arXiv subjects

Richard W. Pogge

Publications and source records attributed to Richard W. Pogge.

At least 109 records · Page 6Linked to original sources

arXiv2022

Systematic KMTNet Planetary Anomaly Search, Paper I: OGLE-2019-BLG-1053Lb, A Buried Terrestrial Planet

In order to exhume the buried signatures of "missing planetary caustics" in the KMTNet data, we conducted a systematic anomaly search to the residuals from point-source point-lens fits, based on a modified version of the KMTNet EventFinder algorithm. This search reveals the lowest mass-ratio planetary caustic to date in the microlensing event OGLE-2019-BLG-1053, for which the planetary signal had not been noticed before. The planetary system has a planet-host mass ratio of $q = (1.25 \pm 0.13) \times 10^{-5}$. A Bayesian analysis yields estimates of the mass of the host star, $M_{\rm host} = 0.61_{-0.24}^{+0.29}~M_\odot$, the mass of its planet, $M_{\rm planet} = 2.48_{-0.98}^{+1.19}~M_{\oplus}$, the projected planet-host separation, $a_\perp = 3.4_{-0.5}^{+0.5}$ au, and the lens distance of $D_{\rm L} = 6.8_{-0.9}^{+0.6}$ kpc. The discovery of this very low mass-ratio planet illustrates the utility of our method and opens a new window for a large and homogeneous sample to study the microlensing planet-host mass-ratio function down to $q \sim 10^{-5}$.

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arXiv2022

KMT-2021-BLG-0171Lb and KMT-2021-BLG-1689Lb: Two Microlensing Planets in the KMTNet High-cadence Fields with Followup Observations

Follow-up observations of high-magnification gravitational microlensing events can fully exploit their intrinsic sensitivity to detect extrasolar planets, especially those with small mass ratios. To make followup more uniform and efficient, we develop a system, HighMagFinder, based on the real-time data from the Korean Microlensing Telescope Network (KMTNet) to automatically alert possible ongoing high-magnification events. We started a new phase of follow-up observations with the help of HighMagFinder in 2021. Here we report the discovery of two planets in high-magnification microlensing events, KMT-2021-BLG-0171 and KMT-2021-BLG-1689, which were identified by the HighMagFinder. We find that both events suffer the ``central-resonant'' caustic degeneracy. The planet-host mass-ratio is $q\sim4.7\times10^{-5}$ or $q\sim 2.2\times10^{-5}$ for KMT-2021-BLG-0171, and $q\sim2.5\times10^{-4}$ or $q\sim 1.8\times10^{-4}$ for KMT-2021-BLG-1689. Together with two events reported by Ryu et al. (2022), four cases that suffer such degeneracy have been discovered in the 2021 season alone, indicating that the degenerate solutions may have been missed in some previous studies. We also propose a new factor for weighting the probability of each solution from the phase-space. The resonant interpretations for the two events are disfavored under this consideration. This factor can be included in future statistical studies to weight degenerate solutions.

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arXiv2022

Four sub-Jovian-mass planets detected by high-cadence microlensing surveys

With the aim of finding short-term planetary signals, we investigated the data collected from the high-cadence microlensing surveys. From this investigation, we found four planetary systems with low planet-to-host mass ratios, including OGLE-2017-BLG-1691L, KMT-2021-BLG-0320L, KMT-2021-BLG-1303L, and KMT-2021-BLG-1554L. Despite the short durations, ranging from a few hours to a couple of days, the planetary signals were clearly detected by the combined data of the lensing surveys. It is found that three of the planetary systems have mass ratios of the order of $10^{-4}$ and the other has a mass ratio slightly greater than $10^{-3}$. The estimated masses indicate that all discovered planets have sub-Jovian masses. The planet masses of KMT-2021-BLG-0320Lb, KMT-2021-BLG-1303Lb, and KMT-2021-BLG-1554Lb correspond to $\sim 0.10$, $\sim 0.38$, and $\sim 0.12$ times of the mass of the Jupiter, and the mass of OGLE-2017-BLG-1691Lb corresponds to that of the Uranus. The estimated mass of the planet host KMT-2021-BLG-1554L, $M_{\rm host}\sim 0.08~M_\odot$, corresponds to the boundary between a star and a brown dwarf. Besides this system, the host stars of the other planetary systems are low-mass stars with masses in the range of $\sim [0.3$--$0.6]~M_\odot$. The discoveries of the planets well demonstrate the capability of the current high-cadence microlensing surveys in detecting low-mass planets.

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arXiv2022

MOA-2019-BLG-008Lb: a new microlensing detection of an object at the planet/brown dwarf boundary

We report on the observations, analysis and interpretation of the microlensing event MOA-2019- BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite source effects were observed. Therefore the angular Einstein ring radius cannot be measured from the light curve alone. However, the large event duration, t E about 80 days, allows a precise measurement of the microlensing parallax. In addition to the constraints on the angular radius and the apparent brightness I s of the source, we employ the Besancon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two Galactic models: the companion is likely a resident of the brown dwarf desert with a mass Mp about 30 MJup and the host is a main sequence dwarf star. The lens lies along the line of sight to the Galactic Bulge, at a distance of less then4 kpc. We estimate that in about 10 years, the lens and source will be separated by 55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground or space-based observatories.

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arXiv2022

KMT-2021-BLG-0240: Microlensing event with a deformed planetary signal

The light curve of the microlensing event KMT-2021-BLG-0240 exhibits a short-lasting anomaly with complex features near the peak at the 0.1~mag level from a single-lens single-source model. We conducted modeling of the lensing light curve under various interpretations to reveal the nature of the anomaly. It is found that the anomaly cannot be explained with the usual model based on a binary-lens (2L1S) or a binary-source (1L2S) interpretation. However, a 2L1S model with a planet companion can describe part of the anomaly, suggesting that the anomaly may be deformed by a tertiary lens component or a close companion to the source. From the additional modeling, we find that all the features of the anomaly can be explained with either a triple-lens (3L1S) model or a binary-lens binary-source (2L2S) model obtained under the 3L1S interpretation. However, it is difficult to validate the 2L2S model because the light curve does not exhibit signatures induced by the source orbital motion and the ellipsoidal variations expected by the close separation between the source stars according to the model. We, therefore, conclude that the two interpretations cannot be distinguished with the available data, and either can be correct. According to the 3L1S solution, the lens is a planetary system with two sub-Jovian-mass planets in which the planets have masses of 0.32--0.47~$M_{\rm J}$ and 0.44--0.93~$M_{\rm J}$, and they orbit an M dwarf host. According to the 2L2S solution, on the other hand, the lens is a single planet system with a mass of $\sim 0.21~M_{\rm J}$ orbiting a late K-dwarf host, and the source is a binary composed of a primary of a subgiant or a turnoff star and a secondary of a late G dwarf. The distance to the planetary system varies depending on the solution: $\sim 7.0$~kpc according to the 3L1S solution and $\sim 6.6$~kpc according to the 2L2S solution.

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arXiv2022

KMT-2021-BLG-1898: Planetary microlensing event involved with binary source stars

The light curve of the microlensing event KMT-2021-BLG-1898 exhibits a short-term central anomaly with double-bump features that cannot be explained by the usual binary-lens or binary-source interpretations. With the aim of interpreting the anomaly, we analyze the lensing light curve under various sophisticated models. We find that the anomaly is explained by a model, in which both the lens and source are binaries (2L2S model). For this interpretation, the lens is a planetary system with a planet/host mass ratio of $q\sim 1.5\times 10^{-3}$, and the source is a binary composed of a turn off or a subgiant star and a mid K dwarf. The double-bump feature of the anomaly can also be depicted by a triple-lens model (3L1S model), in which the lens is a planetary system containing two planets. Among the two interpretations, the 2L2S model is favored over the 3L1S model not only because it yields a better fit to the data, by $Δχ^2=[14.3$--18.5], but also the Einstein radii derived independently from the two stars of the binary source result in consistent values. According to the 2L2S interpretation, KMT-2021-BLG-1898 is the third planetary lensing event occurring on a binary stellar system, following MOA-2010-BLG-117 and KMT-2018-BLG-1743. Under the 2L2S interpretation, we identify two solutions resulting from the close-wide degeneracy in determining the planet-host separation. From a Bayesian analysis, we estimate that the planet has a mass of $\sim 0.7$--0.8~$M_{\rm J}$, and it orbits an early M dwarf host with a mass of $\sim 0.5~M_\odot$. The projected planet-host separation is $\sim 1.9$~AU and $\sim 3.0$~AU according to the close and wide solutions, respectively.

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arXiv2022

Systematic KMTNet Planetary Anomaly Search. V. Complete Sample of 2018 Prime-Field

We complete the analysis of all 2018 prime-field microlensing planets identified by the KMTNet AnomalyFinder. Among the 10 previously unpublished events with clear planetary solutions, 8 are either unambiguously planetary or are very likely to be planetary in nature: OGLE-2018-BLG-1126, KMT-2018-BLG-2004, OGLE-2018-BLG-1647, OGLE-2018-BLG-1367, OGLE-2018-BLG-1544, OGLE-2018-BLG-0932, OGLE-2018-BLG-1212, and KMT-2018-BLG-2718. Combined with the 4 previously published new AnomalyFinder events and 12 previously published (or in preparation) planets that were discovered by eye, thismakes a total of 24 2018 prime-field planets discovered or recovered by AnomalyFinder. Together with a paper in preparation on 2018 sub-prime planets, this work lays the basis for the first statistical analysis of the planet mass-ratio function based on planets identified in KMTNet data. By systematically applying the heuristic analysis of Hwang et al. (2022) to each event, we identify the small modification in their formalism that is needed to unify the so-called close/wide and inner/outer degeneracies, as conjectured by

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arXiv2022

Free-Floating Planets, the Einstein Desert, and 'Oumuamua

We complete the survey for finite-source/point-lens (FSPL) giant-source events in 2016-2019 KMTNet microlensing data. The 30 FSPL events show a clear gap in Einstein radius, $9\,μ{\rm as}<θ_{\rm E} <26\,μ{\rm as}$, which is consistent with the gap in Einstein timescales near $t_{\rm E}\sim 0.5\,$days found by Mroz et al. (2017) in an independent sample of point-source/point-lens (PSPL) events. We demonstrate that the two surveys are consistent. We estimate that the 4 events below this gap are due to a power-law distribution of free-floating planet candidates (FFPs) $dN_{\rm FFP}/d\log M = (0.4\pm 0.2)\,(M/38 M_\oplus)^{-p}$/star, with $0.9\lesssim p \lesssim 1.2$. There are substantially more FFPs than known bound planets, implying that the bound planet power-law index $γ=0.6$ is likely shaped by the ejection process at least as much as by formation. The mass density per decade of FFPs in the Solar neighborhood is of the same order as that of 'Oumuamua-like objects. In particular, if we assume that 'Oumuamua is part of the same process that ejected the FFPs to very wide or unbound orbits, the power-law index is $p=0.92\pm 0.06$. If the Solar System's endowment of Neptune-mass objects in Neptune-like orbits is typical, which is consistent with the results of Poleski et al. (2021), then these could account for a substantial fraction of the FFPs in the Neptune-mass range.

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arXiv2022

KMT-2021-BLG-1077L: The fifth confirmed multiplanetary system detected by microlensing

The high-magnification microlensing event KMT-2021-BLG-1077 exhibits a subtle and complex anomaly pattern in the region around the peak. We analyze the lensing light curve of the event with the aim of revealing the nature of the anomaly. We test various models in combination with several interpretations. We find that the anomaly cannot be explained by the usual three-body (2L1S and 1L2S) models. The 2L2S model improves the fit compared to the three-body models, but it still leaves noticeable residuals. On the other hand, the 3L1S interpretation yields a model explaining all the major anomalous features in the lensing light curve. According to the 3L1S interpretation, the estimated mass ratios of the lens companions to the primary are $\sim 1.56 \times 10^{-3}$ and $\sim 1.75 \times 10^{-3}$, which correspond to $\sim 1.6$ and $\sim 1.8$ times the Jupiter/Sun mass ratio, respectively, and therefore the lens is a multiplanetary system containing two giant planets. With the constraints of the event time-scale and angular Einstein radius, it is found that the host of the lens system is a low-mass star of mid-to-late M spectral type with a mass of $M_{\rm h} = 0.14^{+0.19}_{-0.07}~M_\odot$, and it hosts two gas giant planets with masses of $M_{\rm p_1}=0.22^{+0.31}_{-0.12}~M_{\rm J}$ and $M_{\rm p_2}=0.25^{+0.35}_{-0.13}~M_{\rm J}$. The planets lie beyond the snow line of the host with projected separations of $a_{\perp, {\rm p}_1}=1.26^{+1.41}_{-1.08}~{\rm AU}$ and $a_{\perp, {\rm p}_2}=0.93^{+1.05}_{-0.80}~{\rm AU}$. The planetary system resides in the Galactic bulge at a distance of $D_{\rm L}=8.24^{+1.02}_{-1.16}~{\rm kpc}$. The lens of the event is the fifth confirmed multiplanetary system detected by microlensing following OGLE-2006-BLG-109L, OGLE-2012-BLG-0026L, OGLE-2018-BLG-1011L, and OGLE-2019-BLG-0468L.

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arXiv2022

The COS Legacy Archive Spectroscopy SurveY (CLASSY) Treasury Atlas

Far-ultraviolet (FUV; ~1200-2000 angstroms) spectra are fundamental to our understanding of star-forming galaxies, providing a unique window on massive stellar populations, chemical evolution, feedback processes, and reionization. The launch of JWST will soon usher in a new era, pushing the UV spectroscopic frontier to higher redshifts than ever before, however, its success hinges on a comprehensive understanding of the massive star populations and gas conditions that power the observed UV spectral features. This requires a level of detail that is only possible with a combination of ample wavelength coverage, signal-to-noise, spectral-resolution, and sample diversity that has not yet been achieved by any FUV spectral database. We present the COS Legacy Spectroscopic SurveY (CLASSY) treasury and its first high level science product, the CLASSY atlas. CLASSY builds on the HST archive to construct the first high-quality (S/N_1500 >~ 5/resel), high-resolution (R~15,000) FUV spectral database of 45 nearby (0.002 < z < 0.182) star-forming galaxies. The CLASSY atlas, available to the public via the CLASSY website, is the result of optimally extracting and coadding 170 archival+new spectra from 312 orbits of HST observations. The CLASSY sample covers a broad range of properties including stellar mass (6.2 < logM_star(M_sol) < 10.1), star formation rate (-2.0 < log SFR (M_sol/yr) < +1.6), direct gas-phase metallicity (7.0 < 12+log(O/H) < 8.8), ionization (0.5 < O_32 < 38.0), reddening (0.02 < E(B-V < 0.67), and nebular density (10 < n_e (cm^-3) < 1120). CLASSY is biased to UV-bright star-forming galaxies, resulting in a sample that is consistent with z~0 mass-metallicity relationship, but is offset to higher SFRs by roughly 2 dex, similar to z >~2 galaxies. This unique set of properties makes the CLASSY atlas the benchmark training set for star-forming galaxies across cosmic time.

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arXiv2022

OGLE-2016-BLG-1093Lb: A Sub-Jupiter-mass Spitzer Planet Located in Galactic Bulge

OGLE-2016-BLG-1093 is a planetary microlensing event that is part of the statistical $Spitzer$ microlens parallax sample. The precise measurement of the microlens parallax effect for this event, combined with the measurement of finite source effects, leads to a direct measurement of the lens masses and system distance: $M_{\rm host} = 0.38$--$0.57\, M_{\odot}$, $m_p = 0.59$--$0.87\, M_{\rm Jup}$, and the system is located at the Galactic bulge ($D_L \sim 8.1$ kpc). Because this was a high-magnification event, we are also able to empirically show that the "cheap-space parallax" concept Gould & Yee (2012) produces well-constrained (and consistent) results for $|π_{\rm E}|$. This demonstrates that this concept can be extended to many two-body lenses. Finally, we briefly explore systematics in the $Spitzer$ light curve in this event and show that their potential impact is strongly mitigated by the color-constraint.

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arXiv2021

Systematic KMTNet Planetary Anomaly Search, Paper III: One Wide-Orbit Planet And Two Stellar Binaries

Only a few wide-orbit planets around old stars have been detected, which limits our statistical understanding of this planet population. Following the systematic search for planetary anomalies in microlensing events found by the Korea Microlensing Telescope Network (KMTNet), we present the discovery and analysis of three events that were initially thought to contain wide-orbit planets. The anomalous feature in the light curve of OGLE-2018-BLG-0383 is caused by a planet with mass ratio $q=2.1\times 10^{-4}$ and a projected separation $s=2.45$. This makes it the lowest mass-ratio microlensing planet at such wide orbits. The other two events, KMT-2018-BLG-0998 and OGLE-2018-BLG-0271, are shown to be stellar binaries ($q>0.1$) with rather close ($s<1$) separations. We briefly discuss the properties of known wide-orbit microlensing planets and show that the survey observations are crucial in discovering and further statistically constraining such a planet population.

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arXiv2021

KMT-2018-BLG-1988Lb: microlensing super-Earth orbiting a low-mass disk dwarf

We reexamine high-magnification microlensing events in the previous data collected by the KMTNet survey with the aim of finding planetary signals that were not noticed before. In this work, we report the planetary system KMT-2018-BLG-1988L that was found from this investigation. The planetary signal appears as a deviation with $\lesssim 0.2$~mag from a single-lens light curve and lasted for about 6 hours. The deviation exhibits a pattern of a dip surrounded by weak bumps on both sides of the dip. The analysis of the lensing light curve indicates that the signal is produced by a low mass-ratio ($q\sim 4\times 10^{-5}$) planetary companion located near the Einstein ring of the host star. The mass of the planet, $M_{\rm planet}=6.8^{+4.7}_{-3.5}~M_\oplus$ and $5.6^{+3.8}_{-2.8}~M_\oplus$ for the two possible solutions, estimated from the Bayesian analysis indicates that the planet is in the regime of a super-Earth. The host of the planet is a disk star with a mass of $M_{\rm host} = 0.47^{+0.33}_{-0.25}~M_\odot$ and a distance of $D_{\rm L}= 4.2^{+1.8}_{-.14}$~kpc. KMT-2018-BLG-1988Lb is the seventeenth microlensing planet with a mass below the upper limit of a super-Earth. The fact that 14 out of 17 microlensing planets with masses $\lesssim 10~M_\oplus$ were detected during the last 5 years since the full operation of the KMTNet survey indicates that the KMTNet database is an important reservoir of very low-mass planets.

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arXiv2021

KMT-2021-BLG-0912Lb: A microlensing super Earth around a K-type star

The light curve of the microlensing event KMT-2021-BLG-0912 exhibits a very short anomaly relative to a single-lens single-source form. We investigate the light curve for the purpose of identifying the origin of the anomaly. We model the light curve under various interpretations. From this, we find four solutions, in which three solutions are found under the assumption that the lens is composed of two masses (2L1S models), and the other solution is found under the assumption that the source is comprised of a binary-star system (1L2S model). The 1L2S model is ruled out based on the contradiction that the faint source companion is bigger than its primary, and one of the 2L1S solutions is excluded from the combination of the relatively worse fit, blending constraint, and lower overall probability, leaving two surviving solutions with the planet/host mass ratios of $q\sim 2.8\times 10^{-5}$ and $\sim 1.1\times 10^{-5}$. A subtle central deviation supports the possibility of a tertiary lens component, either a binary companion to the host with a very large or small separation or a second planet lying near the Einstein ring, but it is difficult to claim a secure detection due to the marginal fit improvement, lack of consistency among different data sets, and difficulty in uniquely specifying the nature of the tertiary component. With the observables of the event, it is estimated that the masses of the planet and host are $\sim (6.9~M_\oplus, 0.75~M_\odot)$ according to one solution and $\sim (2.8~M_\oplus, 0.80~M_\odot)$ according to the other solution, indicating that the planet is a super Earth around a K-type star, regardless of the solution.

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arXiv2021

OGLE-2019-BLG-0468Lb,c: two microlensing giant planets around a G-type star

With the aim of interpreting anomalous lensing events with no suggested models, we conducted a project of reinvestigating microlensing data in and before the 2019 season. In this work, we report a multi-planet system OGLE-2019-BLG-0468L found from the project. The light curve of the lensing event OGLE-2019-BLG-0468, which consists of three distinctive anomaly features, could not be explained by the usual binary-lens or binary-source interpretation. We find a solution explaining all anomaly features with a triple-lens interpretation, in which the lens is composed of two planets and their host, making the lens the fourth multi-planet system securely found by microlensing. The two planets have masses $\sim 3.4~M_{\rm J}$ and $\sim 10.2~M_{\rm J}$, and they are orbiting around a G-type star with a mass $\sim 0.9~M_\odot$ and a distance $\sim 4.4$ kpc. The host of the planets is most likely responsible for the light of the baseline object, although the possibility for the host to be a companion to the baseline object cannot be ruled out.

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arXiv2021

Systematic KMTNet Planetary Anomaly Search, Paper II: Six New $q<2\times 10^{-4}$ Mass-ratio Planets

We apply the automated AnomalyFinder algorithm of Paper I (Zang et al. 2021b) to 2018-2019 light curves from the $\simeq 13\,{\rm deg}^2$ covered by the six KMTNet prime fields, with cadences $Γ\geq 2\,{\rm hr}^{-1}$. We find a total of 11 planets with mass ratios $q<2\times 10^{-4}$, including six newly discovered planets, one planet that was reported in Paper I, and recovery of four previously discovered planets. One of the new planets, OGLE-2018-BLG-0977Lb, is in a planetary-caustic event, while the other five (OGLE-2018-BLG-0506Lb, OGLE-2018-BLG-0516Lb, OGLE-2019-BLG-1492Lb, KMT-2019-BLG-0253, and KMT-2019-BLG-0953) are revealed by a "dip" in the light curve as the source crosses the host-planet axis on the opposite side of the planet. These subtle signals were missed in previous by-eye searches. The planet-host separations (scaled to the Einstein radius), $s$, and planet-host mass ratios, $q$, are, respectively, $(s,q\times 10^5) = (0.88, 4.1)$, $(0.96\pm 0.10, 8.3)$, $(0.94\pm 0.07, 13)$, $(0.97\pm 0.07, 18)$, $(0.97\pm0.04,4.1)$, and $(0.74,18)$, where the "$\pm$" indicates a discrete degeneracy. The 11 planets are spread out over the range $-5<\log q < -3.7$. Together with the two planets previously reported with $q\sim 10^{-5}$ from the 2018-2019 non-prime KMT fields, this result suggests that planets toward the bottom of this mass-ratio range may be more common than previously believed.

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arXiv2021

Using Source Proper Motion to Validate Terrestrial Parallax: OGLE-2019-BLG-1058

We show that because the conditions for producing terrestrial microlens parallax (TPRX; i.e., a nearby disk lens) will also tend to produce a large lens-source relative proper motion ($μ_{\rm rel}$), source proper motion (${\boldsymbolμ}_{\rm S}$) measurements in general provide a strong test of TPRX signals, which \citet{gould13} showed were an important probe of free-floating planet (FFP) candidates. As a case study, we report a single-lens/single-source microlensing event designated as OGLE-2019-BLG-1058. For this event, the short timescale ($\sim 2.5$ days) and very fast $μ_{\rm rel}$ ($\sim 17.6\, {\rm mas\, yr^{-1}}$) suggest that this isolated lens is an FFP candidate located in the disk of our Galaxy. For this event, we find a TPRX signal consistent with a disk FFP, but at low significance. A direct measurement of the ${\boldsymbolμ}_{\rm S}$ shows that the large $μ_{\rm rel}$ is due to an extreme ${\boldsymbolμ}_{\rm S}$, and thus, the lens is consistent with being a very low-mass star in the bulge and the TPRX measurement is likely spurious. By contrast, we show how a precise measurement of ${\boldsymbolμ}_{\rm S}$ with the mean properties of the bulge proper motion distribution would have given the opposite result; i.e., provided supporting evidence for an FFP in the disk and the TPRX measurement.

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arXiv2021

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

We conducted a project of reinvestigating the 2017--2019 microlensing data collected by the high-cadence surveys with the aim of finding planets that were missed due to the deviations of planetary signals from the typical form of short-term anomalies. The project led us to find three planets including KMT-2017-BLG-2509Lb, OGLE-2017-BLG-1099Lb, and OGLE-2019-BLG-0299Lb. The lensing light curves of the events have a common characteristic 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 host stars. For all planetary events, the lensing solutions are uniquely determined without any degeneracy. It is estimated that the host masses 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 $2.1\lesssim M/M_{\rm J}\lesssim 6.2$, are heavier than the heaviest planet of the solar system, that is, Jupiter. The planets in all systems lie beyond the snow lines of the hosts, and thus the discovered planetary systems, together with many other microlensing planetary systems, support that massive gas-giant planets are commonplace around low-mass stars. We discuss the role of late-time high-resolution imaging in clarifying resonant-image lenses with very faint sources.

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