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±0.13)×10 −5 . A Bayesian analysis yields estimates of the mass of the host star, M host = 0.61 +0.29 −0.24 M , the mass of its planet, M planet = 2.48 +1.19 −0.98 M ⊕ , the projected planet-host separation, a ⊥ = 3.4 +0.5 −0.5 au, and the lens distance of D L = 6.8 +0.6 −0.9 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 ∼ 10 −5 .

We apply the automated AnomalyFinder algorithm of Paper I to 2018–2019 light curves from the ≃13 deg2 covered by the six KMTNet prime fields, with cadences Γ ≥ 2 hr−1. We find a total of 11 planets with mass ratios q < 2 × 10−4, including 6 newly discovered planets, 1 planet that was reported in Paper I, and recovery of 4 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 × 105) = (0.88, 4.1), (0.96 ± 0.10, 8.3), (0.94 ± 0.07, 13), (0.97 ± 0.07, 18), (0.97 ± 0.04, 4.1), and (0.74, 18), where the “ ± ” 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 ∼ 10−5 from the 2018–2019 nonprime KMT fields, this result suggests that planets toward the bottom of this mass-ratio range may be more common than previously believed.

We report the analysis of OGLE-2019-BLG-0960, which contains the smallest mass-ratio microlensing planet found to date (q = 1.2–1.6 × 10−5 at 1σ). Although there is substantial uncertainty in the satellite parallax measured by Spitzer, the measurement of the annual parallax effect combined with the finite source effect allows us to determine the mass of the host star (M L = 0.3–0.6 M ⊙), the mass of its planet (m p = 1.4–3.1 M ⊕), the projected separation between the host and planet (a ⊥ = 1.2–2.3 au), and the distance to the lens system (D L = 0.6–1.2 kpc). The lens is plausibly the blend, which could be checked with adaptive optics observations. As the smallest planet clearly below the break in the mass-ratio function, it demonstrates that current experiments are powerful enough to robustly measure the slope of the mass-ratio function below that break. We find that the cross-section for detecting small planets is maximized for planets with separations just outside of the boundary for resonant caustics and that sensitivity to such planets can be maximized by intensively monitoring events whenever they are magnified by a factor A > 5. Finally, an empirical investigation demonstrates that most planets showing a degeneracy between (s > 1) and (s < 1) solutions are not in the regime ( ∣ log s ∣ ≫ 0 ) for which the “close”/“wide” degeneracy was derived. This investigation suggests that there is a link between the “close”/“wide” and “inner/outer” degeneracies and also that the symmetry in the lens equation goes much deeper than symmetries uncovered for the limiting cases.

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 observations more uniform and efficient, we develop a system, HighMagFinder, to automatically alert possible ongoing high-magnification events based on the real-time data from the Korea Microlensing Telescope Network (KMTNet). 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 ∼ 4.7 × 10−5 or q ∼ 2.2 × 10−5 for KMT-2021-BLG-0171, and q ∼ 2.5 × 10−4 or q ∼ 1.8 × 10−4 for KMT-2021-BLG-1689. Together with two other events, 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 quantitative factor to weight 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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