Probable brown dwarf companions detected in binary microlensing events during the 2018-2020 seasons of the KMTNet survey

Due to the trait of occurring by the mass of a lensing object regardless of its luminosity, microlensing provides an important tool to detect very faint and even dark astronomical objects. With this trait, microlensing has been applied to search for extrasolar planets, and about 30 planets are annually being detected (Gould et al., 2022; Jung et al., 2022; Gould, 2022) from the combined observations by survey, for example, the KMTNet (Kim et al., 2016), MOA (Bond et al., 2001), and OGLE (Udalski et al., 2015) experiments, and followup groups, for example, the ROME/REA survey (Tsapras et al., 2019).

Brown dwarfs (BDs) are another population of faint astronomical objects to which microlensing is sensitive. Microlensing BDs can be detected through a single-lens event channel, in which a single BD object produces a lensing event with a short time scale, for example, Han et al. (2020). Considering that BDs may have formed via a similar mechanism to that of stars, BDs can be as abundant as its stellar siblings, and, in this case, a significant fraction of short time-scale lensing events being detected by the surveys may be produced by BDs. Observationally, both radial-velocity (Grether & Lineweaver, 2006) and microlensing (Shvartzvald et al., 2016) studies indicate a deficit of BDs companions compared to both stars and planets, suggesting that microlensing may allows us to study the stars, BDs and planet formation mechanism. However, confirming the BD lens nature of a short time-scale event by measuring the mass of the lens is difficult because the event time scale depends not only on the lens mass but also on the distance to the lens and the relative lens-source proper motion. The lens mass can be determined by simultaneously measuring the extra lensing observables of the angular Einstein radius $\theta_{\rm E}$ and microlens parallax $\pi_{\rm E}$, for example, OGLE-2017-BLG-0896 (Shvartzvald et al., 2019), but the fraction of these events is small.

Han et al. (2022), hereafter paper I, investigated the microlensing survey data collected during the early phase of the KMTNet experiment with the aim of finding microlensing binaries containing BD companions. The strategy applied to paper I in finding BD events was picking out lensing events produced by binaries with small companion-to-primary mass ratios $q$, for example, $0.03\lesssim q\lesssim 0.1$. Considering that typical Galactic lensing events are produced by low-mass stars (Han & Gould, 2003), the companions to the lenses of these events are very likely to be BDs.

Following the work done in Paper I, we report four additional BD binary-lensing events found from the systematic investigation of the 2018–2020 season data of the KMTNet survey. For the use of a future statistical analysis on the properties of BDs based on a uniform sample, we consistently apply the same selection criterion as that applied in paper I in the selection of BD events.

The discoveries and analyses of the BD events are presented according to the following organization. In Sect. 2, we mention the procedure of selecting BD binary-lens events and explain the observations conducted for the selected events. We describe the analysis procedure commonly applied to the lensing events in Sect.  3, and detailed analyses for the individual events are presented in the following subsections. In Sect.  4, we characterize the source stars of the events and estimate their angular Einstein radii. In Sect.  5, we estimate the physical parameters of the lens systems by conducting Bayesian analyses of the events using the measured observables of the individual events. A summary of the results found from the analyses and conclusion are presented in Sect. 6.

The KMTNet group has conducted a microlensing survey since 2016 by observing stars lying toward the dense Galactic bulge field with the use of three telescopes that are globally distributed in the Southern Hemisphere. For the searches of binary lenses possessing BD companions, we inspect the microlensing data acquired by the KMTNet survey during the three seasons from 2018 to 2020. The survey in the 2020 season was partially conducted because two of the KMTNet telescopes were shutdown due to Covid-19 pandemic for most of that season.

We sort out binary lensing (2L1S) events with candidate BD lens companions by conducting systematic analyses of all anomalous lensing events observed during the seasons. Anomalies induced by planetary companions to the lenses, with companion-to-primary mass ratios of an order of $10^{-3}$ or less, can be, in most cases, readily identified from the characteristic short-term nature of the anomalies (Gould & Loeb, 1992). However, anomalies induced by BD companions, with mass ratios of an order of $10^{-2}$, usually cannot be treated as perturbations, and thus it is generally much more difficult to distinguish them from those induced by binary lenses with roughly equal-mass components. We, therefore, systematically conducted modelings of all anomalous lensing events detected during the seasons, and then sorted out candidate BD binary-lens events by applying the selection criterion of $q\lesssim 0.1$. The total numbers of lensing events detected by the KMTNet survey are 2781, 3303, and 894 in the 2018, 2019, and 2020 seasons, respectively, and 2L1S events comprise about one tenth of the total events. This fraction of 2L1S events is similar to the one Shvartzvald et al. (2016) found for the OGLE-MOA-Wise sample (12%).

From this procedure, we identified four 2L1S events with candidate BD companions, including KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335. We found no BD event among the events detected in the 2020 season not only because the number of detected lensing events during the season is relatively small but also because the data coverage of the individual events was sparse due to the use of a single telescope during the great majority of the season. Among these events, KMT-2019-BLG-0297 was additionally observed by the MOA group, who labeled the event as MOA-2019-BLG-131, and we include their data in the analysis. For this event, we use the KMTNet ID reference following the convention of the microlensing community of using the ID reference of the first discovery survey

The three KMTNet telescopes are identical with a 1.6 m aperture. The sites of the individual telescopes are the Siding Spring Observatory in Australia (KMTA), the Cerro Tololo Interamerican Observatory in Chile (KMTC), and the South African Astronomical Observatory in South Africa (KMTS). The telescope used for the MOA survey has an aperture of 1.8 m and is located at Mt. John Observatory in New Zealand. The fields of view of the cameras installed on the KMTNet and MOA telescopes are 4 deg² and 2.2 deg², respectively. Images were primarily taken in the $I$ band for the KMTNet survey and in the customized MOA-$R$ band for the MOA survey. For both surveys, a minor portion of images were acquired in the $V$ band to measure the colors of the source stars. The OGLE survey was conducted during the 2018 and 2019 seasons, but none of the events reported in this work was detected by the OGLE survey.

Reductions of the images and photometry of the events were carried out using the pipelines of the individual survey groups developed by Albrow et al. (2009) for the KMTNet group and Bond et al. (2001) for the MOA group. Following the routine of Yee et al. (2012), we readjust the error bars of each data set estimated by the pipelines in order that the error bars are consistent with the scatter of the data and $\chi^{2}$ per degree of freedom (dof) for each data set becomes unity. In the process of readjusting error bars, we use the best-fit model by after rejecting outliers lying beyond a 3$\sigma$ level from the best-fit model. The error-bar normalization is an ever-repeating process because once the error bars are rescaled based on a model obtained at a certain stage, the $\chi^{2}$/dof value can vary in the next modeling run as the model slightly varies from the initial model, and thus the value of $\chi^{2}$/dof can be slightly different from unity. We note that the variation of the lensing parameters caused by the slight change of the $\chi^{2}$/dof value is very minor.

Under the approximation of a rectilinear relative motion between the lens and source, the light curve of a 2L1S event is characterized by 7 basic lensing parameters. The first three parameters $(t_{0},u_{0},t_{\rm E})$ define the lens-source approach, and the individual parameters denote the time of the closest approach, the separation between the lens and source at that time (impact parameter), and the Einstein time scale. The Einstein time scale is defined as the time required for a source to cross the Einstein radius, that is, $t_{\rm E}=\theta_{\rm E}/\mu$, where $\mu$ denotes the relative lens-source proper motion. Another three parameters $(s,q,\alpha)$ define the binary-lens system, and $s$ denotes the projected separation between the lens components with masses $M_{1}$ and $M_{2}$, $q=M_{1}/M_{2}$ is the mass ratio, and $\alpha$ represents the angle between the direction of $\mu$ and $M_{1}$–$M_{2}$, axis (source trajectory angle). Here $\mu$ represents the vector of the relative lens-source proper motion. The parameters $u_{0}$ and $s$ are scaled to $\theta_{\rm E}$. The last parameter $\rho$ 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 characterizes the deformation of a lensing light curve by finite-source effects arising when a source crosses or approaches lens caustics.

Caustics represent source positions at which the lensing magnifications of a point source become infinity. Caustics in binary lensing vary depending on the binary parameters $s$ and $q$, and their topologies are classified into three categories of “close”, “intermediate”, and “wide” (Schneider & Weiss, 1986; Cassan, 2008). A close binary induces three sets of caustics, in which one lies near the heavier lens component and the other two sets lie on the opposite side of the lighter lens component. On the other hand, a wide binary induces two sets of caustics, which lie close to the individual lens components. In the intermediate regime, the caustics merge together to form a single set of a large caustic.

Besides the basic parameters, detailed modeling of lensing light curves for a fraction of events requires consideration of higher-order effects caused by the deviation of the relative lens-source motion from rectilinear. Such a deviation is induced by two major causes, in which the first is the accelerated motion of an observer caused on the orbital motion of Earth, microlens-parallax effects (Gould, 1992), and the second is the orbital motion of the binary lens, lens-orbital effects, for example, Batista et al. (2011) and Skowron et al. (2011). For the consideration of these higher-order effects, extra parameters are required to be added in modeling. The parameters for the consideration of the microlens-parallax effects are $(\pi_{{\rm E},N},\pi_{{\rm E},E})$, which represent the north and east components of the microlens-parallax vector $\mbox{\boldmath$\pi$}_{\rm E}=(\pi_{\rm rel}/\theta_{\rm E})(\mbox{\boldmath$\mu$}/\mu)$, respectively. Here $\pi_{\rm rel}={\rm AU}(D_{\rm L}^{-1}-D_{\rm S}^{-1})$ represents the relative parallax of the lens and source. Under the approximation of a minor change of the lens configuration by the orbital motion, the lens-orbital effects are described by two parameters of $(ds/dt,d\alpha/dt)$, which represent the change rates of the binary separation and source trajectory angle, respectively.

The analyses of the events were carried out by finding lensing solutions, representing a set of parameters describing the observed light curves. The searches for the lensing parameters were done in two steps. In the first step, we conducted grid searches for the binary parameters $s$ and $q$, and for each pair of the grid parameters $s$ and $q$, we found the other parameters using a downhill approach based on the Markov Chain Monte Carlo (MCMC) logic. In this stage, we constructed a $\chi^{2}$ map on the plane of the grid parameters and identified local solutions on the map. In the second step, we refined the individual local solutions by allowing all parameters to vary. If a single solution can be distinguished from the other local minima with a significant $\chi^{2}$ difference, we provide a single global solution. If the degeneracy between local solutions is severe, by contrast, we present all local solutions with the explanations on the causes of the degeneracy. In the following subsections, we present the analyses of the individual events.

In this section, we specify the source stars of the individual lensing events and estimate angular Einstein radii for the events with measured normalized source radii. For each event, the source is specified by measuring its reddening and extinction-corrected (de-reddened) color and magnitude. The measured source color and magnitude are used to deduce the angular source radius, from which the angular Einstein radius is estimated from the relation in Equation (1).

Figure 6 shows the source locations of the individual lensing events in the instrumental color-magnitude diagrams (CMDs) of stars lying adjacent to the source stars constructed from pyDIA (Albrow, 2017) photometry of the KMTC images. The $I$- and $V$-band magnitudes of each source were estimated from the regression of the light curve data measured using the same pyDIA photometry with respect to the lensing magnification. For the three events KMT-2018-BLG-0321, KMT-2018-BLG-0885, and KMT-2019-BLG-0335, the $V$-band source magnitudes could not be securely measured due to the poor quality of the $V$-band data, although their $I$-band magnitudes were measured. In these cases, we first combine the two sets of CMDs, one constructed from the pyDIA photometry of stars in the KMTC image and the other for stars in the Baade’s window observed with the use of the Hubble Space Telescope (Holtzman et al., 1998), align the two CMDs using the centroids of the red giant clump (RGC) in the individual CMDs, and then estimate the source color as the median values for stars in the main-sequence branch of the HST CMD with $I$-band magnitude offsets from the RGC centroid corresponding to the measured values. The estimated instrumental colors and magnitudes of the source stars, $(V-I,I)_{\rm S}$, and RGC centroids, $(V-I,I)_{\rm RGC}$, for the individual events are listed in Table 5.

For the calibration of the source colors and magnitudes, we use the RGC centroid, for which its de-reddened values $(V-I,I)_{0,{\rm RGC}}$ are well defined (Bensby et al., 2013; Nataf et al., 2013), as a reference (Yoo et al., 2004). By measuring the offsets in color and magnitude, $\Delta(V-I,I)$, of the source star from those of the RGC centroid, the de-reddened values are estimated as $(V-I,I)_{0,{\rm S}}=(V-I,I)_{0,{\rm RGC}}+\Delta(V-I,I)$. The estimated de-reddened source colors and magnitudes of the individual events are listed in Table 5. According to the estimated de-reddened colors and magnitudes, it is found that the source of KMT-2018-BLG-0321 is a G-type turnoff star, and those of the other events are main-sequence stars with spectral types ranging from late G to early K.

The angular radii of the source stars were deduced from their measured colors and magnitudes. For this, we first converted $V-I$ color into $V-K$ color using the Bessell & Brett (1988) relation, and then estimated the angular source radius using the Kervella et al. (2004) relation between $(V-K,I)$ and $\theta_{*}$. For the events with measured normalized source radii, the angular Einstein radii were estimated using the relation in Equation (1). The estimated angular radii of the source stars and Einstein rings of the individual events are listed in Table 6. Also listed are the relative proper motions between the lens and source estimated by $\mu=\theta_{\rm E}/t_{\rm E}$. In the cases of the events KMT-2018-BLG-0321 and KMT-2018-BLG-0885, for which only the upper limits of $\rho$ are constrained, we list the lower limits of $\theta_{\rm E}$ and $\mu$.

The basic lensing observable constraining the physical parameters of the lens mass $M$ and distance to the lens $D_{\rm L}$ is the Einstein time scale $t_{\rm E}$, which is related to the physical parameters by

where $\kappa=4G/(c^{2}{\rm AU})$. Besides this observable, the lens mass and distance can be additionally constrained by measuring the extra observables of $\pi_{\rm E}$ and $\theta_{\rm E}$. If both of these extra observables are simultaneously measured, the physical lens parameters can be uniquely determined by the relation

where $\pi_{\rm S}={\rm AU}/D_{\rm S}$ is the parallax of the source, and $D_{\rm S}$ denotes the distance to the source (Gould, 2000). For KMT-2019-BLG-0297, both of these extra parameters are measured, but the uncertainty of the measured microlens parallax is large. For the event KMT-2019-BLG-0335, the Einstein radius is measured, but the values of $\pi_{\rm E}$ are not constrained. For the KMT-2018-BLG-0321 and KMT-2018-BLG-0885, none of the extra observables are measured, and only the lower limits of $\theta_{\rm E}$ are constrained. Due to the incompleteness of the observables, we estimated the physical lens parameters by conducting Bayesian analyses based on the available observables of the individual events.

The Bayesian analysis for each event was carried out by first generating a large number ($10^{7}$) of artificial microlensing events from a Monte Carlo simulation with the use of a prior Galactic model. The Galactic model defines the positions, velocities, and masses of astronomical objects in the Galaxy, and we adopted the Jung et al. (2021) model. For each simulated event, we computed the lens observables of the Einstein time scale, $t_{{\rm E},i}=D_{{\rm L},i}\theta_{{\rm E},i}/v_{\perp,i}$, Einstein radius, $\theta_{{\rm E},i}=(\kappa M_{i}\pi_{{\rm rel},i})^{1/2}$, and microlens parallax, $\pi_{{\rm E},i}=\pi_{{\rm rel},i}/\theta_{{\rm E},i}$. Here, $v_{\perp}$ denotes the transverse lens-source speed. We then constructed a Bayesian posterior distributions of the lens mass and distance by imposing a weight to each simulated event of $w_{i}=\exp(-\chi^{2}_{i}/2)$, where $\chi^{2}_{i}=(O_{i}-O)^{2}/[\sigma(O)]^{2}$ and $[O,\sigma(O)]$ denote the measured value of the observable and its uncertainty, respectively. In the case of the event for which only the lower limit of $\theta_{\rm E}$ is constrained, we set $w_{i}=0$ for events with $\theta_{\rm E}<\theta_{{\rm E,min}}$.

The posterior distributions for the mass of the lens companion and distance to the lens system are presented Figures 7 and 8, respectively. In each distribution, we mark three curves, in which the blue and red curves represent the contributions by the disk and bulge lens populations, respectively, and the black curve is sum of the two contributions. The two vertical lines in the mass posteriors represent the boundaries between planetary, BD, and stellar lens populations. We set the boundary between planets and BDs as $12\leavevmode\nobreak\ M_{\rm J}$ ($M_{2}\sim 0.012\leavevmode\nobreak\ M_{\odot}$) and that between BDs and stars as $0.08\leavevmode\nobreak\ M_{\odot}$.

In Table 7, we summarize the estimated physical lens parameters, including $M_{1}$, $M_{2}$, $D_{\rm L}$, and $a_{\perp}$, where $a_{\perp}=sD_{\rm L}\theta_{\rm E}$ denotes the projected separation between the binary lens components. We take the median values of the posterior distributions as representative values, and the uncertainties are estimated as the 16% and 84% of the distributions. In Table 8, we list the probabilities for the lens companion to be in the planetary ($P_{\rm planet}$), BD ($P_{\rm BD}$), and stellar ($P_{\rm star}$) mass regimes. In all cases of the events, the median values of $M_{2}$ lie in the BD mass regime, and the probabilities for the lens companion to be in the BD mass regime are high. For the events KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335, the probabilities for the lens companions to be in the planetary mass regime are $P_{\rm planet}\sim 25\%$, 34%, and 33%, respectively, and thus it is difficult to completely rule out the possibility that the companions are giant planets. Also listed in Table 8 are the probabilities for the lens to be in the disk, $P_{\rm disk}$, and in the bulge, $P_{\rm bulge}$. It turns out that KMT-2019-BLG-0297L is very likely to be in the disk mainly from the 2-dimensional gaussian constraint of the measured microlens-parallax, that is, Figure 4.

We investigated the microlensing data acquired during the 2018, 2019, and 2020 seasons by the KMTNet survey in order to find lensing events produced by binaries with brown-dwarf companions. For this investigation, we conducted systematic analyses of anomalous lensing events observed during the seasons, and picked out candidate BD binary-lens events by applying the selection criterion that the companion-to-primary mass ratio was less than 0.1. From this procedure, we identified four candidate events with BD companions, including KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335. No candidates were identified in the 2020 season, which was severely affected by the Covid-19 pandemic.

We estimated the masses of the lens companions by conducting Bayesian analyses using the measured observables of the individual events. From this estimation, it was found that the probabilities for the masses of the companions to be in the BD mass regime were high with 59%, 68%, 66%, and 66% for KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335, respectively. We plan to report additional BD binary-lens events from the investigation of the data acquired in the 2021 and 2022 seasons. Together with the previous 6 BD events (OGLE-2016-BLG-0890, MOA-2017-BLG-477, OGLE-2017-BLG-0614, KMT-2018-BLG-0357, OGLE-2018-BLG-1489, and OGLE-2018-BLG-0360) reported in paper I plus KMT-2020-BLG-0414LB recently reported by Zang et al. (2021), the KMTNet sample will be useful for a future statistical analysis on the properties of BDs.