δ(I − H) = − 0.21 ± 0.03 mag bluer than the clump. To put this on a homogeneous basis with other entries in Table 15, we use Bessell & Brett (1988) to translate this offset to Δ(V − I) = − 0.14 ± 0.02, that is, (V − I)_0,S = 0.92 ± 0.02. Due to the fact that the source is a clump giant suffering heavy extinction, we cannot place any useful constraint on blended light.

As in all but one of the events in this paper, we align our measurements to the OGLE-III CMD. To measure the source color, we rely on KMTC03 pyDIA, for which there are two highly magnified V-band points on the night of ${\mathrm{HJD}}^{{\prime} }=7935$ and four moderately magnified points on ${\mathrm{HJD}}^{{\prime} }=7936$ and 7937. The relatively small scatter of the regression of these points (when combined with the mean from the relatively unmagnified points) confirms that the measurement is not strongly affected by the bright variable at 14. This is impressive, given the variable is 6.4 mag brighter than the source in V band. However, as mentioned in Section 3.4, the amplitude of this double-mode pulsator is close to its minimum during these 3 days of high and relatively high magnification.

Combining the resulting θ_ast = 0.318 ± 0.024 μas measurement from Table 15 and the parameters from Table 7 yields

$$\begin{eqnarray}\begin{array}{rcl}{\theta }_{{\rm{E}}} & = & \displaystyle \frac{{\theta }_{\mathrm{ast}}}{\rho }=415\pm 37\,\mu \mathrm{as};\\ {\mu }_{\mathrm{rel}} & = & \displaystyle \frac{{\theta }_{\mathrm{ast}}}{{t}_{\mathrm{ast}}}=5.42\pm 0.41\,\mathrm{mas}\,{\mathrm{yr}}^{-1}.\end{array}\end{eqnarray} \tag{ 13 }$$

Given the proximity of the clump-giant blend at ∼05 and the bright variable at ∼14, we are unable to place useful constraints on the light from the lens.

Because of the central role of OGLE-IV photometry in the removal of the complex trend (Appendix A), we determine I_0,S by calibrating OGLE-IV photometry to OGLE-III (i.e., I_OGLE-III = I_OGLE-IV + 0.064 ± 0.001), but we still evaluate (V − I)_0,S using KMT data as described in the preamble to this section. Indeed, we carry out these procedures twice, once using KMTC42 data and the second time using KMTS42 data. We thereby find $(V-I{)}_{S,\mathrm{OGLE}-\mathrm{III}}^{\mathrm{KMTS}42}=2.005\pm 0.030$ and $(V-I{)}_{S,\mathrm{OGLE}-\mathrm{III}}^{\mathrm{KMTC}42}=1.951\pm 0.025$. We adopt a calibrated value (V − I)_S = 1.97 ± 0.02, which then implies (V − I)_0,S =0.64 ± 0.03. See Table 15.

The resulting θ_ast = 0.490 ± 0.036 μas then implies for the two solutions,

$$\begin{eqnarray}&&{\theta }_{{\rm{E}}}=\displaystyle \genfrac{}{}{0em}{}{63.9\pm 4.7}{72.1\pm 5.3}\,\mu \mathrm{as};\ {\mu }_{\mathrm{rel}}=\displaystyle \genfrac{}{}{0em}{}{358\pm 26}{382\pm 28}\,\mu \mathrm{as}\,{\mathrm{yr}}^{-1},\displaystyle \genfrac{}{}{0em}{}{(\mathrm{Local}\ 1)}{(\mathrm{Local}\ 2)}.\end{eqnarray} \tag{ 14 }$$

We note that two of the "alarming" features of these 2L1S models, namely, the very small θ_E and μ_rel, are qualitatively similar for the single-lens/xallarap model: ${\theta }_{{\rm{E}}}^{1{\rm{L}}1{\rm{S}}}=52.5\,\mu \mathrm{as}$ and ${\mu }_{\mathrm{rel}}^{1{\rm{L}}1{\rm{S}}}=236\,\mu \mathrm{as}\,{\mathrm{yr}}^{-1}$.

Finally, we assess the limits on light from the lens based on both KMTC42 and KMTS42 pyDIA astrometry and on a comparison of KMT pyDIA astrometry with astrometry from OGLE-III and OGLE-IV. We reference all positions to the bright giant because it is in all four of these catalogs and because its position is likely to be well determined.

We find that the offset of the lens position (determined from the difference image) is Δ θ (E, N)_L = (825, 100) mas and (821, 111) mas for KMTC42 and KMTS42, respectively, which confirms that both the lens position and the giant neighbor position are well determined.

There are no stars detected near the position of the source in any of the four star catalogs that we investigated: OGLE-III, OGLE-IV, KMTC42, and KMTS42. However, there are several nearby stars that are detected at roughly comparable distances from the bright star, albeit in different directions. The closest such star is in the OGLE-IV catalog, which is separated by ${\rm{\Delta }}{\boldsymbol{\theta }}(E,N{)}_{{\rm{N}}1}^{{\rm{O}}-\mathrm{IV}}=(320,-750)\,\mathrm{mas}$ with I = 18.99. Hence, the scalar separation is 815 mas, which is comparable to 830 mas for the microlensed source. Again, however, these are separated in angle by 75°, so N1 cannot be the microlensed source. Nevertheless, we can say that if the microlensed source were as bright as N1, it would have been detected, and therefore we can put an upper limit on the lens light I_L > 19.0.

The characterization of the lens system is ambiguous, and so we include the CMD analysis only for completeness. The source photometry and inferred θ_ast are given in Table 15. Among the six events in this paper, OGLE-2017-BLG-0543 is the only one without calibrated photometry. However, because the determination of θ_ast requires only relative photometry, this is not a fundamental limitation. We note that the source is consistent with being unblended.

As was the case for OGLE-2017-BLG-0543, the characterization of the lens system is ambiguous, and so we include the CMD analysis only for completeness. The source photometry and inferred θ_ast are given in Table 15. By subtracting the source flux (derived from fitting the pyDIA light curve to the best model and transforming to the OGLE-III calibrated system) from the OGLE-III baseline flux, we find blended flux with I_B = 20.25. However, we do not show this blend in Figure 9 because we have no information about its color. That is, OGLE-III does not list a color for the baseline object, while KMT pyDIA does not resolve this object. We note that the baseline object lies within about 200 mas of the source, but we do not investigate the astrometry in detail.

OGLE-2017-BLG-1275 has four solutions, inner(++), inner( − − ), outer(++), and outer( − − ), upon which there are a total of four constraints, that is, on t_E, ρ, π _E, and I_L . The first comes from Tables 4 and 5, that is, ${\chi }_{{t}_{{\rm{E}}}}^{2}={({t}_{{\rm{E}},\mathrm{sim}}-{t}_{{\rm{E}},\mathrm{table}})}^{2}/{\sigma }_{{t}_{{\rm{E}}}}^{2}$, where ${t}_{{\rm{E}},\mathrm{sim}}$ is the timescale of the simulated event. The second is found by calculating ${\rho }_{\mathrm{sim}}={\theta }_{{\rm{E}},\mathrm{sim}}/{\theta }_{\mathrm{ast}}$, where ${\theta }_{{\rm{E}},\mathrm{sim}}$ is the Einstein radius of the simulated event and θ_ast is from Table 15, and then applying the χ²(ρ) envelope function from Figure 12. We note that, even at the 1σ level, this constraint only implies μ_rel ≳ 0.8 mas yr⁻¹, which is hardly constraining, but we nevertheless include this constraint for completeness. For the third, we find

$$\begin{eqnarray}&&{\chi }^{2}({{\boldsymbol{\pi }}}_{{\rm{E}}})=\displaystyle \sum _{i,j=1}^{2}({a}_{i}-{a}_{i,0})({a}_{j}-{a}_{j,0}){b}_{i,j}\qquad b\equiv {c}^{-1},\end{eqnarray} \tag{ 15 }$$

where the a_i are the π _E components for the simulated event, while a_i,0 and c_i,j are the mean and covariance matrix of π _E as derived from the MCMC. These have very similar values and error bars as the median-based values shown in Tables 4 and 5, with correlation coefficients, +0.35 (inner(++)), −0.32 (inner( − − )), +0.39 (outer(++)), and −0.40 (outer( − − )). The final constraint is I_L > 20.5, as discussed in Section 4.1.

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For all four solutions, the planet mass peaks near M_planet ∼ 6 M_Jup, while the host is near the M dwarf/K dwarf boundary. Note that the distance is D_L ∼ 7.7 kpc, that is, close to the Galactocentric distance, regardless of whether it belongs to the bulge or disk populations. Also note that the latter is prohibited by π _E measurements for the (+, + ) solutions because their directions are kinematically inconsistent with disk objects. The projected planet-host separation is either about 1.2 au or 2.2 au. By comparison, for an M_host ∼ 0.6 M_⊙ host, the snow line is about a_snow = 2.7 au(M_host/M_⊙) = 1.62 au. Hence, this is a relatively rare case for microlensing, in which the planet could be well inside the snow line, although because a_⊥ is bimodal, it may well be beyond the snow line, even in projection.

Finally, we note that the posterior estimate of the proper motion is μ_rel = 6.7 ± 2.2 mas yr⁻¹. Based on this estimate, the lens and source will be separated by Δθ ∼ 87 ± 29 mas in 2030, which is a plausible date for first light on AO on extremely large telescopes (ELTs). Hence, it is likely that the lens mass could be more precisely measured at AO first light (Gould 2022).

OGLE-2017-BLG-0640 has one solution, upon which there are two constraints, that is, on t_E and ρ. The first comes from Table 6, while the second comes from the ρ-envelope function shown in Figure 12, which is then combined with the θ_ast value from Table 15 to yield a constraint on θ_E.

The planet is of Jovian mass, and the host is an M dwarf, while the system is most likely in the Galactic bulge. The planet lies just beyond the snow line in projection.

The posterior proper-motion estimate is μ_rel = 7.2 ±2.4 mas yr⁻¹, which would imply a similar estimate for the separation at ELT AO first light as in the case of OGLE-2017-BLG-1275. However, the contrast ratio is expected to be much larger because the source is a giant (rather than a subgiant), while the lens is predicted to be a middle M dwarf (rather than near the boundary of M dwarfs and K dwarfs). Hence, it may be more challenging to resolve the lens and source separately for OGLE-2017-BLG-0640 than for OGLE-2017-BLG-1275.

OGLE-2017-BLG-1237 has one solution, upon which there are two constraints, that is, on t_E and θ_E, which come from Table 7 and Equation (13), respectively.

The planet is estimated to be several Jupiter masses, while the host is an early M dwarf. Similar to OGLE-2017-BLG-0640, the system most likely lies in the bulge. The planet lies well beyond the snow line.

In this case, the proper motion is directly measured (rather than being estimated from the Bayesian analysis as in the previous two events): μ_rel = 5.4 ± 0.4 mas yr⁻¹. The source is faint, meaning that the lens and source can certainly be resolved at ELT AO first light. In fact, it may well be possible to resolve the lens earlier than that using 10 m class telescopes. However, light from the clump-giant blend at 05 may make this difficult. Hence, this issue should be carefully evaluated before undertaking such observations.

The OGLE-2017-BLG-1777 event has two solutions, upon which there are a total of four constraints, that is, on t_E, ρ, π _E, and I_L . The first two come from Tables 8 and 9. The second then yields θ_E = θ_ast/ρ, where θ_ast is given in Table 15. The third applies Equation (15) to the mean values and errors of π _E, which are similar to the values in Tables 8 and 9, with correlation coefficients −0.15 and +0.12 for locals 1 and 2, respectively. The final constraint is I_L > 19.0, as discussed in Section 4.4.

The lens system is composed of a bulge BD (or possibly VLM star) orbited by a Neptune-class planet. Insofar as the concept of "snow line" applies to such systems, the planet lies well within the snow line. As we have discussed, the proper motion is extraordinarily low, μ_rel = 0.37 ± 0.03 mas yr⁻¹, which would make it impossible to resolve the source and lens (even if the latter proves to be luminous) using ELT AO for at least several decades. On the other hand, if the lens is luminous, the two could conceivably be resolved using the VLTI GRAVITY interferometer (Dong et al. 2019). However, as we have emphasized, the first additional observation that should be made to clarify the nature of this system is to measure the RV variations induced by the putative BD (or VLM star) companion to the source.

Because OGLE-2017-BLG-0543 has viable nonplanetary explanations, we do not carry out a Bayesian analysis.

Because OGLE-2017-BLG-1694 has viable nonplanetary explanations, we do not carry out a Bayesian analysis.