OGLE-2018-BLG-1428Lb: a Jupiter-mass planet beyond the snow line of a dwarf star

The core accretion model proposes that gas giant planets originated beyond the snow line of their host stars, such as Jupiter and Saturn in the Solar system (Mizuno, 1980; Pollack et al., 1996; Inaba et al., 2003). This model predicts that it takes $\sim 3\,\rm Myr$ to form gas giant planets at $5\,\rm AU$ around Sun-like stars, while for low-mass stars it does not seem to be able to form such planets, because the lifetime of the proto-planetary disk for low-mass stars is not long enough to form such giant planets (Ida & Lin, 2004; Laughlin et al., 2004; Boss, 2006). For example, the formation time of gas giant planets for a $0.4\,M_{\odot}$ dwarf is $\gtrsim 10\,\rm Myr$, whereas its disk lifetime is $<10\,\rm Myr$ (Boss, 2006). On the other hand, the disk instability model is thought to be more likely to form gas giants around beyond the snow line of M dwarfs (Boss, 2006). Actual detections of Jupiter-mass planets orbiting low-mass stars (Boss, 2006 and references therein) are consistent with the disk instability model. Hence, these two planet formation models may actually complement one another, although this remains uncertain.

Currently, the majority of host stars with exoplanets are Sun-like stars, and their planets are mostly located inside the snow line. Those planets have been mostly discovered by the radial-velocity and transit methods. However, most of stars in the Galaxy are low-mass M dwarf stars, which are difficult to observe with the two methods. On the other hand, the microlensing method typically detects low-mass M dwarfs hosting planets located beyond the snow line. This is because the microlensing depends only the mass of objects, not the light. Therefore, microlensing provides very important samples to constrain planet formation models including the core-accretion and gravitational instability models.

However, a majority of masses of microlensing planets were not directly measured but estimated from a Bayesian analysis, which assumes that the planet hosting probability is independent of the host star mass (Vandorou et al., 2020; Bhattacharya et al., 2020). The lens masses estimated from the Bayesian analysis can be confirmed from high-resolution follow-up observations. This is because the lens and source stars are typically separated each other within $\sim 10$ years after the peak time of event, thus making it possible to discriminate the two stars. Until now, the masses of 18 planetary lens systems (e.g., Bennett et al., 2006, 2015; Batista et al., 2015; Fukui et al., 2015; Vandorou et al., 2020; Bhattacharya et al., 2020) have been measured from high-resolution follow-up observations with Keck, VLT, Subaru, or HST.

In addition, the masses of lens systems can be directly measured from the measurement of two parameters of angular Einstein radius ($\theta_{\rm E}$) and microlens parallax ($\pi_{\rm E}$). However, it is usually hard to measure the two parameters. This is because $\theta_{\rm E}$ can be measured from events with high-magnification or caustic-crossing features, while $\pi_{\rm E}$ can be measured from the detection of the distortions induced by the orbital motion of Earth on a standard microlensing light curve (Gould, 1992). In general, the measurement of the microlens parallax is limited to events with long timescale $t_{\rm E}\gtrsim 60\,\rm days$ or large $\pi_{\rm E}$ to detect the light-curve distortion induced by the orbital motion of Earth. This means that for short timescale events induced by low-mass objects (e.g., M dwarfs or brown dwarfs), it is difficult to measure the microlens parallax. The microlensing parallax measurement was first reported ¹¹1The first event with a microlens parallax measurement was MACHO-LMC-5, which was discovered in 1993 (Alcock et al., 1997), but the parallax measurement was only reported eight years after the event (Alcock et al., 2001). in 1995 (Alcock et al., 1995), and it was due to a long timescale of the event, $t_{\rm E}=110\,\rm days$. For the measurement of the microlens parallax for all events, it is required a simultaneous observation of an event from Earth and a satellite (Refsdal S., 1966; Gould, 1994). Then, the microlens parallax is measured from the difference in the light curves as seen from the two observatories (Refsdal S., 1966; Gould, 1994). Over 900 events so far have been detected from ground-based observations and the Spitzer satellite, which is for studying the Galactic distribution of planets (Zhu et al., 2017 and the references therein). Also, the Nancy Grace Roman (Roman, formerly WFIRST) satellite will be launched in near future (Spergel et al., 2015). With this satellite, it is expected to detect $\sim 1400$ bound exoplanets (Penny et al., 2019) and $\sim 250$ free-floating planets (Johnson et al., 2020). Hence, the masses of over 1000 planetary systems can be measured from the Roman together with ground-based observations, such as the Korea Microlensing Telescope Network (KMTNet; Kim et al., 2016). However, we note that the main mass measurement method for the Roman Galactic Exoplanet Survey will be the detection of the exoplanet host stars in the Roman imaging data. The microlensing parallax between the Earth and Roman will be difficult to measure for most events for two reasons. First, most events detected by Roman will be too faint to observe from the ground, particularly with small telescopes. Second, for events without caustic-crossings, the separation between the Earth and Roman’s orbit at L2 will not be large enough to reveal a microlensing parallax measurement. Fortunately, for events with caustic-crossings the Earth-L2 separation yields a useful microlensing parallax measurement as Wyrzykowski et al. (2020) demonstrate. Moreover, for events with anomalies due to terrestrial planets, the microlens parallax may be measurable even in the absence of caustic-crossing features (Gould et al., 2003).

Recently, planetary systems composed of low-mass dwarfs and a giant planet beyond the snow line of the dwarfs have been routinely detected from the KMTNet microlensing survey, even though most of masses of the host stars were estimated from a Bayesian analysis. OGLE-2018-BLG-1428 is one such planetary system. In this paper, we present the analysis of the planetary event OGLE-2018-BLG-1428, which has a short-duration caustic-crossing anomaly. Although the finite source effect was measured from the caustic-crossing feature, the microlens parallax was not measured. Therefore, the physical parameters of the lens system are estimated from a Bayesian analysis.

The planetary lensing event OGLE-2018-BLG-1428 is located at equatorial coordinates $({\rm RA},{\rm decl.})_{\rm J2000}$ = (17:42:11.69, $-26$:08:16.4), corresponding to the Galactic coordinates $(l,b)=(1.99,2.11)$. The event was first alerted at August 6 2018 by the Optical Gravitational lensing Experiment (OGLE; Udalski et al. 2015). OGLE uses 1.3 m Warsaw telescope with $1.4\,\rm deg^{2}$ field of view (FOV) at the La Campanas Observatory in Chile. The event lies in the OGLE-IV field BLG652 with a low cadence of $\Gamma\simeq 0.01-0.1\,{\rm hr}^{-1}$. In addition, the event is very near the edge of the OGLE chip and therefore has many missing data points due to small pointing variations. In spite of this fact, OGLE alerted it at HJD-245000 (${\rm HJD}^{\prime}$)=8337.32, just before the peak. However, due to the sparseness of the data points, the short-duration ($\sim 1$ day) caustic-crossing anomaly was not covered.

In 2018, KMTNet started to run its own alert system, but only for the northern bulge fields (Kim et al., 2018b). From the KMTNet alert system, OGLE-2018-BLG-1428 was independently announced at ${\rm HJD}^{\prime}$=8337.68, and it was designated as KMT-2018-BLG-0423. KMTNet uses three identical telescopes with $4\,\rm deg^{2}$ FOV, which are individually located at CTIO in Chile (KMTC), SAAO in South Africa (KMTS), and SSO in Australia (KMTA). The event lies in the KMT field BLG18 with cadence of $\Gamma\simeq 1$ hr^-1. With this cadence, the anomaly was well covered by KMTNet. While most of KMTNet data were taken in the $I$ band, some of them were taken in the $V$ band in order to characterize the source star. However, we found that the extinction toward the event, $A_{\rm I}=3.07$, is high, and thus it is difficult to use the $V$ band data to constrain the source color. To estimate the source color $(I-H)$, we used the $H$-band data of the VVV microlensing survey (Navarro et al., 2017, 2018), which will be described in Section 4. The KMTNet data were reduced by pySIS based on Difference Image Analysis (DIA; Tomaney & Crotts (1996); Alard & Lupton (1998); Albrow et al. (2009)).

KMTNet data were taken in the $I$- and $V$-bands in order to measure the instrumental source color. Usually, the source color $(V-I)$ is measured from the linear regression of the $V$ on $I$ flux. However, because there is only one $V$ point that is sufficiently magnified to give a significant signal due to high extinction $A_{I}=3.07$, we cannot measure a reliable $(V-I)$.

In order to determine a reliable source color, we use the VVV $H$-band catalog. Because the source is bright and the best-fit model shows negligible blending ($f_{s}\gg f_{b}$), we can attempt to measure the offset between the baseline object and the clump in the instrumental color magnitude diagram (CMD). Here, we assume the baseline object corresponds to the source star due to negligible blending.

Figure 5 shows the calibrated $(I-H,I)$ and $(V-I,I)$ CMDs. The CMDs have been calibrated by first applying the OGLE-IV calibration constants to the OGLE-IV data and then transforming the instrumental KMTC pyDIA data to the calibrated OGLE-IV system, in which the KMTC data are already matched to the VVV stars before the calibration. From the $(I-H,I)$ CMD, we find that $(I-H,I)_{\rm cl}=(3.68,17.55)$ and $(I-H,I)_{\rm s}=(3.52,18.97)$, thus $\Delta(I-H)=-0.15$. Using Bessel & Brett (1988), we find that this corresponds to $\Delta(V-I)=-0.11$. From the $(V-I,I)$ CMD, we find that $(V-I,I)_{\rm cl}=(3.63,17.57)$ and $(V-I,I)_{\rm s}=(3.37,18.97)$, thus $\Delta(V-I)=-0.26$. Note that this baseline measurement derives from a stacking of several dozen images and so is more reliable than the regression method, which relies on a single magnified $V$ point. We finally adopt that $\Delta(V-I)=-0.19$ by taking the average of these two values. The instrumental source magnitude is $I=18.87$ from the best-fit model, and the magnitude and flux of the calibrated source is $I=18.99$ and $f_{\rm s}=0.4017$. The source angular radius $\theta_{\rm\star}$ is estimated from the intrinsic color and magnitude of the source, in which are determined from

With the measured $\Delta(V-I)=-0.19$, $I=18.99$, and $(V-I,I)_{\rm cl,0}=(1.06,14.37)$ (Bensby et al. 2011, Nataf et al. 2013), we find that $(V-I,I)_{0}=(0.87,15.76)$, indicating that the source is a G-type giant. We then estimate the source angular radius by using the $VIK$ color-color relation of Bessel & Brett (1988) and the color-surface brightness relation of Kervella et al. (2004). From this, it is found that $\theta_{\rm\star}=2.717\pm 0.164\ \mu as$. With the $\theta_{\rm\star}$ and $\rho$, the Einstein angular radius of the lens is determined by

and the relative lens-source proper motion is

Because the parallax measurement is unreliable, we perform a Bayesian analysis to estimate physical properties of the lens, i.e., the mass and distance. The Bayesian analysis implicitly assumes that all stars have an equal probability to host a planet of the measured mass ratio. The Bayesian analysis is carried out with the same procedures as Jung et al. (2018) did, but we use a new Galactic model based on more recent data and scientific understanding. The new Galactic model includes the bulge mean velocity and dispersions taken from Gaia, disk density profile and disk velocity dispersion from the Robin-based model in Bennett et al. (2014), while the bulge mean velocity is generally zero and the bulge density profile is the same as the one in Jung et al. (2018). However, we know the proper motion of the source $(\mu_{\alpha},\mu_{\delta})=(-2.607\pm 2.371,-3.014\pm 1.751)$ from Gaia, even though its error is big. We thus use the proper motion value as the mean velocity of the source for bulge-bulge events.

In addition, we should consider the extinction at a given distance for the lens brightness. For the extinction to the lens $A_{\rm L}$, we use the following equation (Bennett et al., 2015; Batista et al., 2015)

where the index $i$ denotes the passband: $V$, $I$, or $K$, and the dust scale height is $h_{\rm dust}=120\ \rm pc$. Here we adopt the extinction to the source of $A_{I,\rm S}=2.98$ and $A_{K,\rm S}=0.35$ from the VVV/KMTC CMD analysis and $VIK$ color-color relation of Bessel & Brett (1988), which were discussed in Section 4.

Figure 6 shows the results of the Bayesian analysis. From this, we find that the lens is a sub Jupiter-mass planet $M_{\rm p}=0.77^{+0.77}_{-0.53}\ M_{\rm J}$ orbiting a star $M_{\rm h}=0.43^{+0.33}_{-0.22}\,M_{\odot}$ at a distance $D_{\rm L}=6.22^{+1.03}_{-1.51}\,\rm kpc$, and the projected star-planet separation is $3.30^{+0.59}_{-0.83}\,\rm AU$. This indicates that OGLE-2018-BLG-1428L is likely to be an M dwarf star hosting a sub Jupiter-mass planet beyond the snow line based on $a_{\rm snow}=2.7\ (M/M_{\odot})$ (Kennedy & Kenyon, 2008). However, it could be also a K or a G dwarf. The lens distribution in Figure 6 shows that the lens is located in the disk and bulge with equal probability. This is consistent with the relative proper motion of $5.6\ \rm mas\ yr^{-1}$.

Figure 6 also shows the Bayesian distributions for the brightness of host star. The distributions show that if the host star is a main-sequence star, its brightness is $I_{L}=25.3^{+0.9}_{-2.4}$ and $K_{L}=20.7^{+0.7}_{-1.8}$. Considering the brightness of the giant source star with $K=14.7$, the lens star is $\sim 240$ times fainter than the source. This high contrast between the source and the lens makes it difficult to resolve the two stars by follow-up observations. However, for both MOA-2007-BLG-400 (Bhattacharya et al., 2020) and MOA-2013-BLG-220 (Vandorou et al., 2020), the lens mass measured from Keck is much closer to the $2\sigma$ upper limit from the Bayesian analysis than the median. Thus, considering the $2\sigma$ upper limit of the lens brightness, the lens with $K=17.1$ is 9 times fainter than the source. Recently, Bhattacharya et al. (2020) reported that lens star with $K=18.9$, which is $\sim 10$ times fainter than the source and is $\sim 50\,\rm mas$ away from the source, can be detected at a separation of $0.53$ FWHM with Keck. For this event, because the proper motion is $5.6\,\rm mas\ yr^{-1}$, the lens will be separated from the source by $56\,\rm mas$ in 2028. Hence, it seems plausible that a lens at $K\sim 17$ would be detectable by Keck, while for a lens at $K\sim 21$ it would be hard to detect with Keck. If the lens is a very faint star at $K\sim 21$, the lens can be resolved by a 30m telescope equipped with a state of the art laser guide star adaptive optics system, even though the contrast between source and lens is high. Such a measurement can resolve the nature of the lens and confirm the results of the Bayesian analysis.

We analyzed the event OGLE-2018-BLG-1428 with a caustic-crossing feature. From the Bayesian analysis, it is found that the lens is a star $M_{\rm L}=0.43^{+0.33}_{-0.22}\ M_{\odot}$ hosting a sub Jupiter-mass planet $M_{\rm p}=0.77^{+0.77}_{-0.53}\ M_{\rm J}$, at a distance $D_{\rm L}=6.22^{+1.03}_{-1.51}\ {\rm kpc}$, and the projected separation between the star and the planet is $3.30^{+0.59}_{-0.83}\,{\rm AU}$, suggesting that the planet orbits beyond the snow line of the host. The lens distance distribution and the proper motion $\mu_{\rm rel}=5.6\ \rm mas\ yr^{-1}$ indicate that the lens is located in the disk and bulge with equal probability. The lens can be resolved by adaptive optics of a 30m telescope in the future.

Work by Y.-H. Kim and S.-J. Chung was supported by the KASI (Korea Astronomy and Space Science Institute) grant 2021-1-830-08. Work by A.G. was supported by JPL grant 1500811. Work by C.H. was supported by the grant of National Research Foundation of Korea (2019R1A2C2085965 and 2020R1A4A2002885). The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to A.U. This research has made use of the KMTNet system operated by the KASI and the data were obtained at three sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia.

The data underlying this article will be shared on reasonable request to the corresponding author.