SPITZER PARALLAX OF OGLE-2015-BLG-0966: A COLD NEPTUNE IN THE GALACTIC DISK

The 2015 Spitzer microlensing campaign is the first project with the specific goal of characterizing the Galactic distribution of planets. Such characterization has three requirements.

• 1.  
  A survey that is sensitive to planets in substantially different Galactic environments.
• 2.  
  Well-characterized selection.
• 3.  
  The ability to determine, at least statistically, the Galactic environment of each potential host, whether or not a planet is detected.

At present, microlensing is the only possible method to attack this problem because all other planet search techniques fail criterion (1). We note that Clarkson et al. (2008) first attempted to answer this question by using Hubble Space Telescope data from the SWEEPS project to measure stellar proper motions and to establish the kinematic population membership of 16 transiting planet candidates from the Sagittarius Windows. Unfortunately, however, these candidates are difficult to confirm due to their faintness. By contrast, microlensing is about equally sensitive to planet-hosting lenses at all distances along the line of sight from the Sun to the Galactic bulge sources that are monitored for microlensing events.

Initially, microlensing planet searches were conducted in a fairly opportunistic way, dominated by targeted follow up of "interesting" events. Because "interesting" was not necessarily well defined, it was difficult to satisfy criterion (2). Nevertheless, Gould et al. (2010) and Cassan et al. (2012) were able to construct subsamples with well characterized selection. In parallel, the RoboNet and MiNDSTEp teams developed robotic algorithms (Horne et al. 2009; Dominik et al. 2010; M. P. G. Hundertmark et al. 2016, in preparation) to carry out the target selection in a repeatable and well characterized manner. With the advent of second generation surveys, (initially MOA and particularly OGLE-IV and most recently KMTNet), uniform selection is becoming routine (see, e.g., Shvartzvald et al. 2016; D. Suzuki et al. 2015, in preparation). In their high-cadence zones, these wide-field surveys can obtain dense enough coverage that additional follow up observations are not necessary to detect and characterize planets. Hence, events can be monitored uniformly with a pre-defined observing sequence.

The main problem has always been to determine the location of the lenses that are being probed for planets, including both those in which planets are detected and those for which they are not. For the great majority of microlensing events, the lens (host) star is not definitively identified and for many it is not detected at all. For these cases, the microlens parallax

$$\begin{eqnarray}{{\boldsymbol{\pi }}}_{{\rm{E}}} & \equiv & \displaystyle \frac{{\pi }_{\mathrm{rel}}}{{\theta }_{{\rm{E}}}}\;\displaystyle \frac{{\boldsymbol{\mu }}}{\mu };\qquad {\theta }_{{\rm{E}}}^{2}\equiv \kappa M{\pi }_{\mathrm{rel}};\\ \kappa & \equiv & \displaystyle \frac{4G}{{c}^{2}\;\mathrm{au}}\simeq 8.1\displaystyle \frac{\mathrm{mas}}{{M}_{\odot }},\end{eqnarray} \tag{ 1 }$$

is the key to determining the lens mass and distance. Here, ${\pi }_{\mathrm{rel}}=\mathrm{au}({D}_{L}^{-1}-{D}_{S}^{-1})$ and ${\boldsymbol{\mu }}$ are, respectively, the lens source relative parallax and proper motion, θ_E is the angular Einstein radius, and M is the lens mass. As detailed by Figure 1 from Gould & Horne (2013), the amplitude π_E = π_rel/θ_E is set by the fact that motion by the observer of 1 au displaces the apparent angular separation of the lens and source by an angle π_rel, which in turn induces microlensing effects according to how large this displacement is compared to the Einstein radius. In principle, there are two ways to observe the displacement caused by parallax. First, the observer can wait to be moved by the Earth's orbital motion, creating a displacement relative to simple rectilinear motion between the source and lens. Second, two observers at substantially different locations can compare their observations.

Some microlens parallaxes have been measured from the ground using the first effect, particularly for long timescale events (Poindexter et al. 2005) and including fortuitously a significant number of microlens planetary events (Gould et al. 2010). However, the sample of events with parallaxes measured from the ground is extremely heavily biased toward nearby lenses because they have projected Einstein radii ${\tilde{r}}_{{\rm{E}}}\equiv \mathrm{au}/{\pi }_{{\rm{E}}}$ ∼ 2–5 au, roughly three times smaller than is typical of bulge lenses. Hence, this sample is almost unusable for measuring the Galactic distribution of planets.

The alternative is space-based parallaxes. At ∼1 au from Earth, Spitzer is ideally located to be such a "microlens parallax satellite," and was used for the first such measurement by Dong et al. (2007). It does, however, face a number of challenges. First, due to Sun-angle viewing restrictions, it can observe Galactic bulge targets (which are near the ecliptic) for only 38 continuous days out of the 8 months they are visible from Earth. Second, microlensing events must first be detected from the ground and identified as reasonably planet-sensitive before they are targeted by Spitzer, and these uploads occur 3–10 days before the observations begin (Figure 1 of Udalski et al. 2015b). Since microlensing events often evolve quite rapidly, these practical constraints intrinsically restrict the pool of targets. Finally, Spitzer observes at λ = 3.6 μm, roughly 4.5 times the wavelength of ground-based microlensing searches. This creates technical problems, some of which are described below. See Yee et al. (2015a) for a more complete discussion.

In 2014 the director granted 100 hr for a pilot program to determine whether Spitzer could function effectively as a parallax satellite. Special protocols were developed to rapidly upload targets (Udalski et al. 2015b). New techniques were developed by Yee et al. (2015b) and Calchi Novati et al. (2015a) to break the famous "4-fold degeneracy" (Refsdal 1966; Gould 1994) that had been believed to require extremely aggressive observational strategies (e.g., Gould 1995; Gaudi & Gould 1997). For the two events with measured (OGLE-2014-BLG-1050, Zhu et al. 2015b) or strongly constrained (OGLE-2014-BLG-0124, Udalski et al. 2015b) θ_E (using the standard technique for events with caustic features, Yoo et al. 2004), the lens mass M and distance D_L were determined using inversions of Equation (1)

$$\begin{eqnarray}&&M=\displaystyle \frac{{\theta }_{{\rm{E}}}}{\kappa {\pi }_{{\rm{E}}}};\qquad {\pi }_{\mathrm{rel}}={\theta }_{{\rm{E}}}{\pi }_{{\rm{E}}};\qquad {D}_{L}=\displaystyle \frac{\mathrm{au}}{{\pi }_{\mathrm{rel}}+{\pi }_{S}}.\end{eqnarray} \tag{ 2 }$$

Here π_S is the source parallax which is almost always well understood because the source is visible. More critically, since the overwhelming majority of single-lens events do not show caustic features, a robust method was developed for estimating distances kinematically for events with measured ${{\boldsymbol{\pi }}}_{{\rm{E}}}$ but not θ_E (Calchi Novati et al. 2015a).

However, the 2014 Spitzer campaign was entirely focused on demonstrating the feasibility of the method, and no systematic effort was made to find planets. Nevertheless, one planet was discovered (Udalski et al. 2015b).

The successes of the 2014 campaign and the breakthroughs it precipitated led to the realization that satellite parallax measurements could be used to measure the Galactic distribution of planets. In 2015, 832 hr were awarded for a program whose primary objective was to do just that (Gould et al. 2014). In fact, as specifically argued in the proposal, several such annual campaigns will be required to acquire sufficient statistics to make this measurement.

As discussed in detail by Yee et al. (2015a), the observational protocols required to (1) maximize the sensitivity of the survey to planets, while (2) maintaining well characterized selection are both intricate and complex. We describe in some detail how these applied to the case of the planetary detection reported below. However, those readers interested in a full understanding must actually study Yee et al. (2015a).

Here, we report the discovery and characterization of the planet OGLE-2015-BLG-0966Lb. This is the second planet (after OGLE-2014-BLG-0124Lb, Udalski et al. 2015b) in the statistical sample of microlens parallax planets that can be used to determine the Galactic distribution. The observations, and the observational protocols that guided them, are described in Section 2. The ground-based and Spitzer light curves are combined to yield microlensing parameters for the event (including the microlens parallax π_E) in Section 3. There are some challenges in the estimate of θ_E relative to the usual case, which are discussed in Section 4. After resolving these, we present the system physical parameters in Section 5. Finally, we discuss some implications of this discovery in Section 6.

2.1. OGLE Alert and Observations

2.2. Spitzer Observations

2.3. MOA Data

2.4. Ground-based Follow-up Data

2.5. Other Bands

OGLE, LCOGT, and CTIO-SMARTS all obtained V-band observations in order to measure the V − I source color in order to characterize the source. As described above, CTIO-SMARTS automatically obtained H-band observations through the IR channel simultaneously with both the V-band and I-band optical observations. These also are used for source characterization and are not included in the analysis.

Table 1.  All Solutions

Parameters	(+, +), wide	(+, −), wide	(−, +), wide	(−, −), wide	(+, +), close	(+, −), close	(−, +), close	(−, −), close
χ2/dof	15136/15278	15138/15278	15137/15278	15135/15278	15136/15278	15151/15278	15154/15278	15135/15278
t0a	7205.1979	7205.1953	7205.1955	7205.1937	7205.1978	7205.1945	7205.1936	7205.1938
	0.0012	0.0013	0.0013	0.0012	0.0012	0.0012	0.0012	0.0012
u0	0.01136	0.01136	−0.01157	−0.01152	0.01136	0.01136	−0.01162	−0.01149
	0.00010	0.00010	0.00010	0.00010	0.00010	0.00010	0.00010	0.00009
tE (days)	57.7	57.8	57.7	57.7	57.7	57.7	57.5	57.8
	0.4	0.4	0.4	0.4	0.4	0.5	0.4	0.4
ρ (10−4)	14.08	14.00	14.06	14.06	14.07	14.02	14.12	14.04
	0.14	0.15	0.14	0.13	0.15	0.15	0.15	0.14
πE,N	0.0234	−0.0561	0.0397	−0.0412	0.0234	−0.0538	0.0317	−0.0412
	0.0012	0.0015	0.0012	0.0013	0.0012	0.0059	0.0094	0.0012
πE,E	−0.238	−0.237	−0.232	−0.237	−0.239	−0.264	−0.272	−0.237
	0.006	0.012	0.003	0.006	0.006	0.007	0.007	0.006
α (deg)	50.7	50.6	−50.4	−50.4	50.6	50.6	−50.3	−50.4
	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
s	1.1141	1.1146	1.1148	1.1147	0.9093	0.9091	0.9088	0.9091
	0.0033	0.0032	0.0033	0.0033	0.0026	0.0025	0.0027	0.0026
q (10−4)	1.67	1.67	1.68	1.68	1.70	1.70	1.71	1.70
	0.05	0.05	0.05	0.05	0.05	0.05	0.06	0.05
Blend	−0.027	−0.024	−0.027	−0.026	−0.027	−0.025	−0.031	−0.024
	0.008	0.009	0.008	0.008	0.008	0.008	0.008	0.008

Note.

^aHJD-2450000.

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Table 2.  Abbreviated Table of Parameter Values Averaged over the Four Solutions. Parameters which could be Estimated by Visual Inspection of the Light Curve Are included for Comparison

Parameters	Wide solution	Close solution	Visual-inspection Solution
Best χ2	15135	15135
t0a	7205.196 ± 0.002	7205.195 ± 0.002	7205.19
$| {u}_{0}|$	0.0115 ± 0.0001	0.0115 ± 0.0001	0.012
tE (days)	57.7 ± 0.4	57.7 ± 0.4	57
ρ (10−4)	14.04 ± 0.15	14.07 ± 0.15	12
$| {\pi }_{{\rm{E}},{\rm{N}}}|$	0.04 ± 0.02	0.03 ± 0.02	⋯
${\pi }_{{\rm{E}},{\rm{E}}}$	−0.24 ± 0.01	−0.25 ± 0.02	⋯
$| \alpha |$ (deg)	50.5 ± 0.2	50.5 ± 0.2	50.5
s	1.115 ± 0.004	0.909 ± 0.003	⋯
q (10−4)	1.68 ± 0.05	1.70 ± 0.06	⋯

Note.

^aHJD–2450000.

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2.6. Data Reduction

Real-time light curve analysis, both manual and automated (Bozza et al. 2010), was conducted during the event, and immediately alerted observers to the presence of the anomaly. Extensive offline analysis was subsequently carried out once data gathering on the event was complete.

The analysis reported below is based on a simultaneous fit to ground-based and Spitzer data. However, the key event characteristics can be most easily understood by considering the two light curves separately, and indeed many characteristics can be inferred by visual inspection.

Ignoring for the moment the post-peak perturbation centered at t_pert = 7205.75, the ground-based light curve shown in Figure 1 peaks at t₀ = 7205.19, almost 4.85 mag above baseline, indicating a high-magnification event A_max ≳ 85 (i.e., more if the baseline source is blended). In the neighborhood of the peak, such events are characterized by flux evolution $F(t)={F}_{{\rm{peak}}}{(1+{(t-{t}_{0})}^{2}/{t}_{\mathrm{eff}}^{2})}^{-1/2}$ where ${t}_{\mathrm{eff}}={u}_{0}{t}_{{\rm{E}}}$, t_E is the Einstein timescale, and u₀ is the impact parameter normalized to θ_E (Gould 1996). Inspection of the peak region shows t_eff = 0.68 days. (For example, CTIO data at ±1.50 days from peak are 0.96 mag below peak. Hence, ${t}_{\mathrm{eff}}=1.5\;{\rm{day}}{({10}^{0.8\times 0.96}-1)}^{-1/2}=0.68\;$ day.) The fact that there is no pronounced dip just prior to the abrupt rise due to a caustic crossing starting at t_cc = 7205.64 shows that the companion/host mass ratio is very small,⁵⁵ i.e., this is a planetary rather than binary system. Hence, the center of mass of the system is very close to the "center of magnification." It is the source motion relative to the "center of magnification" that produces the overall Paczyński (1986) curve over the unperturbed portions of the light curve. The proximity of the single caustic crossing to the peak of the Paczyński curve implies a trajectory which just clips the point of an arrow-shaped caustic. For the rest of the light curve to have remained unperturbed, the widest part of this arrow must lie away from the trajectory. The caustic must lie along the binary axis, so this means that the arrow points toward the center of magnification. Assuming that the source moves at a constant rate relative to the lens binary axis, it is possible to use the time gap between the light curve peaks to estimate the angle of the trajectory relative to that axis, α from a ratio with t_eff. This implies that the source is moving at an angle $\alpha ={\mathrm{tan}}^{-1}({t}_{\mathrm{eff}}/({t}_{{\rm{pert}}}-{t}_{0}))=0.88\;$ radians (505) relative to the planet host axis. There is no dip between the caustic entrance and exit, which implies that the caustic edges are separated by significantly less than the source radius ρ (normalized to θ_E). Hence, the source radius crossing time, t_* ≡ ρt_E, can be estimated ${t}_{*}\simeq ({t}_{{\rm{pert}}}-{t}_{{\rm{cc}}})\times \mathrm{sin}(\alpha )=0.07\;$ days. While it is not obvious by inspection, a simple point lens fit to the unperturbed light curve shows that the source is essentially unblended, so that in fact A_max = 85, so u₀ = 0.012, and hence ${t}_{{\rm{E}}}={t}_{\mathrm{eff}}/{u}_{0}=57\;$ days, and thus ρ = 1.2 × 10⁻³. That is, $({t}_{0},{u}_{0},{t}_{{\rm{E}}},\alpha ,\rho )$ = (7205.19, 0.012, 57 day, 51°, 1.2 × 10⁻³). These by eye estimates agree reasonably well with the parameter values derived from the best-fitting models (described below) presented in Tables 1 and 2. The remaining two parameters that can be extracted from the ground-based light curve, i.e., the planet-star mass ratio q and the planet-star separation s (normalized to θ_E), cannot be estimated by eye and must be determined from the fit. That said, it is worth noting that the shape and scale of the caustic derived by the above arguments restrict the possible combinations of s and q which could have produced the light curve seen.

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The effect of adding the Spitzer data is to determine the microlens parallax ${{\boldsymbol{\pi }}}_{{\rm{E}}}$, which is incorporated directly into the fit in equatorial (north, east) coordinates. However, as illustrated in Figure 1 of Gould (1994), the impact of these measurements is better visualized in the frame defined by the projected Spitzer-Earth axis ${{\boldsymbol{D}}}_{\perp }$, in which

$$\begin{eqnarray}{{\boldsymbol{\pi }}}_{{\rm{E}}} & = & \displaystyle \frac{\mathrm{au}}{{D}_{\perp }}({\rm{\Delta }}\tau ,{\rm{\Delta }}\beta );\qquad {\rm{\Delta }}\tau =\displaystyle \frac{{t}_{0,\oplus }-{t}_{0,\mathrm{sat}}}{{t}_{{\rm{E}}}};\\ {\rm{\Delta }}\beta & = & \pm {u}_{0,\oplus }-\pm {u}_{0,\mathrm{sat}},\end{eqnarray} \tag{ 3 }$$

and where the subscripts indicate parameters as measured from Earth and Spitzer.

For the intuitive analysis of the Spitzer light curve (Figure 1), we begin with the external information that the timescale t_E ≃ 57 days is known from the ground-based light curve. In fact, since the Earth-Spitzer motion (projected on the sky) is about 20 ${\rm{km}}\;{{\rm{s}}}^{-1}$ at the time that we will evaluate Equation (3), the timescales will not be exactly the same. However, this is expected to be a relatively small effect. Hence, we ignore it here with the proviso that we will later check for self-consistency. The Spitzer light curve shows a factor ∼4 rise over the 30 days of observations ending at 7222.14, where it is clearly turning over,⁵⁶ implying a peak t_0,sat ∼ 7225. Thus, the interval between peaks, normalized to the Einstein timescale is ${\rm{\Delta }}\tau =({t}_{0,\oplus }-{t}_{0,\mathrm{sat}})/{t}_{{\rm{E}}}\sim 0.35$. Since 30 days before the peak, u_sat ∼ 0.5 (A ∼ 2), the magnification at peak is at least ${A}_{\mathrm{max},\mathrm{sat}}\gtrsim 8$ (more if the Spitzer source flux is blended), so $| {\rm{\Delta }}\beta | =| {u}_{0,\oplus }-{u}_{0,\mathrm{sat}}| \simeq {u}_{0,\mathrm{sat}}\lesssim 0.12$. Spitzer was 1.39 au from the Earth midway between the peaks, with D_⊥ = 1.27 au after taking account of projection. Since it is approximately due west of Earth, the two coordinates in Equation (3) basically correspond to east and north, respectively. Hence, we derive π_E,E ∼ −0.28, and $| {\pi }_{{\rm{E}},N}| \lt 0.1$ As a final check, we note that these values imply a projected velocity in the Earth frame of $\tilde{v}=\mathrm{au}/({\pi }_{{\rm{E}}}{t}_{{\rm{E}}})\sim 100\;{\rm{km}}\;{{\rm{s}}}^{-1}$, meaning that Earth's motion is not completely negligible. In principle, we could make recursive corrections, but the main point of this exercise is to show that most of the results of the full light curve analysis can basically be derived by simple inspection of the Spitzer and ground-based light curves.

We systematically model the combined Earth-based and Spitzer light curves using software described in Dong et al. (2006, 2009), notwithstanding the above analysis showing that five of the seven Earth-based parameters are well determined by visual inspection and simple analysis. Note that for this thorough analysis we do not assume that the event timescale will be observed from both Earth and space. The location of the Spitzer spacecraft during the event was extracted from the JPL Horizons website,⁵⁷ enabling us to make a precise conversion of the timestamps of its data to Heliocentric Julian Date, with the corresponding conversion made for all ground-based observatories. All data sets are then modeled in the same frame of reference. We conduct a systematic search of parameter space using two different techniques, one based on an (s, q, α) grid and the other based on light curve morphologies. Models are evaluated based on the reduced χ² of the fit per data set (${\chi }_{{\rm{red}}}^{2}$). To account for variations in the estimation of photometric errors in different data sets, we adopt the common practise (e.g., Bachelet et al. 2012) of re-normalizing the errors according to:

$$\begin{eqnarray}&&{e}_{{\rm{new}}}={a}_{0}\sqrt{{e}_{{\rm{orig}}}^{2}+{a}_{1}^{2}}.\end{eqnarray} \tag{ 4 }$$

Coefficients a₀ and a₁ are set such that the ${\chi }_{{\rm{red}}}^{2}$ of each data set relative to the model equal unity.

We found that the only viable solutions do in fact have the five parameters as approximately specified above. Moreover, s and q are well localized, except that (as is often the case) there is a degenerate solution $s\to {s}^{-1}$ (Griest & Safizadeh 1998).

Figures 2 and 3 illustrate the geometries of all eight solutions, and Table 1 gives the parameters for these solutions. The notation (+, −) is used to indicate solutions where the lens source relative trajectory approaches the caustic from the positive or negative θ direction in the lens-plane geometry. Two indices are given for each solution: one for Earth-based observations and one for Spitzer. According to Table 1, the best wide and close solutions differ by Δχ² < 1. Hence, this very common degeneracy is completely unbroken in the present case. However, since the microlensing parameters of these two sets of solutions are very similar, their physical implications are basically the same.

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Within each set of solutions (wide or close), the physical implications are even closer to the point of being nearly identical. Therefore, we present in Table 2 a simplified summary of each set of solutions, with the parameter values being averages over the four solutions and the "errors" taking account of both the fit errors at different minima and the differences between minima.

We estimate θ_E using the standard approach (Yoo et al. 2004), i.e., estimating the source surface brightness from its dereddened color (V − I)₀ and the calibrated color/surface brightness relation of Kervella et al. (2004), and then comparing this to dereddened magnitude I_s,0.

We begin (as is usual) by assuming that the source is behind the same dust column as the bulge clump stars. Visual comparison of V- and I-band images of the field indicates substantial differential reddening, with a region of apparent extinction extending to the southeast of the target. We restricted our analysis to stars within a 60'' radius about the source, wherein the clump appears compact. The centroid I magnitude and (V − I) color of the red clump were measured by calculating the mean values of these parameters for stars within I, (V − I) ranges chosen to isolate the clump on the color–magnitude diagram. The quoted uncertainties refer to the standard error on the mean of each parameter. Table 3 compares the measured I magnitude and (V − I) of the source and the red clump centroid from both the OGLE and the CTIO data. Using OGLE data, we find that the source is ΔI = 3.15 ± 0.05 mag below the clump, whereas using CTIO data we find ΔI = 3.01 ± 0.05 mag. Figure 4 shows the color–magnitude diagrams derived from both data sets. This difference is typical of the difficulty in centroiding the clump in the vertical (magnitude) direction. We adopt ΔI = 3.08 ± 0.07 mag and so ${I}_{s,0}={I}_{{\rm{cl}},0}+{\rm{\Delta }}I=17.49\pm 0.08$ mag, where ${I}_{{\rm{cl}},0}=14.41$ mag is adopted from Nataf et al. (2013). Comparing this value with OGLE's I_cl, we infer the extinction of A(I) = 2.07 mag along this line of sight. Similarly, by comparing OGLE's (V − I)_cl with (V − I)_cl,0 = 1.06 mag from Bensby et al. (2013), we derive a reddening measurement of E(V − I)_cl = 1.73 mag.

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Determining (V − I)_s (and so (V − I)_s,0) presents greater challenges given that the source is quite faint at a baseline of V ∼ 21.9 mag and that the full moon was passing through the bulge when the source was most highly magnified. OGLE systematically acquires V-band data for all its fields, but of course avoids observing near the moon. Hence, the OGLE ${(V-I)}_{0}$ color estimate has relatively large errors: ${\rm{\Delta }}{(V-I)}_{S}=-0.31\pm 0.06$ mag. CTIO deliberately targeted the event near peak (and so moon passage) in order to obtain high signal-to-noise measurements. Some of these observations were corrupted by scattered moonlight, but most appear fine. These data yield ${\rm{\Delta }}{(V-I)}_{S}=-0.35\pm 0.03$ mag We combine these OGLE and CTIO measurements by standard error weighting and obtain ${(V-I)}_{s,0}={(V-I)}_{{\rm{cl}},0}+{\rm{\Delta }}(V-I)=0.72\pm 0.012$ mag, where we have adopted ${(V-I)}_{{\rm{cl}},0}=1.06$ mag from Bensby et al. (2013).

Applying the relation derived by Nataf et al. (2013) to calculate the distance to the Galactic Bar given the viewing angle from Earth, we infer a distance of 8.00 kpc. If we assume that the source is exactly at the distance to the clump and adopt ${M}_{I,\mathrm{cl}}=-0.12$ mag, then this implies ${[{M}_{I},{(V-I)}_{0}]}_{s}\;=(2.96,0.72)$ mag. This is a plausible pair of values for a star just entering the sub-giant branch from the turnoff. That is, the assumption that the source lies behind all the dust is self-consistent, since it implies that the source inhabits a reasonably well-populated part of the color–magnitude diagram.

However, another interpretation is that the source lies on the upper main sequence (since its color is similar to the Sun). Then, M_I ∼ 4.15 mag, so that the star lies 1.2 mag in front of the Bulge in distance modulus, or at D_S ∼ 4.5 kpc from us. In this case, it would still lie about 125 pc below the Galactic plane and so behind most, but possibly not all, the dust toward the Galactic bulge. In Figure 4 we have overplotted solar metallicity PARSEC isochrones (Bressan et al. 2012) for a log g = 4.4 main sequence star and a log g = 3.9 sub-giant at ages where their respective V − I colors were closest to that of the source, for reference.

We first estimate the source radius under the assumption that it is a bluish bulge sub-giant and then address how this estimate may be affected if the source is in fact a disk main sequence star. We used the tabular data presented by Bessell & Brett (1988) to convert (V − I)_s,0 to (V − K)_s,0. They quote an uncertainty of "<0.04 mag," and we adopt 0.02 mag as a reasonable error for the purposes of our analysis. This leads to estimates

$$\begin{eqnarray}{\theta }_{*} & = & 1.07\pm 0.10\;\mu \mathrm{as};\qquad {\theta }_{{\rm{E}}}=\displaystyle \frac{{\theta }_{*}}{\rho }=0.76\pm 0.07\;\mathrm{mas};\\ {\mu }_{\mathrm{geo}} & = & \displaystyle \frac{{\theta }_{{\rm{E}}}}{{t}_{{\rm{E}}}}=4.8\pm 0.5\;{\rm{mas}}\;{{\rm{yr}}}^{-1}.\end{eqnarray} \tag{ 5 }$$

If the source were a disk main sequence star, but nevertheless lay behind all the dust, then these estimates would not be affected at all. Only the dereddened color and magnitude enter the calculation, and these would not change. If the source does lie in front of some of the dust, then it is both intrinsically redder in (V − I) and fainter in I than the above calculations would imply. Of course fainter stars have smaller radii at fixed surface brightness, but redder stars have lower surface brightness (so larger radii) at fixed magnitude. Hence, these two effects tend to cancel. Since the total amount of dust behind the source is unlikely to be large and the two effects tend to cancel, and since at this point we cannot reliably estimate how much dust does lie behind the source, we will proceed on the assumption that the source is behind all of the dust. However, in Section 6, we discuss how this issue could be partly or fully resolved in the future.

The above procedure has become a standard approach for calculating the angular radii of microlensing source stars since Yoo et al. (2004), but we note recent work by Boyajian et al. (2014) to develop improved empirical relations predicting stellar angular size for main sequence stars as functions of photometric color measured from a wider range of color indices. The new V, (V − I_C) relations enable a more direct estimate of θ_* without first converting the measured color to another passband. From this we derive a value of θ_* = 1.04 ± 0.16 μas, consistent with our previous estimate.

The extraction of physical parameters is made simpler by the "resolution" (or rather, irrelevance) of the ambiguity of the amplitude of Δβ (Section 3), but more complicated by the ambiguity in the source distance (Section 4). We therefore begin with the lens mass estimate, which does not depend on the source distance, derived from Gould (2000):

$$\begin{eqnarray}M & = & \displaystyle \frac{{\theta }_{{\rm{E}}}}{\kappa {\pi }_{{\rm{E}}}}=0.38\pm 0.04\;{M}_{\odot };\\ {m}_{{\rm{planet}}} & = & {qM}=21\pm 2{M}_{\oplus }.\end{eqnarray} \tag{ 6 }$$

Similarly, for the projected velocity in the geocentric and heliocentric frames (Gould & Yee 2014)

$$\begin{eqnarray}&&{\tilde{{\boldsymbol{v}}}}_{\mathrm{geo}}(N,E)=\displaystyle \frac{\mathrm{au}}{{t}_{{\rm{E}}}}\;\displaystyle \frac{{{\boldsymbol{\pi }}}_{{\rm{E}}}}{{\pi }_{{\rm{E}}}^{2}}=(0\pm 16,-124\pm 40)\;{\rm{km}}\;{{\rm{s}}}^{-1}\\ &&{\tilde{{\boldsymbol{v}}}}_{\mathrm{hel}}={\tilde{{\boldsymbol{v}}}}_{\mathrm{geo}}+{{\boldsymbol{v}}}_{\oplus ,\perp }=(0\pm 16,-95\pm 40)\;{\rm{km}}\;{{\rm{s}}}^{-1},\end{eqnarray} \tag{ 7 }$$

where ${{\boldsymbol{v}}}_{\oplus ,\perp }(N,E)=(-0.8,28.8)\;{\rm{km}}\;{{\rm{s}}}^{-1}$ is the Earth's velocity projected on the plane of the sky at the peak of the event and where we have ignored the slight differences among the four wide solutions.

Regardless of the source location, the relative parallax is well-determined

$$\begin{eqnarray}&&{\pi }_{\mathrm{rel}}={\theta }_{{\rm{E}}}{\pi }_{{\rm{E}}}\quad =\quad 0.19\pm 0.01\;\mathrm{mas}.\qquad \end{eqnarray} \tag{ 8 }$$

enabling us to constrain the distance to the lens through the relation:

$$\begin{eqnarray}&&{\pi }_{\mathrm{rel}}={\pi }_{L}-{\pi }_{S}=\displaystyle \frac{{au}}{{D}_{L}}-\displaystyle \frac{{au}}{{D}_{S}}.\end{eqnarray} \tag{ 9 }$$

However, depending on the distance to the source, this leads to two different distance estimates for the lens D_L = 3.3 kpc (bulge source) or D_L = 2.5 kpc (disk source). However, within the context of our program of determining the Galactic distribution of planets, these two outcomes are basically similar: foreground disk lens. In Section 6, we discuss how this ambiguity may be resolved with future observations.

Finally, the ambiguity in D_L gives rise to an ambiguity of the same size in the star-planet projected separation ${r}_{\perp }=s{\theta }_{{\rm{E}}}{D}_{L}=2.7\;\mathrm{au}$ (bulge source) or 2.1 au (disk source). Adopting a snowline r_snow = 2.7 au (M/M_⊙), these separations are at r_⊥/r_snow = 2.2 and 1.7 snowline distances, respectively. Hence, in either case, this planet is a "cold Neptune." Note that in making these estimates, we have adopted s = 1, i.e., midway between (and 10% different from) the close and wide solutions. The physical parameters of this system are summarized in Table 4.

This is the second microlensing planet (after OGLE-2014-BLG-0124Lb), whose mass and distance have been measured with the aid of parallax observations using Spitzer. However, it is the first to be so characterized as part of a program specifically designed to measure the Galactic distribution of planets by means of well defined selection criteria (Yee et al. 2015a). While naively such well defined criteria might seem to lead to clear cut observing decisions, the example of OGLE-2015-BLG-0966 demonstrates that they in fact create a set of complex interlocking constraints, both hard and soft, on decision processes of multiple semi-autonomous decision makers working toward a common goal. Specifically, there was the struggle to determine whether surveys would cover this event, including both static but non-obvious (KMT) information and dynamic OGLE information, the impact on balancing with coverage of other events (also impacted by survey coverage), and wild oscillations in Spitzer cadence due to objective criteria. See Section 2.

In the present case, these follow up observations that were subject to these interlocking constraints led to the detection and characterization of a planet while preserving the integrity of the selection process. In subsequent papers, we will show that similar sensitivity to planets (while maintaining sample integrity) was achieved under similar conditions for several other high-magnification events.

The character of the planet continues to confirm that "cool Neptunes are common" (Gould et al. 2006), even though that original claim was based on just two detections. However, the central focus of the present effort is not the frequency of planets as a function of mass, but of Galactocentric radius. Nothing can be said so far about this in part because there are so far only two planets in the sample, but mainly because the sensitivity of the surveys to planets as a function of Galactocentric radius has not yet been determined (although see Zhu et al. 2015a for initial work in that direction). Nevertheless, it is intriguing to note that both detected planets are in the near to mid-disk.

While the lens is clearly in the disk, it is unknown at this point whether the source is in the bulge or the disk. While the source distance is of overall secondary interest, it does affect the lens distance D_L and planet-star separation r_⊥ at the 25% level and therefore should be resolved if possible. We note that the heliocentric projected velocity ${\tilde{{\boldsymbol{v}}}}_{\mathrm{hel}}$ does tend to favor a disk source just because the solutions all have the heliocentric projected velocities pointing basically out of the Galactic plane, and indeed somewhat retrograde. By contrast, as expected naively (and confirmed by Calchi Novati et al. 2015a), events with bulge sources and disk lenses tend to have ${\tilde{{\boldsymbol{v}}}}_{\mathrm{hel}}$ aligned with Galactic rotation. This is because the Sun and the lens both basically partake of this rotation while bulge source proper motions tend to be both isotropically distributed and of low amplitude.

The situation would be greatly clarified by measuring the proper motion of the source, as Yee et al. (2015b) did for the Spitzer event OGLE-2014-BLG-0939. In contrast to that case, however, in which the source was bright and easily distinguished from neighbors, which enabled precise astrometric measurements from over a decade of OGLE observations, the OGLE-2015-BLG-0966 source star is both too faint and too close (07) to a neighbor for reliable astrometry. However, using difference image astrometry applied to high-magnification images, the current position of the lens is measured with a precision of about 20 mas. Hence, a single epoch of high-resolution imaging 10 years from now should be able to reliably determine whether the source proper motion is consistent with disk motion (typically about 6 ${\rm{mas}}\;{{\rm{yr}}}^{-1}$).

This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.

The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to A.U.

Work by J.C.Y., A.G., and S.C. was supported by JPL grant 1500811. Work by W.Z. and A.G. was supported by NSF AST 1516842. Work by J.C.Y. was performed under contract with the California Institute of Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. The Spitzer Team thanks Christopher S. Kochanek for graciously trading us his allocated observing time on the CTIO 1.3 m during the Spitzer campaign.

Work by C.H. was supported by the Creative Research Initiative Program (2009-0081561) of National Research Foundation of Korea.

G.D. acknowledges Regione Campania for support from POR-FSE Campania 2014–2020.

T.S. acknowledges the financial support from the JSPS, JSPS23103002, JSPS24253004, and JSPS26247023. The MOA project is supported by the grants JSPS25103508 and 23340064. The US portion of the MOA Collaboration acknowledges financial support from the NSF (AST-1211875) and NASA (NNX12AF54G).

Work by Y.S. was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Oak Ridge Associated Universities through a contract with NASA.

This publication was made possible by NPRP grant #X-019-1-006 from the Qatar National Research Fund (a member of Qatar Foundation).

S.D. is supported by the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (grant No. XDB09000000).

Work by S.M. has been supported by the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences Grant No. XDB09000000, and by the National Natural Science Foundation of China (NSFC) under grant numbers 11333003 and 11390372.

M.P.G.H. acknowledges support from the Villum Foundation. Based on data collected by MiNDSTEp with the Danish 1.54 m telescope at the ESO La Silla observatory. J. Surdej and O.W. acknowledge support from the Communaut franaise de Belgique Actions de recherche concertes Acadmie Wallonie-Europe. S.H.G. and X.B.W. acknowledge the financial support from National Natural Science Foundation of China through grants Nos. 10873031 and 11473066.

N.P. acknowledges funding by the Gemini-Conicyt Fund, allocated to the project No. 32120036.

This work makes use of observations from the LCOGT network, which includes three SUPAscopes owned by the University of St Andrews. The RoboNet programme is an LCOGT Key Project using time allocations from the University of St Andrews, LCOGT, and the University of Heidelberg together with time on the Liverpool Telescope through the Science and Technology Facilities Council (STFC), UK. This research has made use of the LCOGT Archive, which is operated by the California Institute of Technology, under contract with the Las Cumbres Observatory.