Abstract
We report an analysis of the planetary microlensing event OGLE-2018-BLG-1185, which was observed by a large number of ground-based telescopes and by the Spitzer Space Telescope. The ground-based light curve indicates a low planet–host star mass ratio of q = (6.9 ± 0.2) × 10−5, which is near the peak of the wide-orbit exoplanet mass-ratio distribution. We estimate the host star and planet masses with a Bayesian analysis using the measured angular Einstein radius under the assumption that stars of all masses have an equal probability of hosting the planet. The flux variation observed by Spitzer is marginal, but still places a constraint on the microlens parallax. Imposing a conservative constraint that this flux variation should be and a planet mass of
. A Bayesian analysis including the full parallax constraint from Spitzer suggests smaller host star and planet masses of
and
, respectively. Future high-resolution imaging observations with the Hubble Space Telescope or Extremely Large Telescope could distinguish between these two scenarios and help reveal the planetary system properties in more detail.
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1. Introduction
The gravitational microlensing method has a unique sensitivity to low-mass planets (Bennett & Rhie 1996) beyond the snow line of the host star (Gould & Loeb 1992), where, according to core accretion theory predictions, planet formation is most efficient (Lissauer 1993; Pollack et al. 1996). The Microlensing Observations in Astrophysics (MOA) Collaboration (Bond et al. 2001; Sumi et al. 2003) presented the most complete statistical analysis of planets found by microlensing to date and the best measurement of the planet distribution beyond the snow line in Suzuki et al. (2016). They found that the mass-ratio distribution from the 2007 to 2012 MOA-II microlensing survey combined with earlier samples (Gould et al. 2010; Cassan et al. 2012) is well fitted by a broken power-law model.
Their result shows the mass-ratio distribution peaks at with power-law slopes of
and
above and below qbr, respectively.
70
This result is consistent with previous microlensing analyses, which suggest that Neptune-mass-ratio planets are more common than larger gas giants (Gould et al. 2006; Sumi et al. 2010), and further indicates that Neptune-mass-ratio planets are, in fact, the most common type of planet (large or small) in wide orbits.
Additionally, Suzuki et al. (2018) revealed a disagreement between the measured mass-ratio distribution in Suzuki et al. (2016) and the predictions of the runaway gas accretion scenario (Ida & Lin 2004), which is part of the standard core accretion theory. Population synthesis models based on core accretion, including runaway gas accretion, predict too few planets in the mass range of approximately 20–80M⊕ compared to those inferred from microlensing observations. Similar tension is indicated by Atacama Large Millimeter/submillimeter Array (ALMA) observations. Nayakshin et al. (2019) compared the wide-orbit (9–99 au) planet candidates with masses of 0.01MJup to a few MJup suggested by ALMA protoplanetary disk observations to a population synthesis prediction from the runaway gas accretion scenario. They found that the scenario predicts fewer sub-Jovian planets than the ALMA observations inferred. Three-dimensional hydrodynamical simulations of protoplanetary disks do not support the runaway gas accretion scenario either (Lambrechts et al. 2019).
The peak position of the mass-ratio function and its slope at low-mass ratios are uncertain due to the lack of planets with mass ratios of q < 5.8 × 10−5 in the Suzuki et al. (2016) sample. Udalski et al. (2018) and Jung et al. (2019b) used samples of published planets to refine estimates of the peak and the low-mass-ratio slope of the mass-ratio function. Udalski et al. (2018) confirmed the turnover shown in Suzuki et al. (2016) and obtained the slope index in the low-mass regime, p ∼ 0.73, using seven published planets with q < 1 × 10−4. Jung et al. (2019b) found qbr ≃ 0.55 × 10−4 using 15 published planets with low-mass ratios (q < 3 × 10−4). The Jung et al. (2019b) study was subject to "publication bias." That is, the planets were not part of a well-defined statistical sample. Instead, these planets were selected for publication for reasons that are not well characterized. Nevertheless, the authors make the case that this publication bias should not be large enough to invalidate their results. By contrast, the Udalski et al. (2018) study only made the implicit assumption that all planets with q < 1 × 10−4 (and greater than that of the actual published planet) would have been published. If this is true (which is very likely), the study is not subject to publication bias.
A more definitive improvement of the Suzuki et al. (2016) mass-ratio function can be obtained with an extension of the MOA-II statistical sample to include additional microlensing seasons (D. Suzuki et al. 2021, in preparation). The low-mass-ratio planet analyzed in this paper, OGLE-2018-BLG-1185Lb, will be part of that extended sample, and it will contribute to an improved characterization of the low end of the wide-orbit exoplanet mass-ratio function.
The statistical analysis of the wide-orbit planet population can also be improved by including information on the lens physical parameters, such as the lens mass, ML, and the distance to the lens star, DL. While the lens planet–host mass ratios, q, are usually well constrained from the light-curve modeling, we need at least two mass–distance relations in order to derive ML and DL directly. There are three observables that can yield mass–distance relations: finite source effects, microlens parallax effects, and direct detection of the lens flux.
In recent years, lens flux detection by high-resolution imaging follow-up observations (such as by the Hubble Space Telescope (HST) or Keck) has been done for several microlens planetary systems after the lens and the source are separated enough to be detected (Bennett et al. 2006, 2007, 2015, 2020; Batista et al. 2014, 2015; Bhattacharya et al. 2017, 2018; Koshimoto et al. 2017; Vandorou et al. 2020). However, the required separation for resolving the lens and source depends on their relative brightnesses, and even if they are comparable in brightness, it typically takes a few years for them to separate sufficiently.
If both the Einstein radius
![Equation (1)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn1.gif)
where DS is the distance to the source (Gould 1992, 2000). Finite source effects are detected in most planetary-lens events through the observation of a caustic crossing or a close approach to a caustic cusp, thus enabling the measurement of
The most common method for measuring the microlens parallax has been via the effects of the motion of the observer, which is called the orbital parallax effect. In order to detect the orbital parallax, the ratio of tE (typically tE is ∼30 days) to Earth's orbital period (365 days) should be significant. Thus, we only measure the orbital parallax effect for microlensing events with long durations and/or relatively nearby lens systems, yielding mass measurements in less than half of the published microlensing planetary systems.
The most effective method for routinely obtaining a microlens parallax measurement is via the satellite parallax effect (Refsdal 1966), which is caused by the separation between two observers. Because the typical Einstein radius projected onto the observer plane, , is about 10 au, the satellite parallax effect can be measured for a wide range of microlenses provided the separation between Earth and the satellite is about 1 au (as was the case for Spitzer).
For the purpose of measuring the Galactic distribution of planets and making mass measurements through the satellite parallax effect, the Spitzer microlensing campaign was carried out from 2014 to 2019 (Gould & Yee 2013; Gould et al. 2014, 2015a, 2015b, 2016, 2018). During the six-year program, close to 1000 microlensing events were simultaneously observed from the ground and by Spitzer, and there are 11 published 71 planets with satellite parallax measurements from Spitzer: OGLE-2014-BLG-0124Lb (Udalski et al. 2015), OGLE-2015-BLG-0966Lb (Street et al. 2016), OGLE-2016-BLG-1067Lb (Calchi Novati et al. 2019), OGLE-2016-BLG-1195Lb (Shvartzvald et al. 2017), OGLE-2016-BLG-1190Lb (Ryu et al. 2018), OGLE-2017-BLG-1140Lb (Calchi Novati et al. 2018), TCP J05074264 + 2447555 (Nucita et al. 2018; Fukui et al. 2019; Zang et al. 2020), OGLE-2018-BLG-0596Lb (Jung et al. 2019), KMT-2018-BLG-0029Lb (Gould et al. 2020), OGLE-2017-BLG-0406Lb (Hirao et al. 2020), and OGLE-2018-BLG-0799Lb (Zang et al. 2020). Comparison of planet frequency in the disk to that in the bulge could probe the effects of the different environments on the planet formation process.
Obvious correlated noise in Spitzer photometry was first noted by Poleski et al. (2016) and Zhu et al. (2017), but those works did not expect the systematic errors would have a significant effect on the parallax measurements. Indeed, two comparisons of small, heterogeneous samples of published Spitzer microlensing events have confirmed this expectation (Shan et al. 2019; Zang et al. 2020). However, a larger study (Koshimoto & Bennett 2020) of the 50-event statistical sample of Zhu et al. (2017) indicated a conflict between the Spitzer microlensing parallax measurements and Galactic models. It suggested that this conflict was probably caused by systematic errors in Spitzer photometry. Based, in part, on the Koshimoto & Bennett (2020) analysis, the Spitzer microlensing team has made a greater effort to understand these systematic errors, including obtaining baseline data in 2019 for many of the earlier planetary events. These additional baseline data proved very useful in the characterization of systematics in Spitzer photometry for three previously published events (Gould et al. 2020; Hirao et al. 2020; Zang et al. 2020). Those analyses show that systematics in Spitzer photometry can be present at the level of 1–2 instrumental flux units, so observed signals in Spitzer photometry on those scales should be interpreted with caution.
In this paper, we present an analysis of the planetary microlensing event OGLE-2018-BLG-1185, which was simultaneously observed by many ground-based telescopes and the Spitzer Space Telescope. From ground-based light-curve analysis, the planet–host star mass ratio turns out to be very low, q ∼ 6.9 × 10−5, which is thought to be near the peak of the wide-orbit exoplanet mass-ratio distribution in Suzuki et al. (2016), Udalski et al. (2018), and Jung et al. (2019b). Section 2 explains the observations and the data reductions. Our ground-based light-curve modeling method and results are shown in Section 3. In Section 4, we derive the angular Einstein radius from the source magnitude and color and the finite source effect in order to constrain the physical parameters of the planetary system. In Section 5, we estimate the physical properties such as the host star and planet masses based on the ground-based light curve alone by performing a Bayesian analysis using the measured angular Einstein radius under the assumption that stars of all masses have an equal probability of hosting the planet. We present our parallax analysis including the Spitzer data in Section 6. Finally, we discuss the analysis and summarize our conclusions in Section 7.
2. Observations and Data Reductions
2.1. Ground-based Survey Observations
The microlensing event OGLE-2018-BLG-1185 was first discovered on 2018 July 7 ( = HJD − 2,450,000 ∼ 8306), at J2000 equatorial coordinates (R.A., decl.) = (17h59m10
26, −27°50'06
3) corresponding to Galactic coordinates (l, b) = (2
465, −2
004), by the Optical Gravitational Lensing Experiment (OGLE) Collaboration (Udalski 2003). The OGLE Collaboration conducts a microlensing survey using the 1.3 m Warsaw Telescope with a 1.4 deg2 field-of-view (FOV) CCD camera at Las Campanas Observatory in Chile and distributes alerts of the discovery of microlensing events by the OGLE-IV Early Warning System (Udalski et al. 1994; Udalski 2003). The event is located in the OGLE-IV field BLG504, which is observed with a cadence of one observation per hour.
The event was also discovered independently on 2018 July 9 by the MOA Collaboration and identified as MOA-2018-BLG-228 by the MOA alert system (Bond et al. 2001). The MOA Collaboration conducts a microlensing exoplanet survey toward the Galactic bulge using the 1.8 m MOA-II telescope with a 2.2 deg2 wide FOV CCD camera, MOA-cam3 (Sako et al. 2008), at the University of Canterbury's Mount John Observatory in New Zealand. The MOA survey uses a custom wideband filter referred to as RMOA, corresponding to the sum of the Cousins R and I bands, and also uses a Johnson V-band filter. The event is located in the MOA field gb10, which is observed at a high cadence of one observation every 15 minutes. The Korea Microlensing Telescope Network (KMTNet) Collaboration (Kim et al. 2016) conducts a microlensing survey using three 1.6 m telescopes each with a 4.0 deg2 FOV CCD camera. The telescopes are located at the Cerro Tololo Inter-American Observatory (CTIO) in Chile (KMTC), the South African Astronomical Observatory (SAAO) in South Africa (KMTS), and Siding Spring Observatory (SSO) in Australia (KMTA). This event is located in an overlapping region between two fields (KMTNet BLG03 and BLG43) and was identified by the KMTNet EventFinder (Kim et al. 2018) as KMT-2018-BLG-1024.
2.2. Spitzer Observations
In order to construct statistical samples from the Spitzer microlensing campaign, Yee et al. (2015) established detailed protocols for the selection and observational cadence of Spitzer microlensing targets. On 2018 July 8 (), OGLE-2018-BLG-1185 was selected as a "subjective, immediate" (SI) target to be observed with the "objective" cadence by the Spitzer microlensing team. The selection as SI meant that this event was observed even though it never met the objective criteria established in Yee et al. (2015). The Spitzer Space Telescope began to observe this event on 2018 July 14 (
), which was 3 days after the peak observed from the ground-based telescopes. The objective cadence resulted in approximately one observation per day for the remainder of the observing window (27 days total). These observations were taken with the Infrared Array Camera in the 3.6
2.3. Ground-based Follow-up Observations
After the event was selected for Spitzer observations, some ground-based follow-up observations were conducted. The Microlensing Network for the Detection of Small Terrestrial Exoplanets (MiNDSTEp) used the 1.54 m Danish Telescope at La Silla Observatory in Chile and the 0.6 m telescope at Salerno University Observatory in Italy. The Microlensing Follow-up Network (
Table 1. The Number of Data Points in the Light Curves and the Normalization Parameters
Name | Site | Collaboration | Aperture (m) | Filter | k |
![]() | Nuse/Nobs |
---|---|---|---|---|---|---|---|
OGLE | Chile | OGLE | 1.3 | I | 1.660 | 0.003 | 3045/3045 |
OGLE | Chile | OGLE | 1.3 | V | 1.301 | 0.003 | 68/68 |
MOA | New Zealand | MOA | 1.8 | RMOA | 1.650 | 0.003 | 7277/7509 |
MOA | New Zealand | MOA | 1.8 | V | 1.321 | 0.003 | 240/240 |
KMT SSO f03 | Australia | KMTNet | 1.6 | I | 1.900 | 0.003 | 2087/2706 |
KMT SSO f43 | Australia | KMTNet | 1.6 | I | 1.824 | 0.003 | 2080/2658 |
KMT CTIO f03 | Chile | KMTNet | 1.6 | I | 1.579 | 0.003 | 2304/2486 |
KMT CTIO f43 | Chile | KMTNet | 1.6 | I | 1.443 | 0.003 | 2195/2363 |
KMT SAAO f03 | South Africa | KMTNet | 1.6 | I | 2.444 | 0.003 | 1813/2096 |
KMT SAAO f43 | South Africa | KMTNet | 1.6 | I | 1.900 | 0.003 | 1846/2078 |
Danish | Chile | MiNDSTEp | 1.54 | Z | 1.015 | 0.003 | 139/154 |
Salerno | Italy | MiNDSTEp | 0.6 | I | ... | ... | 0/5 |
LCO SSO | Australia | LCO–Spitzer | 1.0 |
![]() | 2.528 | 0.003 | 31/44 |
LCO CTIO | Chile | LCO–Spitzer | 1.0 |
![]() | 1.129 | 0.003 | 17/17 |
LCO SAAO | South Africa | LCO–Spitzer | 1.0 |
![]() | ... | ... | 0/19 |
CTIO 1.3 m | Chile |
| 1.3 | I | 0.852 | 0.003 | 18/18 |
CTIO 1.3 m | Chile |
| 1.3 | V | 0.566 | 0.003 | 3/3 |
LCO SSO | Australia | ROME/REA | 1.0 | g | ... | ... | 0/25 |
LCO SSO | Australia | ROME/REA | 1.0 |
![]() | ... | ... | 0/74 |
LCO SSO | Australia | ROME/REA | 1.0 | r | ... | ... | 0/29 |
LCO CTIO | Chile | ROME/REA | 1.0 | g | 1.110 | 0.003 | 33/33 |
LCO CTIO | Chile | ROME/REA | 1.0 |
![]() | 1.589 | 0.003 | 61/61 |
LCO CTIO | Chile | ROME/REA | 1.0 | r | 1.337 | 0.003 | 31/31 |
LCO SAAO | South Africa | ROME/REA | 1.0 | g | ... | ... | 0/17 |
LCO SAAO | South Africa | ROME/REA | 1.0 |
![]() | ... | ... | 0/19 |
LCO SAAO | South Africa | ROME/REA | 1.0 | r | ... | ... | 0/45 |
Spitzer | Earth-trailing orbit | Spitzer | 0.85 | L | 2.110 | ⋯ | 26/26 |
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2.4. Data Reduction
The OGLE, MOA, and KMTNet data were reduced using the OGLE difference image analysis (DIA) photometry pipeline (Udalski 2003), the MOA DIA photometry pipeline (Bond et al. 2001), and the KMTNet pySIS photometry pipeline (Albrow et al. 2009), respectively. The MiNDSTEp data were reduced using DanDIA (Bramich 2008; Bramich et al. 2013). The
It is known that the photometric error bars calculated by data pipelines can be underestimated (or more rarely overestimated). Various factors, such as observational conditions, can cause systematic errors. In order to get proper errors of the parameters in the light-curve modeling, we empirically normalize the error bars by using the standard method of Bennett et al. (2008). We use the formula
![Equation (2)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn2.gif)
where is the ith renormalized error,
are the renormalizing parameters. We set the value of
to account for systematic errors that dominate at high magnification, and we adjust the value of k to achieve
3. Ground-based Light-curve Analysis
3.1. Binary-lens model
The magnification of the binary-lens model depends on seven parameters: the time of lens–source closest approach, t0; the Einstein radius crossing time tE; the impact parameter in units of the Einstein radius, u0; the planet–host mass ratio q; the planet–host separation in units of the Einstein radius, s; the angle between the trajectory of the source and the planet–host axis,
![Equation (3)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn3.gif)
where A(t) is the magnification of the source star, and fS and fb are the unmagnified flux from the source and the flux from any unresolved blend stars, respectively.
We also adopt a linear limb-darkening model for the source star,
![Equation (4)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn4.gif)
where S and a metallicity of
, we select limb-darkening coefficients of uI
= 0.5494, uV
= 0.7105, uR
= 0.6343, uZ
= 0.6314, ug
= 0.7573, ur
= 0.6283, and ui
= 0.5389 from the ATLAS model (Claret & Bloemen 2011). For the RMOA passband, we use the coefficient for uRed = 0.5919, which is the mean of uI
and uR
.
We first conducted light-curve fitting with only ground-based data. We employed a Markov Chain Monte Carlo algorithm (Verde et al. 2003) combined with the image-centered ray-shooting method (Bennett & Rhie 1996; Bennett 2010). We conducted grid search analysis following the same procedure in Kondo et al. (2019). First, we performed a broad grid search over the (q, s, ,
, and 0 <
The parameters of the best-fit models are summarized in Table 2. The light curve and the caustic geometry are shown in Figures 1 and 2. As a result of the grid search, we found that the best-fit binary-lens model is favored over the single-lens model by to ∼8311.8, which are well fitted by the approach to the central caustic for the best binary-lens model. Although the additional magnification from the cusp approach to the planetary caustic is small, the asymmetric feature on the right side of the light curve due to the approach to the central caustic shows clear residuals from the single-lens model, which suggest the existence of a companion. The best binary-lens model suggests that the lens system has a very-low-mass ratio, q ∼ 6.9 × 10−5, with a normalized separation s ∼ 0.96. It is well known that there is a close/wide degeneracy in high-magnitude binary-lens events (Griest & Safizadeh 1998; Dominik 1999; Chung et al. 2005), which is due to the similar shape and size of the central caustic between s and s−1. From the grid search, we found the best wide binary-lens model (s > 1) has q ∼ 9.2 × 10−5 and s ∼ 1.14. The separation of this wide model is slightly different from the reciprocal of the separation of the close model (s < 1), yielding a different shape and size for the central caustic from those of the best close model. We ruled out the wide model because the best close binary-lens model is favored over the wide model by
Figure 1. The light curve and models with the ground-based data for OGLE-2018-BLG-1185. The top panel shows the light curve, models, and residuals from the best-fit close binary-lens (2L1S) model. The blue line shows the best-fit close 2L1S model. The red, orange, and green dotted lines show the single-lens (1L1S) model, the wide 2L1S model, and the binary-source (1L2S) model, respectively. The left and right bottom panels show zoomed-in views of the light curve, where we can find clear deviations of the data points from the 1L1S and 1L2S models.(The data used to create this figure are available.)
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Standard image High-resolution imageFigure 2. Caustic geometry of the best-fit model. The caustics are shown as red lines. The blue line shows the source trajectory on the lens plane and the arrow indicates the direction of the source/lens relative proper motion. The blue open circle indicates the source size and position at t0.
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Standard image High-resolution imageTable 2. The Best-fit Models for Ground-only Data
Parameters | Unit | 2L1S (Close) | 2L1S (Wide) | 1L2S |
---|---|---|---|---|
| ... | 23,221.473/23,252 | 23,489.306/23,252 | 23,601.431/23,249 |
t0,1 | HJD' | 8310.7772 ± 0.0003 | 8310.7793 ± 0.0003 | 8310.7726 ± 0.0003 |
t0,2 | HJD' | ⋯ | ⋯ | 8311.5874 ± 0.0010 |
tE | days | 15.931 ± 0.133 | 16.312 ± 0.144 | 15.730 ± 0.189 |
u0,1 | 10−3 | 6.877 ± 0.063 | 6.606 ± 0.067 | 7.777 ± 0.131 |
u0,2 | 10−3 | ⋯ | ⋯ | 8.773 ± 1.515 |
q | 10−5 | 6.869 ± 0.229 | 9.164 ± 0.552 | ⋯ |
s | ... | 0.963 ± 0.001 | 1.144 ± 0.003 | ⋯ |
| rad | 0.114 ± 0.001 | 3.261 ± 0.002 | ⋯ |
| 10−3 | 3.468 ± 0.083 | <1.026 a | 7.234 ± 0.241 |
| 10−3 | ⋯ | ⋯ | 1.613 ± 0.956 |
qf,I | 10−2 | ⋯ | ⋯ | 1.699 ± 0.192 |
fS (OGLE) b | ... | 107.777 ± 0.437 | 106.493 ± 0.448 | 108.583 ± 0.550 |
fb (OGLE) b | ... | 396.165 ± 0.594 | 397.397 ± 0.440 | 393.516 ± 0.587 |
Notes.
a The value is the 3![${I}_{{\rm{S}}}=25-2.5\mathrm{log}({f}_{{\rm{S}}})$](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baieqn27.gif)
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3.2. Binary-source model
We checked the possibility that the observed light curve can be explained by the binary-source model because it is known that there is a possible degeneracy between the single-lens binary-source (1L2S) model and the binary-lens single-source (2L1S) model (Griest & Hu 1993; Gaudi 1998). For the 1L2S model, the total effective magnification of the source stars A is expressed as follows:
![Equation (5)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn5.gif)
where A1 and A2 are the magnification of the two sources with model flux f1 and f2, respectively, and qf
is the flux ratio between the two sources (= f2/f1). In order to explain the magnification of the second source, we introduce additional parameters: the time of lens–source closest approach t0,2, the impact parameter in units of the Einstein radius u0,2, and the ratio of the angular source size to the angular Einstein radius,
3.3. Ground-based Parallax
The magnification of the binary-lens model with parallax effects needs two additional parameters: the north and east components of the parallax vector
4. Angular Einstein Radius
We can estimate the angular Einstein radius
We derived the OGLE-IV instrumental source color and magnitude from the light-curve fitting and then converted them to the standard ones by using the following color–color relation from Udalski et al. (2015):
![Equation (6)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn6.gif)
![Equation (7)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn7.gif)
The apparent color and the standard magnitude of the source star are (V − I, I)S,O4,calib = (2.344 ± 0.031, 20.082 ± 0.012).
We also derived the apparent source color and magnitude from the CT13 measurements in the I and V bands from the light-curve fitting, and then converted them to the standard ones following the procedure explained in Bond et al. (2017). We cross-referenced isolated stars in the CT13 catalog reduced by DoPHOT (Schechter et al. 1993) with the stars in the OGLE-III map within 120'' of the source star and obtained the color–color relations
![Equation (8)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn8.gif)
![Equation (9)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn9.gif)
The apparent color and magnitude of the source star are (V − I, I)S,CT13,calib = (2.335 ± 0.025, 20.105 ± 0.013). This color is consistent with (V − I)S,O4,calib within 1
To obtain the extinction-corrected source color and magnitude, we used the standard method from Yoo et al. (2004). The intrinsic color and magnitude are determined from the source location relative to the color and magnitude of the red clump giant (RCG) centroid in the color–magnitude diagram (CMD). In Figure 3, the red point shows the RCG centroid color and magnitude, (V − I, I)RCG = (2.720, 16.325) ± (0.009, 0.032), for the field around the source star. Assuming that the source star suffers the same reddening and extinction as the RCGs, we compared these values to the expected extinction-corrected RCG color and magnitude for this field, (V − I, I)RCG,0 = (1.060, 14.362) ± (0.070, 0.040) (Bensby et al. 2013; Nataf et al. 2013). As a result, we obtained an extinction of AI = 1.963 ± 0.051 and a color excess of E(V − I) = 1.660 ± 0.071. Finally, the intrinsic source color and magnitude were derived:
![Equation (10)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn10.gif)
As a reference for later discussion of future follow-up observations, we also estimated the intrinsic source magnitudes in the H and K bands from the color–color relation in Kenyon & Hartmann (1995), including a 5% uncertainty. Then, we applied the extinction in the H and K bands, which was derived from the extinction in the I and V bands of the RCGs according to Cardelli et al. (1989).
Figure 3. The CMD. The stars in the OGLE-III catalog within 120'' of the source star are shown as black dots. The green dots indicate the HST CMD of Holtzman et al. (1998), which is transformed to the same reddening and extinction of the field of the event. The red dot shows the centroid of the RCG distribution. The colors and magnitudes of the source star and the blend are shown in blue and pink, respectively.
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Standard image High-resolution imageFigure 3 shows that the source is consistent with being part of the standard bulge sequence of stars, i.e., it falls within the distribution of stars from Holtzman et al. (1998) after they have been shifted to the same reddening and extinction as the field for OGLE-2018-BLG-1185. However, the source also has a similar color to the Sun. Thus, it would also be consistent with having an absolute magnitude similar to that of the Sun but being somewhat in the foreground, e.g., at ∼6 kpc. Thus, we also checked how a different assumption about the source would affect our results. If the source was more in the foreground, it would then suffer less extinction and reddening than the RCGs. However, even if we assume 10% less extinction and reddening than those of the RCGs, the value of
Table 3. The Source Colors and Magnitudes
Parameters | Unit | Source | Source | Source |
---|---|---|---|---|
(Apparent) | (Intrinsic) a | (Intrinsic) b | ||
I | mag | 20.082 ± 0.012 c | 18.119 ± 0.053 | 18.315 ± 0.053 |
V − I | mag | 2.344 ± 0.031 c | 0.684 ± 0.077 | 0.850 ± 0.077 |
H d | mag | 18.012 ± 0.143 | 17.444 ± 0.095 | ⋯ |
K d | mag | 17.756 ± 0.145 | 17.394 ± 0.095 | ⋯ |
Notes.
a Extinction-corrected magnitudes assuming that the source star suffers the same reddening and extinction as the RCGs. b Extinction-corrected magnitudes assuming that the source star suffers reddening and extinction 0.9 times those of the RCGs. c The magnitude and color are measured from the light-curve fitting. d The magnitudes are estimated from the color–color relation in Kenyon & Hartmann (1995) and the extinction law in Cardelli et al. (1989).Download table as: ASCIITypeset image
Applying the empirical formula (see Fukui et al. 2015 but also Boyajian et al. 2014), where
![Equation (11)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn11.gif)
![Equation (12)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn12.gif)
Finally, we obtained the source angular radius and the lens–source relative proper motion in the geocentric frame:
![Equation (13)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn13.gif)
![Equation (14)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn14.gif)
This
5. Lens Physical Parameters by Bayesian Analysis
If we can measure both the finite source effects and the parallax effects, the lens physical parameters such as the host mass Mhost and the distance to the lens DL are calculated directly, following the equations
![Equation (15)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn15.gif)
where
In order to estimate the probability distributions of ML and DL, we conducted a Bayesian analysis with the Galactic model of Koshimoto et al. (2021a).
72
We randomly generated a 50 million simulated microlensing event sample. Then we calculated the probability distributions for the lens physical parameters by weighting the microlensing event rate by the measured tE and
We calculated some parameters in addition to the lens physical parameters, ML and DL. For instance, the lens–source proper motion in the geocentric frame,
![Equation (16)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn16.gif)
where v ⊕,⊥ = (v⊕,N, v⊕,E) = (−0.78, 27.66) km s−1 is the projected velocity of Earth at t0.
We also calculated the I- and V-band magnitudes of the lens from the mass–luminosity relations of main-sequence stars (Kenyon & Hartmann 1995), and the 5 Gyr isochrone for brown dwarfs from Baraffe et al. (2003). Then we estimated the H- and K-band magnitudes of the lens from the color–color relation in Kenyon & Hartmann (1995), including a 5% uncertainty. In order to estimate the extinction in the foreground of the lens, we assumed a dust scale height of hdust = 0.10 ± 0.02 kpc (Bennett et al. 2015):
![Equation (17)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn17.gif)
where the index
The results are shown in Table 4 and Figure 4. According to Figure 4, the lens system is likely to be a super-Earth with a mass of orbiting a late M dwarf with a mass of
at a projected separation of
. The system is located at
kpc from Earth. For reference, we also plot the source magnitudes in the V, I, H, and K bands as red lines; the H- and K-band magnitudes were estimated in Section 4. We also show the parallax contour derived from the Bayesian analysis in Figure 5.
Figure 4. Probability distribution of lens properties derived from the Bayesian analysis with a Galactic prior and constrained by tE and
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Standard image High-resolution imageFigure 5. Left: The parallax contours for OGLE-2018-BLG-1185 expected from the Galactic model of Koshimoto et al. (2021a) after imposing the two observational constraints of the angular Einstein radius,
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Standard image High-resolution imageTable 4. The Lens Physical Parameters
Bayesian | Naive Spitzer-only | |||||
---|---|---|---|---|---|---|
Parameters | Unit | Ground-only | Ground + | Ground +
| (u0 > 0) | (u0 < 0) |
Mhost | M⊙ |
![]() |
![]() |
![]() | 0.073 ± 0.011 | 0.070 ± 0.010 |
mp | M⊕ |
![]() |
![]() |
![]() | 1.7 ± 0.3 | 1.6 ± 0.2 |
DL | kpc |
![]() |
![]() |
![]() | 4.96 ± 0.74 | 4.89 ± 0.66 |
a⊥ | au |
![]() |
![]() |
![]() | 1.01 ± 0.18 | 0.99 ± 0.16 |
| ... |
![]() |
![]() |
![]() | 0.354 ± 0.042 | 0.369 ± 0.037 |
| mas yr−1 |
![]() |
![]() | 4.86 ± 0.44 | ⋯ | ⋯ |
V | mag |
![]() |
![]() |
![]() | ⋯ | ⋯ |
I | mag |
![]() |
![]() |
![]() | ⋯ | ⋯ |
H | mag |
![]() |
![]() |
![]() | ⋯ | ⋯ |
K | mag |
![]() |
![]() |
![]() | ⋯ | ⋯ |
Download table as: ASCIITypeset image
6. Analysis Including Spitzer Data
We measure the microlens parallax vector
![Equation (18)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn18.gif)
where D⊥ is the Earth–satellite separation projected on the plane of the sky, and t0,sat and u0,sat are the time of lens–source closest approach and the impact parameter as seen by the satellite. The Einstein timescale tE is assumed to be the same for both Earth and the satellite. In practice, we fully model Spitzer's location as a function of time.
The Spitzer light curve for OGLE-2018-BLG-1185 shows a very weak decline of
![Equation (19)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn19.gif)
which gives an expected source flux from Spitzer of fS,Spz = 0.6254 flux units for the best-fit value of ICT13. This constraint and the best-fit ground-based model (Table 4) together imply some tension with the observed Spitzer light curve unless there is a significant parallax effect. They predict that the observed Spitzer flux should have been substantially brighter at the start of the Spitzer observations ( flux units) and declined by a total of
Figure 6. The light curve and models with the Spitzer data. The blue dotted line shows the Spitzer flux predicted by the 2L1S best-fit model derived from the ground-based analysis for
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Standard image High-resolution imageWe can use limits on the change in Spitzer flux (
The results are given in Table 4 (as "Ground + host with an
planet at a projected separation
. We adopt these values as our conservative Bayesian estimates of the properties of the lens system.
Figure 7. Same as Figure 4, but with the addition of the constraint
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Standard image High-resolution image6.1. Spitzer-only Parallax
If we take the Spitzer light curve at face value, we can derive stronger constraints on the parallax using the Spitzer-only parallax method. This method has been used in several previous analyses (starting with Gould et al. 2020) to show how the Spitzer light curve constrains the parallax. For this analysis, we hold the microlensing parameters t0, u0, and tE fixed at values found by fitting the ground-based data and make the assumption that the Spitzer light curve is in the point lens regime. 73 Then, for a grid of parallax values, we fit for the Spitzer flux while applying the color constraint from Equation (19). We repeat the analysis for −u0, which produces an indistinguishable ground-based light curve and, as expected, only slight variations in the parallax.
The resulting parallax contours are shown in Figure 8. The four minima correspond to the well-known satellite parallax degeneracy (Refsdal 1966; Gould 1994) and the overall arc shape follows the expectation from the Gould (2019) osculating circle formalism. The values for the magnitude of the microlens parallax vector are
Figure 8. Parallax contours from Spitzer-only analysis (see text). The colors—black, red, yellow, green, cyan, blue, and magenta—indicate 1
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Standard image High-resolution image6.2. Physical Lens Properties from Spitzer Parallax
We can derive the physical properties of the lens by combining the measurement of the parallax from the Spitzer-only analysis with the measurement of
In order to estimate the lens magnitude, we also performed a Bayesian analysis including the and the measured tE and
orbiting a very low mass (VLM) dwarf with a mass of
.
Figure 9. Same as Figure 4, but with the addition of the
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Standard image High-resolution image6.3. Implications
Hence, if the Spitzer-only parallax is correct, this would be the second detection of a terrestrial planet orbiting a VLM dwarf from the Spitzer microlensing program. The first was OGLE-2016-BLG-1195Lb (Bond et al. 2017; Shvartzvald et al. 2017), which is an planet orbiting an
VLM dwarf at a separation of
au. The distance to the OGLE-2016-BLG-1195L system is also comparable:
kpc. One curiosity about OGLE-2016-BLG-1195L is that the lens–source relative proper motion suggests that the lens could be moving counter to the direction of Galactic rotation, which would be unusual for a disk lens.
Therefore, we also consider the implications of the Spitzer-only
. Hence, for the velocity dispersion, we use (
(for (R⊙, z⊙) = (8160, 25) pc). We combine the two velocities to estimate the proper motion of disk stars. Finally, by applying Equation (16), we can derive the expected source proper motion
Figure 10. Test of source proper motion predicted by the Spitzer-only parallax. Black points: Derived source proper motions for
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Standard image High-resolution imageTable 5. Disk Star Velocities and Proper Motions at D = 4.9 ± 0.7 kpc
Star Component | Velocity Component | Unit | −2 | −1 | Median | +1 | +2 |
---|---|---|---|---|---|---|---|
Thin Disk | vl | km s−1 | 110.7 | 163.6 | 205.9 | 242.4 | 280.7 |
v b | km s−1 | −95.0 | −48.8 | −13.7 | 22.4 | 71.1 | |
| mas yr−1 | −5.615 | −3.349 | −1.577 | −0.024 | 1.656 | |
| mas yr−1 | −4.364 | −2.388 | −0.884 | 0.653 | 2.690 | |
Thick Disk | vl | km s−1 | 60.7 | 125.2 | 181.4 | 236.5 | 293.7 |
v b | km s−1 | −147.8 | −86.4 | −12.1 | 63.3 | 128.6 | |
| mas yr−1 | −7.662 | −4.995 | −2.602 | −0.275 | 2.177 | |
| mas yr−1 | −6.577 | –3.987 | −0.808 | 2.379 | 5.102 | |
All | vl | km s−1 | 103.6 | 161.0 | 204.9 | 242.2 | 281.3 |
v b | km s−1 | −101.1 | −50.5 | −13.6 | 24.4 | 77.4 | |
| mas yr−1 | −5.878 | −3.457 | −1.620 | −0.034 | 1.685 | |
| mas yr−1 | −4.611 | −2.462 | −0.883 | 0.737 | 2.960 |
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Finally, in order to include the event in the statistical sample for the study of the Galactic distribution of planets, Zhu et al. (2017) proposed the criteria
![Equation (20)](https://content.cld.iop.org/journals/1538-3881/162/2/77/revision1/ajac00baeqn20.gif)
We find D8.3 = 5.15 ± 0.28 kpc for the (u0 > 0) case and D8.3 = 5.04 ± 0.28 kpc for the (u0 < 0) case by combining the measurement of
7. Discussion and Summary
We analyzed the microlensing event OGLE-2018-BLG-1185, which was simultaneously observed from a large number of ground-based telescopes and the Spitzer telescope. The ground-based light-curve modeling indicates a low-mass ratio of q = (6.9 ± 0.2) × 10−5, which is close to the peak of the wide-orbit exoplanet mass-ratio distribution derived by Suzuki et al. (2016) and investigated further by Udalski et al. (2018) and Jung et al. (2019b). Suzuki et al. (2016) derived the wide-orbit planet occurrence rate using a sample of 30 planets, primarily from the MOA-II microlensing survey during 2007–2012. The planet presented here, OGLE-2018-BLG-1185Lb, will be included in an extension of the MOA-II statistical analysis (Suzuki et al. 2021, in preparation), and its low-mass ratio will help define the mass-ratio function peak.
From the ground-based light-curve modeling, only the finite source effect is detected, yielding a measurement of the angular Einstein radius. However, the physical properties of the lens as derived from the light curve are unclear because the observed flux variation of the Spitzer light curve is marginal. Using only the constraint from the measured angular Einstein radius and a conservative constraint on the change in Spitzer flux, we estimate the host star and planet masses with a Bayesian analysis under the assumption that stars of all masses have an equal probability of hosting the planet. This analysis indicates a host mass of and a planet mass of
located at
kpc. By contrast, the Spitzer data favor a larger microlensing parallax, which implies a VLM host with a terrestrial planet (
,
) that is either in the disk at DL ∼ 5 kpc or in the bulge at DL ∼ 7.5 kpc (these values include a Galactic prior but are not significantly different from the values without the prior; see Table 4).
Figure 11 compares the Bayesian estimates from the conservative Spitzer flux constraint and the full Spitzer parallax measurement of the host and planet mass for OGLE-2018-BLG-1185 to those of other planetary systems. The pink circles show the microlens planets without mass measurements, and the red circles show the microlens planets with mass measurements from ground-based orbital parallax effects and/or detection of the lens flux by high-resolution follow-up observations. The red squares represent microlens planets with mass measurements from the satellite parallax effect observed by Spitzer. Figure 11 indicates that if the Spitzer parallax is correct, this is one of the lowest-mass planets discovered by microlensing.
Figure 11. The mass distribution of the detected exoplanets as of 2021 February 25. 74 The purple stars indicate OGLE-2018-BLG-1185. The pink circles show the microlens planets without mass measurements, and the red circles show the microlens planets with mass measurements from ground-based orbital parallax effects and/or detection of the lens flux by high-resolution follow-up observations. The red squares represent the microlens planets with mass measurements from satellite parallax effects by Spitzer. The blue, yellow, and black dots indicate planets found by the transit, direct imaging, and radial velocity methods, respectively.
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Standard image High-resolution imageHowever, the result that this is a terrestrial planet orbiting a VLM dwarf in the disk should be treated with caution, because the amplitude of the Spitzer signal is at the level of systematics seen in other events. A comparison of these properties to the Bayesian posteriors (Figure 4) demonstrates that a higher-mass system is preferred given tE,
Adaptive optics observations are one way to test the Spitzer parallax signal. The Bayesian analysis with ground-based + mag, which is about 3 mag fainter than the source. By contrast, if the Spitzer-only parallax is correct and the lens is a VLM dwarf, it should be
mag and therefore, much fainter and possibly undetectable. The Bayesian estimate of the heliocentric relative proper motion,
If the Spitzer parallax is verified, this event confirms the potential of microlensing for measuring the wide-orbit planet frequency into the terrestrial planet regime. Although the number of microlens planets with mass measurements is small for now, observing the satellite parallax effect can continue to increase the number. In particular, this effect can be measured for terrestrial planets by simultaneous observations between the ground and L2 (Gould et al. 2003). This can be achieved with the PRIME telescope (principal investigator: Takahiro, Sumi) and the Roman Space Telescope (Spergel et al. 2015; Penny et al. 2019) in the mid-2020s.
Work by I.K. was supported by JSPS KAKENHI grant No. 20J20633. Work by J.C.Y. was supported by Jet Propulsion Laboratory grant 1571564. Work by D.P.B., A.B., and C.R. was 5
supported by NASA through grant NASA-80NSSC18K0274. T.S. acknowledges financial support from the JSPS (JSPS23103002, JSPS24253004, and JSPS26247023). Work by N.K. is supported by JSPS KAKENHI grant No. JP18J00897. A.S. is a University of Auckland doctoral scholar. Y.T. acknowledges the support of DFG priority program SPP 1992 Exploring the Diversity of Extrasolar Planets (WA 1047/11-1). T.C.H. acknowledges financial support from the National Research Foundation (No. 2019R1I1A1A01059609). U.G.J. acknowledges support from H2020-MSCA-ITN-2019, grant No. 860470 (CHAMELEON), and the NovoNordisk Foundation grant No. NNF19OC0057374. W.Z. and S.M. acknowledge support by the National Science Foundation of China (grant Nos. 11821303 and 11761131004). Work by C.H. was supported by grants of the National Research Foundation of Korea (2020R1A4A2002885 and 2019R1A2C2085965). Funding for B.S.G. was provided by NASA grant NNG16PJ32C and the Thomas Jefferson Chair for Discovery and Space Exploration. The MOA project is supported by JSPS KAKENHI grant Nos. JSPS24253004, JSPS26247023, JSPS23340064, JSPS15H00781, JP16H06287, 17H02871, and 19KK0082. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to
Software: OGLE DIA pipeline (Udalski 2003), MOA DIA pipeline (Bond et al. 2001), KMTNet pySIS pipeline (Albrow et al. 2009), DanDIA (Bramich 2008; Bramich et al. 2013), DoPHOT (Schechter et al. 1993), ISIS (Alard & Lupton 1998; Alard 2000; Zang et al. 2018), image-centered ray-shooting method (Bennett & Rhie 1996; Bennett 2010).
Appendix: Constraints on the Blended Light and Discrepancy with Gaia
The blended light in this event is roughly four times brighter than the source. In principle, the blend could be the lens itself or a companion to either the lens or the source. If so, it could constrain the flux and proper motion of the lens or the proper motion of the source.
From the KMTNet images, we measure the astrometric offset between the source and the baseline object and find an offset of 0175. This offset is larger than the astrometric uncertainties. Therefore, if it is a companion to the lens or source, it must be a very wide separation companion (∼1000 au). However, the large separation also suggests that it could be an ambient star unrelated to the microlensing event.
We measure the proper motion of the baseline object based on 10 yr of OGLE survey data and find
For completeness, we note that the OGLE measurement of the proper motion of the baseline object is inconsistent with the reported Gaia proper motion of the nearest Gaia source (4062756831332827136; Gaia Collaboration et al. 2016). Gaia EDR3 (Gaia Collaboration et al. 2021) reports there is a G = 20.1 mag star 0177 from the OGLE coordinates for the baseline star (17:59:10.26–27:50:06.3). The reported proper motion of this source is
u
(R.A., decl.) = (−12.173 ± 1.247, −9.714 ± 0.870) mas yr−1, which is an outlier relative to the typical proper motions for stars in this field. Gaia DR2 (Gaia Collaboration et al. 2018) reports an only slightly less extreme proper motion of
u
(R.A., decl.) = (−8.475 ± 2.234, −4.039 ± 1.985) mas yr−1. The nature of this discrepancy is unknown, but because the Gaia proper motion is highly unusual (and the OGLE proper motion is typical), and the Gaia measurement varies significantly between DR2 and EDR3, this suggests a problem with the Gaia measurement.
Footnotes
- 70
These values are the median and 68% confidence level by Markov Chain Monte Carlo analysis with a 30-planet sample, which is given in Table 5 of Suzuki et al. (2016). So the 1
σ range of the mass-ratio distribution peaks is roughly qbr ∼ (0.5–2) × 10−4. At the same time, they also show that the best-fitting parameters are qbr = 1.65 × 10−4 with power-law slopes of n = −0.92 and p = 0.47 in Table 4 of Suzuki et al. (2016). - 71
In addition Yee et al. (2021) have submitted a paper on OGLE-2019-BLG-0960.
- 72
The code for microlensing simulation using the Galactic model has been published (Koshimoto & Ranc 2021b) and can be downloaded at https://github.com/nkoshimoto/genulens as a prior.
- 73
In principle, we should calculate the Spitzer magnification using the full planetary model, but in practice, this makes almost no difference because the Spitzer observations start well after the planetary perturbation.
- 74