Three faint-source microlensing planets detected via resonant-caustic channel

During the early phase of planetary microlensing experiments, for example, OGLE (Udalski et al., 1994), MACHO (Alcock et al., 1993), EROS (Aubourg et al., 1993) surveys, for which the annual detection rate of lensing events was several dozens, individual events could be thoroughly inspected to check the existence of planet-induced anomalies in the light curves of the lensing events. With the advent of high-cadence surveys, that is, MOA (Sumi et al., 2013), OGLE-IV (Udalski et al., 2015), KMTNet (Kim et al., 2016), the detection rate has soared to more than 3000 per year. With the greatly increased number of events together with the large quantity of data for each event, planetary signals for some events may escape detection.

Two projects have been carried out since 2020 with the aim of finding missed planets in the survey data collected in and before the 2019 season. One project has been conducted to find planet-induced anomalies via an automatized algorithm. Hwang et al. (2021) applied the automated AnomalyFinder software (Zang et al., 2021) to the 2018–2019 lensing light curves from the $\sim 13\leavevmode\nobreak\ {\rm deg}^{2}$ of sky covered by the six KMTNet prime fields with cadences $\geq 2\leavevmode\nobreak\ {\rm hr}^{-1}$. From this investigation, they reported 6 newly detected planets with mass ratios $q<2\times 10^{-4}$, including OGLE-2019-BLG-1053Lb, KMT-2019-BLG-0253Lb, OGLE-2018-BLG-0506Lb, OGLE-2018-BLG-0516Lb, OGLE-2019-BLG-1492Lb, and OGLE-2018-BLG-0977. The signals of these planets were not only very short but also weak, and thus they had not been noticed from visual inspections. A more extensive searches for missing planetary signals are underway by applying the automated algorithm to all the lensing light curves detected by the KMTNet survey (Y. K. Jung et al. 2021, in preparation).

The other project has been conducted by visually inspecting the previous survey data to find unnoticed planetary signals. This project led to the discoveries of 10 planets. The first planet was KMT-2018-BLG-0748Lb (Han et al., 2020b), for which the planetary signal had been missed due to the faintness of the source combined with relatively large finite-source effects. This discovery was followed by the detections of KMT-2016-BLG-2364Lb, KMT-2016-BLG-2397Lb, OGLE-2017-BLG-0604Lb, and OGLE-2017-BLG-1375Lb, for all of which the lensing events involved faint source stars (Han et al., 2021a), KMT-2019-BLG-1339Lb, for which the planetary signal was partially covered (Han et al., 2020a), KMT-2018-BLG-1976Lb, OGLE-2019-BLG-0954Lb, KMT-2018-BLG-1996Lb, for which the planetary signals were produced through a non-caustic-crossing channel, and thus weak (Han et al., 2021b), and KMT-2018-BLG-1025Lb, for which the planetary signal had been missed due to the low mass ratio of the planet ($q\sim 0.8\times 10^{-4}$ or $1.6\times 10^{-4}$ for two degenerate solutions) together with the non-caustic-crossing nature of its planetary signal (Han et al., 2021c). Visually inspecting missing planets can provide various types of planetary signals that are prone to being missed, and thus can help to develop a more complete algorithm for automatized planet detections.

In this paper, we report three additional planets with similar planetary signatures and event characteristics found from the (visual) inspection of the 2017–2019 season data collected by the OGLE and KMTNet surveys. The common feature of these planetary events is that the planetary signals were produced by the crossings of faint source stars over the resonant caustics formed by giant planets located near the Einstein rings of the lens systems. Detecting such planetary signals requires a visual inspection of lensing light curves, because the durations of the planet-induced anomalies comprise important portions of the event durations, making them difficult to be detected by an automatized system that is optimized to detecting very short-term anomalies. An example of such a planetary event is found in the case of OGLE-2016-BLG-0596 (Mróz et al., 2017).

For the presentation of the work, we organize the paper as follows. In Sect. 2, we mention the observations of the lensing events and the acquired data. In Sect. 3, we mention the characteristics of the anomalies in the lensing light curves of the events, and describe the detailed analyses conducted to explain the observed anomalies. In Sect. 4, we specify the source types of the events, and constrain the angular Einstein radii. In Sect. 5, we determine the physical parameters of the planetary systems using the observables of the events. In Sect. 6, we discuss the role of high-resolution follow-up observations for faint-source planetary events with resonant caustic features in clarifying the nature of the lens system. A summary of the results and conclusion are presented in Sect. 7.

The newly reported three planetary lensing events are KMT-2017-BLG-2509, OGLE-2017-BLG-1099/KMT-2017-BLG-2336, and OGLE-2019-BLG-0299/KMT-2019-BLG-2735. The first event was detected solely by the KMTNet survey, and the latter two events were detected by both the OGLE and KMTNet surveys. Hereafter, we designate the events by the identification numbers of the surveys that first found the lensing events. In Table 1, we list the equatorial and galactic coordinates of the source stars, alert dates, and $I$-band baseline magnitudes, $I_{\rm base}$, of the individual events. The notation “postseason” indicates that the event was detected from the postseason inspection of the data.

After one year test observations in the 2015 season, the KMTNet group has carried out a lensing survey toward the Galactic bulge field since 2016 with the use of three identical 1.6 m telescopes that are distributed in the three continents of the Southern Hemisphere, at the Siding Spring Observatory in Australia, the Cerro Tololo Interamerican Observatory in Chile, and the South African Astronomical Observatory in South Africa. We designate the individual telescopes as KMTA, KMTC, and KMTS, respectively. The camera mounted on each telescope has a 4 deg² field of view. The OGLE team has conducted a lensing survey since its commencement of the first phase experiment in 1992 (Udalski et al., 1994), and now the survey is in the fourth phase (OGLE-IV) with the use of an upgraded camera yielding a 1.4 deg² field of view (Udalski et al., 2015). The OGLE telescope with an aperture of 1.3 m is located at the Las Campanas Observatory in Chile. For both surveys, images of the events were obtained mainly in the $I$ band, and a fraction of $V$-band images were acquired for the source color measurements. In Table 2, we list the data sets used in the analysis, the fields of the individual surveys, and the cadence of observations. We note that the KMTNet cadences of the events, ranging 1.0–2.5 hr, are substantially lower than the cadence of the prime fields, 15 min, and this partially contributed to the difficulty of identifying the planetary nature of the events.

The data used in the analyses were reduced using the photometry pipelines of the individual survey groups. These pipelines, developed by Albrow et al. (2009) for KMTNet and by Woźniak (2000) for OGLE, utilize the difference imaging technique (Tomaney & Crotts, 1996; Alard & Lupton, 1998), which is optimized for the photometry of stars in very dense star fields. A subset of the KMTC data were additionally processed using the pyDIA photometry code (Albrow, 2017) to construct color-magnitude diagrams (CMD) of stars around the source stars and to specify the source types. See Sect. 4 for details. For the data used in the analyses, we readjusted the error bars of the photometric data by $\sigma=k(\sigma_{\rm min}^{2}+\sigma_{0}^{2})^{1/2}$ following the prescription depicted in Yee et al. (2012). Here $\sigma_{0}$ denotes the error bar from the pipelines, $\sigma_{\rm min}$ is a factor used to make the scatter of data consistent with error bars, and $k$ is a scaling factor used to make the $\chi^{2}$ per degree of freedom for each data equal to unity. In Table 3, we list the error-bar readjustment factors and the number of data, $N_{\rm data}$, of the individual data sets.

In this section, we present the detailed analyses of the individual lensing events. The light curves of all events exhibit anomaly features that include caustic crossings, and thus we model the light curves under a binary-lens and single-source (2L1S) interpretation.

The modeling is done by searching for the set of the lensing parameters that best explain the observed data. The first three of these parameters describe the source–lens approach, including $(t_{0},u_{0},t_{\rm E})$, which represent the time of the closest source approach to a reference position of the lens, the separation (normalized to the angular Einstein radius $\theta_{\rm E}$) between the source and the lens reference position at $t_{0}$, and the event time scale, respectively. For the reference position of the lens, we use the center of mass for a binary lens with a separation less than $\theta_{\rm E}$ (close binary), and the effective position, defined by Di Stefano & Mao (1996) and An & Han (2002), for the lens with a separation greater than $\theta_{\rm E}$ (wide binary). The next three parameters $(s,q,\alpha)$ describe the lens binarity, and they denote the projected separation (normalized to $\theta_{\rm E}$) and mass ratio between the lens components, $M_{1}$ and $M_{2}$, and the angle between the source motion and the binary axis (source trajectory angle), respectively. The last parameter is $\rho$, which is defined as the ratio of the angular source radius, $\theta_{*}$, to $\theta_{\rm E}$, that is, $\rho=\theta_{*}/\theta_{\rm E}$ (normalized source radius), and it is included to account for finite-source effects that affect the caustic-crossing parts of lensing light curves. We incorporate limb-darkening effects in the finite magnification computations by modeling the surface brightness variation of the source as $S\propto 1-\Gamma(1-3\cos\phi/2)$, where $\Gamma$ is the limb-darkening coefficient, $\phi$ represents the angle between two lines extending from the source center: one to the observer and the other to the source surface. As will be discussed in Sect. 4, the source stars of all events have similar spectral types, early K-type main-sequence stars, and thus we adopt an $I$-band limb-darkening coefficient of $\Gamma_{I}=0.5$ from Claret (2000), assuming that the effective temperature, surface gravity, and turbulence velocity are $T_{\rm eff}=5000$ K, $\log(g/g_{\odot})=0.05$, and $v_{\rm turb}=2\leavevmode\nobreak\ {\rm km}\leavevmode\nobreak\ {\rm s}^{-1}$, respectively.

For a fraction of events with long time scales comprising an important protion of a year, lensing light curves may deviate from the form expected from a rectilinear lens-source motion. One cause for this deviation is the motion of an observer induced by the orbital motion of Earth (microlens-parallax effect: Gould, 1992), and the other is the orbital motion of the binary lens (lens-orbital effects: Dominik, 1998). It is expected that the signature of the microlens parallax, $\pi_{\rm E}$, will be small for OGLE-2017-BLG-1099 and OGLE-2019-BLG-0299 due to their short time scales, which are $\sim 19$ days and $\sim 30$ days, respectively, but the signature might not be small for KMT-2017-BLG-2509 due to its relatively long time scale of $\sim 67$ days. We check these higher-order effects and find that it is difficult to detect the higher-order signatures for any of the events, mainly because the photometric quality is not high enough to detect the subtle deviations induced by these higher-order effects. A microlens parallax can provide an important constraint on the physical lens parameters. As will be discussed in Sect. 5, the uncertainties of the physical lens parameters are large for all events due to the absence of the $\pi_{\rm E}$ constraint.

The 2L1S modeling is carried out in two steps. In the first step, the binary lensing parameters $s$ and $q$ are searched for using a grid approach with different starting values of $\alpha$ evenly distributed in the 0 – $2\pi$ range with 21 grids, while the 5 non-grid lensing parameters, that is, $(t_{0},u_{0},t_{\rm E},\alpha,\rho)$, are found using a downhill approach based on the Markov Chain Monte Carlo (MCMC) algorithm. The ranges of the grid parameters are $-1.0\leq\log s<1.0$ and $-4.0\leq\log q<1.0$, and they are divided into 70 grids. We then identify local solutions that appear in the $\Delta\chi^{2}$ map on the $s$–$q$ parameter plane. In the second step, we refine the individual local solutions found in the first step by letting all parameters vary. Then the global solution is found by comparing $\chi^{2}$ values of the local solutions, if there is more than one. Figure 1 shows the $\Delta\chi^{2}$ maps on the $\log s$–$\log q$ parameter plane obtained from the first-step modeling of the individual events. It shows that there exist a single local solution for all events.

In this section, we estimate the angular Einstein radii of the events. The Einstein radius is determined by $\theta_{\rm E}=\theta_{*}/\rho$. The $\rho$ value is measured or constrained from the analysis of the caustic-crossing parts, which are affected by finite-source effects. With the measured $\rho$, then it is required to estimate the angular source radius $\theta_{*}$. The value of $\theta_{*}$ is deduced from the color and magnitude of the source.

In general, the source color is estimated by measuring the source magnitudes in two passbands, $I$ and $V$ bands in our case, by regressing the data of the individual passbands with the variation of the lensing magnification. The $I$-band magnitudes are securely measured by this method for all events. However, the $V$-band magnitudes are difficult to be measured by this method due to the large uncertainties of the data, making it difficult to securely estimate the source colors. We, therefore, estimate the source color using the Bennett et al. (2008) method, which utilizes the CMD constructed from the Hubble Space Telescope (HST) observations (Holtzman et al., 1998). In the first step of this method, the HST CMD is aligned with the CMD obtained from ground-based observations using the well defined centroid of the red giant clump (RGC). In the second step, the source position in the CMD is interpolated from the branch of main-sequence or giant stars on the HST CMD using the well measured $I$-band magnitude difference between the RGC centroid and the source. In the final step, the source color and its uncertainty are estimated as the mean and standard deviation of stars located on the branch.

Figure 11 shows the source locations (black filled dots with error bars) with respect to the RGC centroids (red filled dot) in the combined CMD, in which the HST CMD is represented by brown dots and the CMD from the ground-based observations is represented by grey dots. In Table 5, we list the positions of the source, $(V-I,I)$, and the RGC centroid, $(V-I,I)_{\rm RGC}$, measured on the instrumental CMD. Then, the reddening and extinction corrected (de-reddened) color and magnitude of the source, $(V-I,I)_{0}$, are determined using the offsets from the RGC centroid, $\Delta(V-I,I)$, together with the known de-reddened values of RGC, $(V-I,I)_{{\rm RGC},0}$ (Bensby et al., 2013; Nataf et al., 2013), by the relation

The values of $(V-I,I)_{0}$, $\Delta(V-I,I)$, $(V-I,I)_{{\rm RGC},0}$ for the individual events are listed in Table 5. We note that the de-reddened $I$-band magnitudes of the RGC centroids, that is, $I_{{\rm RGC},0}$, vary depending on the event, because we consider the varying distance depending on the source location using Table 1 of Nataf et al. (2013). The measured colors and magnitudes, which are in the ranges of $0.9\lesssim(V-I)_{0}\lesssim 1.1$ and $19.5\lesssim I_{0}\lesssim 20.2$, respectively, indicate that the source stars of the events have similar spectral types of early K-type main sequence stars.

The measured $(V-I)$ color is then converted into $(V-K)$ color using the color-color relation of Bessell & Brett (1988), and then the source radius is deduced from the $(V-K)$–$\theta_{*}$ relation of Kervella et al. (2004). With the measured source radius, then, the Einstein radius and the relative lens-source proper motion are estimated by the relations $\theta_{\rm E}=\theta_{*}/\rho$ and $\mu=\theta_{\rm E}/t_{\rm E}$, respectively. We list the estimated values of $\theta_{*}$, $\theta_{\rm E}$, and $\mu$ in Table 5. We note that the lower limits $\theta_{\rm E}$ and $\mu$ are presented for OGLE-2019-BLG-0299, because only the upper limit of $\rho$ is constrained for the event.

We estimate the physical lens parameters of the lens mass, $M$, and distance, $D_{\rm L}$, by conducting a Bayesian analysis. The lensing observables that can be used to constrain $M$ and $D_{\rm L}$ include $t_{\rm E}$, $\theta_{\rm E}$, and $\pi_{\rm E}$, where the first two observables are related to $M$ and $D_{\rm L}$ by

and the additional measurement of $\pi_{\rm E}$ would allow one to uniquely determine the lens parameters by

Here $\kappa=4G/(c^{2}{\rm AU})$, $\pi_{\rm S}={\rm AU}/D_{\rm S}$, and $D_{\rm S}$ denotes the distance to the source (Gould, 2000). The available observables vary depending on the events: $t_{\rm E}$ and $\theta_{\rm E}$ for KMT-2017-BLG-2509 and OGLE-2017-BLG-1099, and $t_{\rm E}$ and the lower limit of $\theta_{\rm E}$ for OGLE-2019-BLG-0299. The value of $\pi_{\rm E}$ is not measured for any of the events.

In the first step of the Bayesian analysis, we produce artificial lensing events by conducting a Monte Carlo simulation. In the simulation, we use a prior Galactic model, which describes the physical and dynamical distributions and the mass function of Galactic objects. We adopt the Jung et al. (2021) Galactic model, in which the physical distribution of disk and bulge objects are described by the Robin et al. (2003) and Han & Gould (2003) models, respectively, the dynamical distributions of the disk and bulge objects are depicted by the Jung et al. (2021) and Han & Gould (1995) models, respectively, and the Jung et al. (2018) mass function model is commonly used for both populations. In the second step, we choose events with $t_{\rm E}$ and $\theta_{\rm E}$ values consistent with the measured observables, and construct the posterior distributions of $M$ and $D_{\rm L}$ for these events. Then, the representative values of the lens parameters are determined as the median values of the posterior distributions, and the lower and upper limits are determined as 16% and 84% of the distributions, respectively.

In Figures 12 and 13 , we present the Bayesian posterior distributions of $M_{1}$ and $D_{\rm L}$, respectively. In Table 6, we list the estimated masses of the host, $M_{\rm host}\equiv M_{1}$, and planet, $M_{\rm planet}\equiv M_{2}$, distance, and projected planet-host separation, $a_{\perp}$. The projected separation is calculated by $a_{\perp}=sD_{\rm L}\theta_{\rm E}$. It is estimated that the host masses are in the range of $0.45\lesssim M_{\rm host}/M_{\odot}\lesssim 0.59$, which corresponds to early M to late K dwarfs, and thus the host stars are less massive than the sun. On the other hand, the planet masses, which are in the range of $2.1\lesssim M_{\rm planet}/M_{\rm J}\lesssim 6.2$, are heavier than the mass of the heaviest planet of the solar system, that is, Jupiter. Considering that the snow line distance is $a_{\rm sl}\sim 2.7(M/M_{\odot})$ AU, and $a_{\perp}$ is the separation in projection, the planets in all systems lie beyond the snow lines of the hosts. Therefore, the discovered planetary systems, together with many other microlensing planetary systems, support that massive gas-giant planets are commonplace around low-mass stars. See the distribution of exoplanets with respect to $a_{\perp}/a_{\rm sl}$ presented in Figure 6 of Gaudi (2012). The contributions to the posterior distribution by the disk and bulge lens populations are marked by blue and red curves, respectively. The disk/bulge contributions are 28%/72% for KMT-2017-BLG-2509, 33%/67% for OGLE-2017-BLG-1099, and 48%/52% for OGLE-2019-BLG-0299. The relatively low disk contribution for KMT-2017-BLG-2509 arises due to the constraint of the low relative lens-source proper motion, $\mu\sim 1.3$ mas/yr, because low proper motion is difficult to produce for disk lenses.

In the general case of a lensing event, high-resolution observations using space-borne telescopes or ground-based adaptive optics instruments allow one to measure the lens flux and the lens-source separation. The lens flux allows one to estimate the lens mass $M$, and the lens-source separation allows one to estimate the relative lens-source proper motion $\mu$, which in turn constrains the Einstein radius by $\theta_{\rm E}=\mu t_{\rm E}$.

For faint-source planetary lensing events with resonant caustic features, high-resolution follow-up observations are especially important for clarifying the planetary lens systems. The size of a resonant planetary caustic scales to the planet/host mass ratio as $\Delta\zeta_{\rm c}\propto q^{1/3}\theta_{\rm E}$, and thus the duration of the planetary anomaly is related to the event time scale by $\Delta t=\Delta\zeta_{\rm c}/\mu\propto q^{1/3}t_{\rm E}$. For a given anomaly duration, then, the event time scale and the mass ratio are related by $q\propto t_{\rm E}^{-3}$. For faint-source events, the very faint sources can make it difficult to precisely determine $t_{\rm E}$, and this leads to a large uncertainty of $q$, because $\Delta q\propto 3\Delta t_{\rm E}$. Late time observations in two passbands can yield the source flux and color, and so $I$-band source-flux estimate. The well estimated source flux can further constrain $t_{\rm E}$, and this leads to a tight constraint on the planet mass ratio. High-resolution image data could have resulted in best constraints if they had been acquired at the time of the event to provide a comparison. Unfortunately, no such images were taken because the planetary nature of the events were not known at the times of the event discoveries. However, post-event imaging can still help to constrain the physical parameters the lens systems.

We reported three microlensing planets KMT-2017-BLG-2509Lb, OGLE-2017-BLG-1099Lb, and OGLE-2019-BLG-0299Lb that were found from the reinvestigation of the microlensing data collected by the KMTNet and OGLE surveys during the 2017–2019 seasons. For all of these lensing events, the planetary signals deviated from the typical form of short-term anomalies, because they were produced by the crossings of the source stars over the resonant caustics formed by the giant planets located at around the Einstein rings of host stars. The faintness of the source stars and the relatively low observational cadences also contributed to the difficulty of finding the planetary signals. Due to the resonant nature of the caustics, the lensing solutions were uniquely determined without any degeneracy. The estimated masses of the planet hosts are in the range of $0.45\lesssim M/M_{\odot}\lesssim 0.59$, which corresponds to early M to late K dwarfs, and thus the host stars are less massive than the sun. On the other hand, the planets, with masses in the range of $2.1\lesssim M_{\rm planet}/M_{\rm J}\lesssim 6.2$, are heavier than Jupiter of the solar system. The planets in all systems lie beyond the snow lines of the hosts, and thus the discovered planetary systems support the conclusion that massive gas-giant planets are commonplace around low-mass stars.