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We investigate the nature of the short-term anomaly that appears in the lensing light curve of KMT-2023-BLG-1866. The anomaly was only partly covered due to its short duration, less than a day, coupled with cloudy weather conditions and restricted nighttime duration. Considering intricacy of interpreting partially covered signals, we thoroughly explore all potential degenerate solutions. Through this process, we identify three planetary scenarios that equally well account for the observed anomaly. These scenarios are characterized by the specific planetary parameters: \\((s, q)_{\\rm inner} = [0.9740 \\pm 0.0083, (2.46 \\pm 1.07) \\times 10^{-5}]\\), \\((s, q)_{\\rm intermediate} = [0.9779 \\pm 0.0017, (1.56 \\pm 0.25)\\times 10^{-5}]\\), and \\((s, q)_{\\rm outer} = [0.9894 \\pm 0.0107, (2.31 \\pm 1.29)\\times 10^{-5}]\\), where \\(s\\) and \\(q\\) denote the projected separation (scaled to the Einstein radius) and mass ratio between the planet and its host, respectively. We identify that the ambiguity between the inner and outer solutions stems from the inner-outer degeneracy, while the similarity between the intermediate solution and the others is due to an accidental degeneracy caused by incomplete anomaly coverage. Through Bayesian analysis utilizing the constraints derived from measured lensing observables and blending flux, our estimation indicates that the lens system comprises a very low-mass planet orbiting an early M-type star situated approximately (6.2 -- 6.5)~kpc from Earth in terms of median posterior values for the different solutions. The median mass of the planet host is in the range of (0.48 -- 0.51)~\\(M_\\odot\\), and that of the planet's mass spans a range of (2.6 -- 4.0)~\\(M_{\\rm E}\\), varying across different solutions. The detection of KMT-2023-BLG-1866Lb signifies the extension of the lensing surveys to very low-mass planets that have been difficult to be detected from earlier surveys.

We report the discoveries of low-mass free-floating planet (FFP) candidates from the analysis of 2006-2014 MOA-II Galactic bulge survey data. In this dataset, we found 6,111 microlensing candidates and identified a statistical sample consisting of 3,535 high quality single lens events with Einstein radius crossing times in the range \\(0.057 < t_{\\rm E}/{\\rm days} < 757\\), including 13 events that show clear finite source effects with angular Einstein radii of \\(0.90<\\theta_{\\rm E}/{\\rm \\mu as} <332.54\\). Two of the 12 events with \\(t_{\\rm E} < 1\\) day have significant finite source effects, and one event, MOA-9y-5919, with \\(t_{\\rm E}=0.057\\pm 0.016\\) days and \\(\\theta_{\\rm E}= 0.90 \\pm 0.14\\) \\(\\mu\\)as, is the second terrestrial mass FFP candidate to date. A Bayesian analysis indicates a lens mass of \\(0.75^{+1.23}_{-0.46}\\) \\(M_\\oplus\\) for this event. The low detection efficiency for short duration events implies a large population of low-mass FFPs. The microlensing detection efficiency for low-mass planet events depends on both the Einstein radius crossing times and the angular Einstein radii, so we have used image-level simulations to determine the detection efficiency dependence on both \\(t_{\\rm E}\\) and \\(\\theta_{\\rm E}\\). This allows us to use a Galactic model to simulate the \\(t_{\\rm E}\\) and \\(\\theta_{\\rm E}\\) distribution of events produced by the known stellar populations and models of the FFP distribution that are fit to the data. Methods like this will be needed for the more precise FFP demographics determinations from Nancy Grace Roman Space Telescope data.

We carried out a project involving the systematic analysis of microlensing data from the Korea Microlensing Telescope Network survey. The aim of this project is to identify lensing events with complex anomaly features that are difficult to explain using standard binary-lens or binary-source models. Our investigation reveals that the light curves of microlensing events KMT-2021-BLG-0284, KMT-2022-BLG-2480, and KMT-2024-BLG-0412 display highly complex patterns with three or more anomaly features. These features cannot be adequately explained by a binary-lens (2L1S) model alone. However, the 2L1S model can effectively describe certain segments of the light curve. By incorporating an additional source into the modeling, we identified a comprehensive model that accounts for all the observed anomaly features. Bayesian analysis, based on constraints provided by lensing observables, indicates that the lenses of KMT-2021-BLG-0284 and KMT-2024-BLG-0412 are binary systems composed of M dwarfs. For KMT-2022-BLG-2480, the primary lens is an early K-type main-sequence star with an M dwarf companion. The lenses of KMT-2021-BLG-0284 and KMT-2024-BLG-0412 are likely located in the bulge, whereas the lens of KMT-2022-BLG-2480 is more likely situated in the disk. In all events, the binary stars of the sources have similar magnitudes due to a detection bias favoring binary source events with a relatively bright secondary source star, which increases detection efficiency.

We present the analysis of microlensing event OGLE-2014-BLG-0221, a planetary candidate event discovered in 2014. The photometric light curve is best described by a binary-lens single-source model. Our light curve modeling finds two degenerate models, with event timescales of \\(t_\\mathrm{E}\\sim70\\) days and \\(\\sim110\\) days. These timescales are relatively long, indicating that the discovered system would possess a substantial mass. The two models are similar in their planetary parameters with a Jupiter mass ratio of \\(q \\sim 10^{-3}\\) and a separation of \\(s \\sim 1.1\\). While the shorter timescale model shows marginal detection of a microlensing parallax signal, the longer timescale model requires a higher order effect of microlensing parallax, lens orbital motion or xallarap to explain the deviation in the light curve. However, the modeling shows significant correlation between the higher order effects and suffers the ecliptic degeneracy that results in a failure to determine the parallax parameters. Bayesian inference is used to estimate the physical parameters of the lens, revealing the lens to be either a late-type star supported by the shorter timescale model or a stellar remnant supported by the longer timescale model. If the lens is a remnant, this would be the second planet found by microlensing around a stellar remnant. Since the models predict different values for relative proper motion and source flux, future high angular resolution follow-up observations (e.g. Keck adaptive optics) are required to rule out either of the models.