Systematic KMTNet Planetary Anomaly Search. IX. Complete Sample of 2016 Prime- field Planets In-Gu Shin1 , Jennifer C. Yee1 , Weicheng Zang1,2 , Hongjing Yang2 , Kyu-Ha Hwang3 , Cheongho Han4 , Andrew Gould5,6, Andrzej Udalski7 , Ian A. Bond8 (Leading authors), Michael D. Albrow9 , Sun-Ju Chung3 , Youn Kil Jung3,10, Yoon-Hyun Ryu3 , Yossi Shvartzvald11 , Sang-Mok Cha3,12, Dong-Jin Kim3, Seung-Lee Kim3 , Chung-Uk Lee3 , Dong-Joo Lee3, Yongseok Lee3,12, Byeong-Gon Park3 , Richard W. Pogge6 (The KMTNet Collaboration), Przemek Mróz7, Michał K. Szymański7 , Jan Skowron7 , Radosław Poleski7 , Igor Soszyński7 , Paweł Pietrukowicz7 , Szymon Kozłowski7 , Krzysztof A. Rybicki7,11, Patryk Iwanek7 , Krzysztof Ulaczyk13 , Marcin Wrona7 , Mariusz Gromadzki7 (The OGLE Collaboration), and Fumio Abe14, Richard Barry15 , David P. Bennett15,16 , Aparna Bhattacharya15,16, Hirosane Fujii14, Akihiko Fukui17,18 , Ryusei Hamada19, Yuki Hirao19 , Stela Ishitani Silva15,20, Yoshitaka Itow14 , Rintaro Kirikawa19, Iona Kondo19 , Naoki Koshimoto21 , Yutaka Matsubara14 , Shota Miyazaki19 , Yasushi Muraki14 , Greg Olmschenk15 , Clément Ranc22 , Nicholas J. Rattenbury23 , Yuki Satoh19 , Takahiro Sumi19 , Daisuke Suzuki19 , Mio Tomoyoshi19, Paul J. Tristram24, Aikaterini Vandorou15,16, Hibiki Yama19, and Kansuke Yamashita19 (the MOACollaboration) 1 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA; ingushin@gmail.com 2 Department of Astronomy, Tsinghua University, Beijing 100084, Peopleʼs Republic of China 3 Korea Astronomy and Space Science Institute, Daejon 34055, Republic of Korea 4 Department of Physics, Chungbuk National University, Cheongju 28644, Republic of Korea 5 Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany 6 Department of Astronomy, The Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210, USA 7 Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland 8 Institute of Natural and Mathematical Sciences, Massey University, Auckland 0745, New Zealand 9 University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand 10 University of Science and Technology, Korea, (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea 11 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel 12 School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Republic of Korea 13 Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK 14 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 464-8601, Japan 15 NASA Goddard Space Flight Center, Code 667, Greenbelt, MD 20771, USA 16 Department of Astronomy, University of Maryland, College Park, MD 20742, USA 17 Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 18 Instituto de Astrofísica de Canarias, Vía Láctea s/n, E-38205 La Laguna, Tenerife, Spain 19 Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan 20 Department of Physics, The Catholic University of America, Washington, DC 20064, USA 21 Department of Astronomy, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 22 Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, F-75014 Paris, France 23 Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand 24 University of Canterbury Mt. John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand Received 2023 March 29; revised 2023 May 30; accepted 2023 July 19; published 2023 August 14 Abstract As a part of the “Systematic KMTNet Planetary Anomaly Search” series, we report five new planets (namely, OGLE- 2016-BLG-1635Lb, MOA-2016-BLG-532Lb, KMT-2016-BLG-0625Lb, OGLE-2016-BLG-1850Lb, and KMT-2016- BLG-1751Lb) and one planet candidate (KMT-2016-BLG-1855), which were found by searching 2016 KMTNet prime fields. These buried planets show a wide range of masses from Earth-class to super-Jupiter-class and are located in both the disk and the bulge. The ultimate goal of this series is to build a complete planet sample. Because our work provides a complementary sample to other planet detection methods, which have different detection sensitivities, our complete sample will help us to obtain a better understanding of planet demographics in our Galaxy. Unified Astronomy Thesaurus concepts: Gravitational microlensing exoplanet detection (2147) The Astronomical Journal, 166:104 (26pp), 2023 September https://doi.org/10.3847/1538-3881/ace96d © 2023. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. 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Introduction To build a complete microlensing planet sample, we conduct a series of works called “Systematic KMTNet Planetary Anomaly Search” based on a large microlensing survey archive obtained by the Korea Microlensing Telescope Network (KMTNet; Kim et al. 2016). We identify planet-like anomalies using the “Anomaly- Finder” algorithm (Zang et al. 2021, 2022a) instead of a traditional “by-eye” method, which can systematically identify almost all candidates showing anomalies on the light curve.25 However, to reveal the origin of the anomaly requires (preliminary) models, including possible degenerate solutions to figure out the mass ratio of the lens component (i.e., q). Also, it requires investigating the data for the anomaly to check whether or not the anomaly is caused by a false-positive signal. Thus, detailed analyses for all anomalous events found by the AnomalyFinder require significant resources and human efforts. Hence, for the KMTNet data obtained from 2016 to 2021, we conduct the work separately for each bulge season and for observing fields with different cadences, which are divided into prime (high cadence; Γ= 2.0–4.0 hr−1) and subprime (low cadence; Γ= 0.2–1.0 hr−1) fields. The KMTNet field informa- tion is described in Kim et al. (2018). Gould et al. (2022) introduced the systematic analysis of AnomalyFinder candi- dates. We have already done the systematic searches for the 2018 prime field (Gould et al. 2022; Hwang et al. 2022; Wang et al. 2022), 2018 subprime fields (Jung et al. 2022), 2019 prime fields (Zang et al. 2021, 2022a; Hwang et al. 2022), and 2019 subprime fields (Jung et al. 2023). In addition, Zang et al. (2023) presented a complete sample of planets with the mass ratio q< 10−4 discovered from all candidate events observed from 2016 to 2019. This is the ninth work to build the complete sample, which is conducted for the 2016 prime fields (i.e., BLG01, BLG41, BLG02, BLG42, BLG03, and BLG43). The AnomalyFinder algorithm and candidate review identified 106 anomalous events (plus 14 events that were already published). Based on visual inspection and/or preliminary modeling, 79 were eliminated as binaries. For the remaining 13 new candidates with at least one solution with q< 0.06, we re-reduce the photometry to check for/remove the systematics in the data sets. Based on further analysis with the best-quality data sets, seven were eliminated because they had no reliable planetary solutions (i.e., q< 0.03)26 with Δχ2< 10.0. We also investi- gate one additional 2016 prime-field event for the detailed analysis, which was identified using the by-eye method and reported as a planet-like event but was not in the final AnomalyFinder candidate list (see Appendix B). Then, we find five new planets and one planet candidate based on detailed analyses: OGLE-2016-BLG-1635Lb, MOA-2016-BLG-532Lb, KMT-2016-BLG-0625Lb, OGLE-2016-BLG-1850Lb, KMT- 2016-BLG-1751Lb, and KMT-2016-BLG-1855. We note that these planetary systems are designated by the survey projects that first announced the events, as is traditional, even though the planetary systems were discovered based on the systematic search using the KMTNet data archive. We describe the observations of each survey in Section 2. Then, we describe the light-curve analysis for the planet candidates in Section 3. We note that, for the nine nonplanetary events, we report the analysis results in Appendix A for the record. In Section 4, we present analyses for the color–magnitude diagrams (CMDs) of the five planetary events. In Section 5, we present the properties of the planetary systems determined based on the Bayesian analyses. Lastly, we summarize the results of this work in Section 6. 2. Observations In Tables 1 and 2 (see Appendix A), we present observational information for the anomalous events, which have at least one solution with q< 0.06 found from preliminary modeling. For the anomalous events, we gather all available data taken from microlensing surveys for preliminary model- ing. The KMTNet pipeline data are available from the KMTNet Alert System (Kim et al. 2018; https://kmtnet.kasi. re.kr/~ulens/). They were obtained using three identical 1.6 m telescopes equipped with wide-field (4 deg2) cameras. The telescopes are located at the Cerro Tololo Inter-American Observatory in Chile (KMTC), the South African Astronomical Observatory in South Africa (KMTS), and the Siding Spring Observatory in Australia (KMTA), which are in well-separated time zones to achieve near-continuous observations. Thus, the prime fields of the KMTNet have high cadences (Γ� 2 hr−1) in the I band (Johnson–Cousins BVRI filter system). Also, for the KMTC observations, KMTNet regularly takes one observation in the V band for every 10th I-band observation. We note that, for the KMTS observations, it takes one V-band observation for every 20th I-band observation. The Optical Gravitational Lensing Experiment (OGLE; Udalski 2003; Udalski et al. 2015) data are available from the OGLE Early Warning System (Udalski et al. 1994; http:// ogle.astrouw.edu.pl/ogle4/ews/ews.html) and were obtained using the 1.3 m Warsaw telescope with a 1.4 deg2 camera located at Las Campanas Observatory in Chile. The OGLE observations were mainly made in the I band. Also, they periodically observe in the V band. The Microlensing Observations in Astrophysics (MOA; Bond et al. 2001; Sumi et al. 2003) data are available on their alert system website (http://www.massey.ac.nz/~iabond/ moa/alerts/) and were obtained using a 1.8 m telescope located at Mt. John University Observatory in New Zealand. The MOA observations were taken using the MOA-Red filter (hereafter referred to as the R band), which is roughly the sum of the Cousins R and I bands (wavelength ranges: 609–1109 nm; transmission ranges: 0.0–0.978). The data of each survey were reduced by their own pipelines (KMTNet, Albrow et al. 2009; OGLE, Wozniak 2000; and MOA, Bond et al. 2001), which adopt/modify the difference image analysis technique (Tomaney & Crotts 1996; Alard & Lupton 1998). We note that, for the planet-like events listed in Tables 1 and 2, the KMTNet data are re-reduced using an optimized version of pySIS (H. Yang et al. 2023, in preparation) to obtain the best-quality data sets (hereafter tender loving care, TLC, reductions) for the analyses. Also, we reduce the V-band data to determine the source color using the 25 Although the AnomalyFinder detects anomalies using criteria optimized to the KMTNet data, some anomalous events can be omitted because the criteria are not yet perfect. For example, AnomalyFinder missed KMT-2021-BLG- 2294Lb (Shin et al. 2023). Thus, the by-eye method can help us to improve the criteria and understand the completeness of the final planet sample. 26 The threshold of q < 0.03 as the definition of a planet is somewhat arbitrary, but no more so than a mass threshold of Mplanet < 13 MJup. Note that for Mhost = 0.3 Me, q = 0.03 corresponds to a planet mass Mplanet ∼ 10 MJup. Considering that the majority of hosts in our Galaxy are M dwarfs, our threshold covers almost all planets (although, in some extreme cases, e.g., black hole hosts, the secondary would not be a planet). 2 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. https://kmtnet.kasi.re.kr/~ulens/ https://kmtnet.kasi.re.kr/~ulens/ http://ogle.astrouw.edu.pl/ogle4/ews/ews.html http://ogle.astrouw.edu.pl/ogle4/ews/ews.html http://www.massey.ac.nz/~iabond/moa/alerts/ http://www.massey.ac.nz/~iabond/moa/alerts/ pyDIA package (Bramich et al. 2013; Albrow 2017). We also note that some events require re-reduced data obtained from the OGLE and MOA surveys for the detailed analyses. The MOA did not alert the KMT-2016-BLG-1751 and KMT-2016-BLG- 0374 events. However, the events are located in the MOA fields. Therefore, the MOA team provided re-reduced data for these two events. Event OGLE-2016-BLG-1850 has a long baseline extending to the 2017 season. The OGLE team provided re-reduced data for this event including the long baseline. 3. Light-curve Analysis 3.1. Basics of the Analysis We conduct a detailed analysis of 13 candidates with re- reduced data sets using the optimized pySIS package (H. Yang et al. 2023, in preparation). The analysis of the five planetary events and one planet candidate is presented in this section, and the remaining seven events are briefly presented in Appendix A. We follow the methodology of the light-curve analysis described in Shin et al. (2023). We briefly describe the analysis process, which consists of two steps, to present the terminology used in this work. First, we conduct a grid search to find all possible solutions, in particular, local minima having planetary mass ratios (i.e., q 0.03). For the grid search, we start from the static 2L1S case, i.e., without motions of the lenses or source (we treat the static model as a standard (STD) model), where nLmS indicates the number of lenses (n) and sources (m), respectively. To describe a microlensing light curve, the STD model requires seven parameters (t0, u0, tE, s, q, α, and ρ*), which are respectively defined as the time at the peak of the light curve, impact parameter, Einstein timescale, projected separation between binary lens components in units of the angular Einstein radius (θE), mass ratio of the lens components (i.e., q≡Msecondary/Mprimary), angle between the source trajectory and binary axis, and angular source radius (θ*) scaled by θE (i.e., ρ*≡ θ*/θE). We set (s, q) as grid parameters for the grid search. Because these are most sensitive parameters to describe anomalies on the light curve. The ranges of (s, q) are slog 1.0, 1.010( ) [ ]Î - and qlog 5.5, 1.010( ) [ ]Î - with 100 grid points for each range. We optimize the five remaining parameters using a χ2 minimizing method called the Markov Chain Monte Carlo algorithm (Doran & Müller 2004). We note that α is treated as a semi-grid parameter because it is also sensitive to describing the anomalies; we start 21 seeds for the α parameter within the range of αä [0, 2π]. Second, once we find all plausible models, we refine the model parameters for all cases by allowing all parameters to freely vary within physically possible ranges. During this second process, we rescale the errors of the data sets based on the best-fit model to make each data point contribute χ2∼ 1.0. The error rescaling procedure is described in Yee et al. (2012). Briefly, e k e eR O 2 S 2= + , where eR is the rescaled error, k is the rescaling factor, eO is the original error, and eS is the systematics term. Based on the STD models, we consider higher-order effects if the solutions have a high chance of detecting the effects. Specifically, we first consider the annual microlens parallax (APRX) effect (Gould 1992) if the models show relatively long timescales (i.e., tE 15 days at least). Once we find the APRX effect, we also consider the lens-orbital (OBT) effect because the OBT may affect the APRX measurements. Lastly, in the cases where the APRX effect is detected, we test the “xallarap” Table 2 Observations of 2016 Nonplanetary Events Event Location Obs. Info. KMTNet OGLE MOA R.A. (J2000) Decl. (J2000) (ℓ, b) AI Γ (hr−1) 0020 0987 L 17h56m34 37 27 59 31. 99-  ¢  (+2°. 04, − 1°. 59) 1.78 4.0 0106 L 123 17h54m17 90 28 55 15. 74-  ¢  (+0°. 99, − 1°. 62) 1.72 1.0 0157 0558 L 17h57m45 40 28 20 07. 40-  ¢  (+1°. 88, − 1°. 98) 1.61 4.0 0374 L Avail. 17h54m48 45 30 59 04. 42-  ¢  (−0°. 74, − 2°. 76) 1.43 4.0 0425 0185 L 17h52m35 43 31 19 51. 60-  ¢  (−1°. 28, − 2°. 52) 2.24 4.0 0446 L L 17h51m52 02 28 50 00. 17-  ¢  (+0°. 79, − 1°. 12) 3.13 4.0 1716 1722 555 17h55m21 82 30 42 36. 90-  ¢  (−0°. 44, − 2°. 72) 1.73 4.0 1863 0974 351 18h01m23 99 27 33 20. 30-  ¢  (+2°. 95, − 2°. 29) 1.41 4.0 Note. Bold indicates the “discovery” name of each event. Table 1 Observations of 2016 Planetary Events Event Location Obs. Info. KMTNet OGLE MOA R.A. (J2000) Decl. (J2000) (ℓ, b) AI Γ (hr−1) 0269 1635 L 17h54m01 22 30 46 38. 10-  ¢  (−0°. 65, − 2°. 51) 1.82 2.0 0506 1749 532 17h57m44 18 29 06 25. 60-  ¢  (+1°. 20, − 2°. 37) 1.56 4.0 0625 L L 18h05m39 66 27 13 36. 70-  ¢  (+3°. 70, − 2°. 96) 0.95 4.0 1307 1850 L 17h52m00 18 32 12 38. 20-  ¢  (−2°. 10, − 2°. 86) 2.01 4.0 1751 L Avail. 17h53m28 62 32 09 06. 52-  ¢  (−1°. 89, − 3°. 10) 2.11 4.0 1855 L L 17h50m13 25 29 12 26. 39-  ¢  (+0°. 29, − 1°. 00) 5.97 4.0 Note. Bold indicates the “discovery” name of each event. 3 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. effect (“parallax” spelled backward; Griest & Hu 1992; Han & Gould 1997; Paczynski 1997; Poindexter et al. 2005), which reflects the accelerating orbital motion of the secondary source without its brightness contribution. Because the xallarap effect can mimic the APRX effect, the xallarap test is required to confirm the APRX measurements. From the detailed analysis, we claim the detection of planetary systems if the fiducial solutions satisfy both detection criteria: the solution(s) should have (1) q< 0.03 and (2) Δχ2< 10 compared to other nonplanetary solution(s). Lastly, we note that, to indicate the degenerate solutions that we found, we follow the unified notation of the s† formalism described in Hwang et al. (2022) and Ryu et al. (2022). Also, we can check our solutions using the formalism for validation. Here we briefly present the s† formalism for the description of each event in the following sections. The separations (s† ) caused by major and minor images (Gould & Loeb 1992) are expected as s u u4 2 , 1anom 2 anom ( )† º +   where u uanom anom 2 0 2 1 2( )t= + is the offset of the source position from the host obtained from the scaled time offset from the peak of the light curve, τanom≡ (tanom− t0)/tE. The expected s†  can be compared to the empirical results. The comparison depends on the type of anomaly shape and the number of solutions. In general, the “bump”-shaped anomaly caused by the major image perturbation should correspond to the s† + expectation, while the “dip”-shaped anomaly caused by the minor image perturbation should correspond to the s † - expectation. For the number of solutions (i.e., degenerate cases), if we have a unique solution, the empirical s should correspond to one of s† . If we have two degenerate solutions, such as s±, the empirical solutions have a relation of s s s , 2( )† = + - which should correspond to one of the s†  values. The α can also be predicted as u tan . 30 anom ( )a t = More specifically, u jtan 1 0 anom( )a t p= +- , where j= (0, 1) for (major, minor) images, and the range of tan−1 is defined as [0, π]. We note that the α expectation depends on the coordinate system of the modeling. Lastly, in the case of the dip-shaped anomaly, we can obtain the first-order approx- imation of the q values, i.e., q t t s u t t s u4 sin 4 sin . 4 dip E 2 2 anom dip E 2 0 3 ⎜ ⎟ ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ∣ ∣ ∣ ∣ ( )a a= D = D We note that the predicted q generally matches the empirical q value within a factor of ∼2. This expectation is useful for judging how valuable an event is to conduct a detailed analysis (i.e., whether or not it is a planetary event), even if the expectation could not be very accurate. The theoretical origins of the heuristic analysis and such degeneracies are described in Gaudi & Gould (1997), Griest & Safizadeh (1998), and Zhang & Gaudi (2022). 3.2. OGLE-2016-BLG-1635 The light curve of OGLE-2016-BLG-1635 (which we identified as KMT-2016-BLG-0269) exhibits a bump-shaped anomaly at HJD′ = 7,624.6. In Figure 1, we present the light curve with degenerate (i.e., s±) models. We also present the model parameters in Table 3. From a heuristic analysis, we find τanom= 0.023 and uanom= 0.036 based on tanom= 7624.60, t0= 7624.12, u0= 0.028, and tE= 21 days. As a result, we expect s 0.98† =- and s 1.02† =+ . The s † - is consistent with s†= 0.99 for our solutions. Although degenerate solutions exist, the mass ratios of both cases are less than 0.03, which implies that the companion is a planet by our formal definition. The timescale of this event is about 21 days, which implies that there is a possibility of measuring the APRX considering the empirical criterion of tE 15 days. Thus, we test the APRX models for this event. We find χ2 improvements ofΔχ2= 7.24 and 9.96 for the s− and s+ cases, respectively. The Δχ2 values are too small to claim the APRX detection. Moreover, the APRX parameters are not converged for the s− case. For the s+ case, the APRX model favors values of |πE|> 10 that are not reliable because they are caused by overfitting systematics at the baseline. Hence, we conclude that the STD models should be the fiducial solutions for OGLE-2016-BLG-1635. We can only measure the upper limits of ρ* (i.e., 3σ ranges) because the source does not cross the caustic as shown in Figure 1. 3.3. MOA-2016-BLG-532 In Figure 2, we present the light curve of MOA-2016-BLG- 532 (which we identified as KMT-2016-BLG-0506), which shows a clear deviation from the 1L1S model with a finite source. Although the anomaly is neither obviously bump- shaped nor dip-shaped, we find that the heuristic analysis is valid. It yields τanom= −0.032 and uanom= 0.034 from tanom= 7636.20 and tE= 21 days. Then, we expect s 1.017† =+ , which matches exactly with s†= 1.017 (derived from the modeling). The light curve can be well described by a 2L1S interpretation with both planet and binary cases (see light curves and geometries in Figure 2). In Table 4, we present the best-fit parameters. However, we find that the binary case shows worse fits by Δχ2= 20.62 and 22.32 for the s+ and s− cases, respectively. The Δχ2 amounts are larger than our criterion to claim the planet detection. Although we conclude that this event is caused by a planetary lens system, we report both cases because the crucial part of the light curve (HJD′ = 7,637.1–7,637.4) for clearly distinguishing between planet and binary solutions is not covered. For this event, ρ* is measured. The signal of the finite-source effect comes from the peak of the light curve, which cannot be properly described by the 1L1S interpretation (see the residual of Figure 2). The peak part can be described by 2L1S solutions (planet cases) by touching the cusp of the central caustic (see Figure 2). As a result, ρ* is well measured. We also test the APRX effect because of the relatively long timescale of the event (i.e., tE∼ 21 days). We find χ2 improvements of Δχ2= 21.57 and 12.73 for the s+ and s− cases, respectively. However, the APRX fits show values too big for both cases, i.e., |πE,N|> 10, which comes from overfitting systematics at the baseline. This fact implies that the APRX measurement is not reliable. Thus, we do not adopt the results of the APRX models. 4 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. 3.4. KMT-2016-BLG-0625 As shown in Figure 3, the light curve of KMT-2016-BLG- 0625 shows a clear bump-shaped anomaly at HJD′∼ 7,662.95. Based on the heuristic analysis, we find τanom= 0.609 and uanom= 0.613 from tanom= 7662.95 and tE= 11.5 days. Then, we can expect that s 0.739† =- and s 1.352† =+ , which are consistent with s−= 0.741 and s+= 1.367, respectively, among the solutions presented in Table 5. Also, we expect α= 0.12 or 3.26 rad, which is consistent with α= 0.12 and 3.22 for the s+ and s− cases, respectively. As shown in Table 5, we find four planetary solutions (s± and s ¢) that can explain the anomaly. Because of the gaps near the anomaly, the Δχ2 values between the models (i.e., Figure 1. Light curve of OGLE-2016-BLG-1635 with s± models and their caustic geometries. Table 3 Model Parameters of OGLE-2016-BLG-1635 Parameter s− s+ χ2/Ndata 5434.309/5436 5442.023/5436 t0 HJD[ ]¢ 7,624.124 ± 0.013 7,624.118 ± 0.014 u0 0.028 ± 0.004 0.028 ± 0.003 tE [days] 20.908 ± 2.239 21.997 ± 2.252 s 0.587 ± 0.014 1.684 ± 0.043 q (×10−4) 254.587 ± 33.644 247.586 ± 30.858 qlog10á ñ −1.594 ± 0.058 −1.620 ± 0.056 α [rad] 5.056 ± 0.028 5.047 ± 0.030 ρ*,limit <0.0037 <0.0041 Note. HJD′ = HJD–2,450,000.0. 5 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. Δχ2= 0.98–3.30) are too small to distinguish between them, although the model light curves show quite different features caused by the different caustic geometries presented in Figure 4. Although we cannot break the degeneracy of the planetary solutions, all cases indicate that the companion of the lens system is a planet, i.e., q 10 4( )= - (see Table 5). Figure 2. Light curve of MOA-2016-BLG-532 with the best-fit planetary model. We compare the planetary solution (black solid line) to the binary (blue dotted line) and 1L1S with finite-source (cyan dashed line) models. We also present caustic geometries of 2L1S models on the right side for comparison. Table 4 Model Parameters of MOA-2016-BLG-532 Cases Planet Binary Parameter s− s+ Parameter s− s+ χ2/Ndata 12,638.981/12,647 12,637.673/12,647 binary planet 2cD - 22.322 20.619 t0 HJD[ ]¢ 7,636.877 ± 0.003 7,636.885 ± 0.003 t0 HJD[ ]¢ 7,636.934 ± 0.003 7,636.938 ± 0.003 u0 0.009 ± 0.001 0.009 ± 0.001 u0 0.009 ± 0.001 0.007 ± 0.001 tE [days] 20.786 ± 1.356 20.547 ± 1.491 tE [days] 21.606 ± 1.392 25.921 ± 1.427 s 0.653 ± 0.018 1.584 ± 0.048 s 0.278 ± 0.013 4.742 ± 0.362 q (×10−4) 40.382 ± 5.534 40.441 ± 6.491 q 0.156 ± 0.029 0.232 ± 0.062 qlog10á ñ −2.387 ± 0.058 −2.403 ± 0.070 qlog10á ñ −0.765 ± 0.073 −0.595 ± 0.100 α [rad] 2.938 ± 0.008 2.949 ± 0.008 α [rad] 3.026 ± 0.010 3.036 ± 0.008 ρ* (×10−4) 46.956 ± 3.995 47.591 ± 5.055 ρ* (×10−4) 73.386 ± 5.591 59.520 ± 3.267 Note. HJD′ = HJD–2,450,000.0. Bold indicates our fiducial solutions. 6 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. Figure 3. Light curve of KMT-2016-BLG-0625 with degenerate models. Table 5 Model Parameters of KMT-2016-BLG-0625 Parameter s− s ¢- s+ s ¢+ Parameter 1L2S χ2/Ndata 8014.084/8021 8015.097/8021 8015.065/8021 8017.379/8021 χ2/Ndata 8021.432/8021 t0 HJD[ ]¢ 7,655.951 ± 0.008 7,655.948 ± 0.008 7,655.951 ± 0.008 7,655.950 ± 0.008 t S0, 1 HJD[ ]¢ 7,655.953 ± 0.008 u0 0.073 ± 0.004 0.072 ± 0.004 0.075 ± 0.005 0.076 ± 0.004 u S0, 1 0.078 ± 0.007 tE [days] 11.494 ± 0.466 11.576 ± 0.466 11.335 ± 0.508 11.217 ± 0.405 tE [days] 10.946 ± 0.491 s 0.741 ± 0.009 0.741 ± 0.009 1.367 ± 0.018 1.358 ± 0.015 t S0, 2 HJD[ ]¢ 7,662.943 ± 0.010 q (×10−4) 2.357 ± 1.123 1.793 ± 1.048 0.727 ± 0.254 0.317 ± 0.173 u S0, 2 (×10−4) 3.751 ± 19.751 qlog10á ñ −3.451 ± 0.130 −3.498 ± 0.136 −4.154 ± 0.159 −4.321 ± 0.159 L L α [rad] 3.217 ± 0.008 3.220 ± 0.008 0.122 ± 0.003 0.121 ± 0.002 qflux 0.005 ± 0.001 ρ* (×10−4) 12.256 ± 6.613 20.969 ± 7.334 17.498 ± 7.796 17.656 ± 7.383 * S, 2 r (×10−4) 51.309 ± 13.447 Note. HJD′ = HJD–2,450,000.0. We note that * S, 1 r is not measured for the 1L2S case. Only the upper limit (3σ range) can be measured: * 0.117S, 1 r < . 7 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. As shown in Figure 4, all planetary solutions produce the anomaly by crossing the caustic(s). As a result, we can measure the ρ* despite the nonoptimal coverage. We do not test for the APRX measurement because of the relatively short timescale (i.e., tE∼ 11 days). Because the bump-type planetary anomaly can often lead to a 2L1S/1L2S degeneracy (Gaudi 1998), we check the 1L2S case for this event. In Table 5, we present the best-fit model of the 1L2S interpretation. We find that the 1L2S case is disfavored by Δχ2= 7.35. However, the Δχ2 amount is not enough to conclusively resolve the 2L1S/1L2S degeneracy. Nevertheless, because we measure the ρ* of the secondary source, we can measure the lens-source relative proper motion of the secondary source ( rel,S2 m ) to check the 1L2S model. We find (see Section 4) that 0.83 0.22 mas yrrel,S 1 2 m =  - . By comparison, Gould (2022) found that for observed microlen- sing events with planetary-type anomalies, low proper motions have probabilities p 2 1 2 4 2.8 10 1 mas yr , 5 rel rel 1 rel 2 2 2 rel 1 2  ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ( ) ( ) [( ) ]! ( ) m m s n m s m = +   ´ m n m + - - where σμ= 3 mas yr−1 and ν= 1. See also Equation (9) of Jung et al. (2023). Applying this formula to the 1L2S solution, we find p= 1.9%. This would, in itself, be a reasonably strong argument against the 1L2S solution. When combined with the fact that this solution is disfavored by Δχ2= 7.35, we consider it to be decisive. Therefore, we reject the 1L2S solution and conclude that KMT-2016-BLG-0625 is caused by a planetary lens system. However, we note that the mass ratio q varies by a factor of ∼3 over the four degenerate solutions. Figure 4. Caustic geometries of KMT-2016-BLG-0625 for the 2L1S models. 8 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. 3.5. OGLE-2016-BLG-1850 The light curve of OGLE-2016-BLG-1850 (which we identified as KMT-2016-BLG-1307) shows a dip-shaped anomaly at HJD′∼ 7,663. Based on the heuristic analysis, we can expect s 0.812† =- and q= 0.9× 10−4 (based on the τanom= 0.126 and uanom= 0.419 that are found from tanom= 7663.15 and tE= 63.0 days), which corresponds well with the empirical values: s†= 0.813 and q∼ 1.0× 10−4. In Figure 5, we present the observed light curve with zoom- ins of the anomaly. We also present the best-fit model light curves of the STD and APRX cases shown in Table 6. We find that both STD models (i.e., inner and outer cases) can describe the planetary anomaly as shown in Figure 6. However, the STD cases show a very long timescale (tE∼ 210 days), which implies that the light curve is likely to be affected by a strong APRX effect. As expected, we find that the STD model cannot properly describe the 2017 baseline. Thus, we consider the ARPX effect. Then, we find a substantial χ2 improvement of Δχ2 100, which mostly comes from the better fit of the 2017 baseline (see Figure 5). Also, all APRX solutions can well describe the planetary anomaly as shown in Figure 6. In Figure 7, we present caustic geometries of all cases for comparison. We note that OGLE-2016-BLG-1850 is a non- caustic-crossing event. As a result, we cannot precisely measure ρ* (only upper limits are available). In Figure 8, we present the distributions of the APRX measurements, which are well converged. However, tests are required before we conclude that the APRX models should be Figure 5. Light curve of OGLE-2016-BLG-1850 with STD (cyan) and APRX (black) models. 9 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. Figure 6. Zoom-in of the anomaly part of OGLE-2016-BLG-1850 for comparing all models with their residuals. Table 6 Model Parameters of OGLE-2016-BLG-1850 STD APRX Parameter Inner Outer Inner (u0 > 0) Outer (u0 > 0) Inner (u0 < 0) Outer (u0 < 0) χ2/Ndata 8108.940/7995 8108.800/7995 8004.449/7995 8006.818/7995 8007.775/7995 8009.766/7995 t0 HJD[ ]¢ 7,654.235 ± 0.192 7,654.229 ± 0.192 7,655.221 ± 0.175 7,655.137 ± 0.177 7,655.258 ± 0.177 7,655.195 ± 0.178 u0 0.106 ± 0.009 0.105 ± 0.010 0.401 ± 0.023 0.397 ± 0.020 −0.397 ± 0.020 −0.398 ± 0.031 tE [days] 209.677 ± 16.086 211.183 ± 18.672 62.803 ± 3.843 63.190 ± 3.114 59.885 ± 2.917 60.581 ± 5.596 s 0.929 ± 0.005 0.961 ± 0.006 0.801 ± 0.010 0.826 ± 0.009 0.802 ± 0.008 0.825 ± 0.014 q (×10−4) 0.416 ± 0.066 0.443 ± 0.068 1.009 ± 0.141 1.258 ± 0.161 1.072 ± 0.140 1.334 ± 0.180 qlog10á ñ −4.378 ± 0.068 −4.366 ± 0.068 −3.983 ± 0.057 −3.923 ± 0.058 −3.945 ± 0.052 −3.890 ± 0.060 α [rad] 4.332 ± 0.011 4.329 ± 0.011 4.401 ± 0.012 4.394 ± 0.012 −4.385 ± 0.012 −4.384 ± 0.012 ρ*,limit <0.003 <0.003 <0.007 <0.009 <0.007 <0.009 πE,N L L 0.075 ± 0.059 0.070 ± 0.060 0.095 ± 0.080 0.074 ± 0.084 πE,E L L 0.455 ± 0.037 0.441 ± 0.034 0.465 ± 0.035 0.449 ± 0.048 Note. HJD′ = HJD–2,450,000.0. 10 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. the fiducial solutions for this event. First, because the OBT motion can affect the APRX measurements (especially the uncertainty of the APRX measurement), we test the OBT effect. We conduct OBT+APRX models for each APRX case. We find that the OBT+APRX models show negligible χ2 improvements of Δχ2 0.5 for the inner cases and Δχ2 3.0 for the outer cases. We also find that there is no effect on the uncertainties of the APRX measurements. Second, to check the APRX models, we add xallarap to the models by introducing five parameters: the north and east components of the xallarap vector (ξE,N, ξE,E), the phase angle (f), the inclination of the orbit (i), and the orbital period (P). We find that the xallarap cases show χ2 improvements of Δχ2= 17.0–22.1 compared to the APRX cases, which are marginal Δχ2 amounts to firmly claim that the xallarap models can be fiducial solutions for this event. Moreover, although the Figure 7. Caustic geometries of OGLE-2016-BLG-1850. Figure 8. The APRX distributions of OGLE-2016-BLG-1850. 11 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. best-fit model favors Plog 0.210( ) = , as shown in Figure 9, we find that the xallarap models at Plog 0.010( ) = showΔχ2 6.0 compared to the best-fit xallarap model of each case. The clues imply that the asymmetry of the light curve is due to the APRX effect rather than the xallarap effect. Thus, we conclude that the fiducial solutions for this event are the APRX models. 3.6. KMT-2016-BLG-1751 In Figure 10, we present the observed light curve of KMT- 2016-BLG-1751, which shows a clear planetary anomaly (i.e., dip feature) at the peak of the light curve. Based on the heuristic analysis (τanom∼ 0.00 and uanom= 0.11 from tanom= 7501.00 and tE= 10.0 days), we expect s 0.946† =- , which is well matched to both s s s 0.944† = =- + and s s s 0.947† = ¢ ¢ =- + . We also expect q; 0.003 (for both s† cases), which agrees with the q values presented in Table 7 to within a factor of ∼2. We find that several solutions can explain the anomaly because the coverage of the anomaly (HJD′= 7,500.8–7,502.4) is nonoptimal. Thus, despite including MOA data, the gap in the anomaly produces degenerate solutions. In Table 7, we present model parameters of the solutions. In Figures 11 and 12, we also present the s–q parameter space with the locations of each solution and their caustic geometries. The competing solutions show relatively small Δχ2 values compared to the best-fit solution (i.e., s+ case): 8.53, 5.70, 8.78, and 10.78 for the s ¢+, s−, s ¢-, and s - cases, respectively. For the s± and s ¢ cases, we obtain a best-fit value for ρ*. However, as might be expected from the geometries, we find that the measurements are consistent with zero at 3σ. Thus, in these cases, we effectively have only an upper limit on ρ*, so we will apply a ρ* weight function in the Bayesian analysis in Section 5. For the s - case, ρ* is measured from the caustic crossing. However, the s - solution does not satisfy our χ2 criterion (i.e., Δχ2< 10.0). Thus, we remove the s - case from our fiducial solutions for determining the lens properties of this event. However, because the Δχ2 of this case is very close to the χ2 criterion, we present the parameters and figures of this solution for completeness. Lastly, because of the short timescale (i.e., tE∼ 10 days), we do not conduct the APRX modeling for this event. 3.7. KMT-2016-BLG-1855 In Figure 13, we present the observed light curve of KMT- 2016-BLG-1855 with the best-fit model curve and caustic geometry. The observed light curve exhibits anomalies at the peak. We find that the anomaly can be described by a source approaching a diamond-shaped central caustic, which is in the regime of a Chang–Refsdal (C-R) lens (Chang & Refsdal 1979). The best-fit model shows 0.023 0.012 q 1 =  , which satisfies our mass-ratio criterion to claim planet detection. However, we find that there are possible solutions caused by the close/wide (Griest & Safizadeh 1998), offset (Zhang & Gaudi 2022; Zhang et al. 2022b), and 2L1S/1L2S (Gaudi 1998) degeneracies. We also check for the α-degeneracy (i.e., the degeneracy caused by the angle of the source trajectory), which can occur for C-R lenses. These solutions are denoted n(π/2), where n= (1, 2, 3). In Tables 8 and 9, we present model parameters of the best-fit and degenerate models. In Figures 14 and 15, we present all possible solutions with their caustic geometries and residuals for comparison. Figure 9. The Plog10( ) and χ2 plots of the xallarap models of OGLE-2016-BLG-1850. The crosses indicate the χ2 of the APRX models. 12 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. Figure 10. Light curve of KMT-2016-BLG-1751 with degenerate models. Table 7 Model Parameters of KMT-2016-BLG-1751 Parameter s+ s ¢+ s− s ¢- s - χ2/Ndata 8995.960/8994 9004.487/8994 9001.658/8994 9004.738/8994 9006.742/8994 t0 HJD[ ]¢ 7,501.132 ± 0.016 7,501.187 ± 0.021 7,501.106 ± 0.017 7,501.176 ± 0.019 7,501.214 ± 0.016 u0 0.113 ± 0.005 0.111 ± 0.005 0.107 ± 0.005 0.110 ± 0.005 0.103 ± 0.006 tE [days] 9.625 ± 0.293 9.475 ± 0.292 9.997 ± 0.301 9.469 ± 0.284 9.591 ± 0.298 s 1.050 ± 0.014 1.027 ± 0.017 0.848 ± 0.011 0.873 ± 0.015 0.950 ± 0.007 q (×10−4) 64.992 ± 4.479 39.995 ± 8.312 61.147 ± 3.556 38.161 ± 7.169 7.207 ± 2.902 qlog10á ñ −2.200 ± 0.031 −2.447 ± 0.113 −2.212 ± 0.025 −2.485 ± 0.104 −3.036 ± 0.130 α [rad] 4.339 ± 0.022 4.470 ± 0.049 4.318 ± 0.021 4.467 ± 0.044 4.643 ± 0.035 ρ*,limit <0.019 <0.020 <0.021 <0.020 L ρ* L L L L 0.019 ± 0.002 Note. HJD′ = HJD–2,450,000.0. Bold indicates our fiducial solutions. 13 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. We find a total of seven degenerate solutions including the 1L2S case. For the 2L1S cases, we find the initial parameters of the A, B, C, and D solutions based on the grid search. We also find initial parameters for their paired offset-degeneracy solutions (i.e., A¢, B¢, C¢, and D¢) using heuristic analysis: s s s2( )†¢ =  , where subscripts + and − indicate the s> 1 and s< 1 cases, respectively. Note that we transform our coordinate system from “secondary” to “primary” components to conduct the heuristic analysis because the analysis is valid for the primary coordinate system. Then, we refine the model parameters to check the degeneracy (note that we restore the coordinates for direct comparison). For the A and A¢ pair, the heuristic analysis predicts s 3.680¢ = . The paired offset-degeneracy solution of the A case (i.e., A¢) is consistent with the 3(π/2) C-R case, which has an empirical value of s= 3.780± 0.088. This A family degen- eracy can be resolved (see below). For the B and B¢ pair, the heuristic analysis predicts s 3.600¢ = , which is consistent with the empirical s= 3.708± 0.121 from the B¢ case. This B family is a C-R lensing case, which shows large uncertainties in the set of (tE, s, q) parameters. For the C and C¢ pair, the heuristic analysis predicts s 1.162¢ = , which is consistent with the empirical value of s= 1.161± 0.042 from the C¢ case. Indeed, the C family is caused by close/wide degeneracy. For the D case, the heuristic analysis expects s 2.951¢ = . However, we find that the paired offset solution evolves toward the B case. Indeed, the caustic geometry of the D case is asymmetric, which is different from the C-R lens case. Thus, because the source trajectory is not perpendicular to the binary axis, the paired solution from the heuristic analysis cannot describe the peak of the light curve, and we would not necessarily expect it to (Gaudi & Gould 1997). In all cases, the ρ* measurements are uncertain and give only upper limits of ρ* values, as expected from non-caustic-crossing geometries. All of the 2L1S models nominally have long timescales (tE), but they also have q> 1.0 (i.e., they approach the secondary, less massive lens component). For these cases, the actual timescale (tE¢) of the event should be scaled by t t qE E¢ = as shown in Tables 8 and 9. Hence, given that t 15E¢ ~ days, it is not surprising that we do not detect the APRX effect (i.e., 2.7STD APRX 2cD =- ). Thus, we conclude that the STD models are the fiducial solutions for this event. As shown in Figures 14 and 15, all cases describe the peak anomaly well. Although they nominally have Δχ2> 10 compared to the best-fit case, we find that the χ2 differences mostly come from the baseline part (HJD 7,600¢ > ). The best- fit case has a wide caustic, which creates a very shallow bump peaking at HJD 7,717¢ ~ , ΔI∼ 0.01 mag above the baseline observations (see the blue dashed line shown in Figure 13). However, systematics may exist in the baseline data at this level, especially considering the dispersion of the baseline data (i.e., ΔI∼ 0.65 mag). Thus, we compute Δχ2 without the baseline data of HJD 7,600¢ > (i.e., t0+1.5 tE∼ 7595.25) because the χ2 contributions at the baseline cannot be considered reliable. After this cut, the Δχ2 values for all cases (except the A¢ case) are less than 9, as shown in Tables 8 and 9. Hence, we cannot claim to resolve most degenerate solutions. The 1L2S model is completely degenerate with the 2L1S models and cannot be excluded based on physical considera- tions. First, the finite-source effect is not measured; the ρ* distributions of both sources reach zero within 3σ. Moreover, because of the severe extinction (AI= 5.97; Gonzalez et al. 2012), additional information to conclusively resolve the Figure 11. The s–q parameter space of KMT-2016-BLG-1751 showing possible solutions. 14 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. degeneracy, such as the source color (see Section 4), is not available for this event. Thus, we treat KMT-2016-BLG-1855 as a planet candidate, and we strongly counsel against cataloging it as a planet. 4. CMD Analysis For the five planetary events, we measure the angular source radius (θ*) using the conventional method described in Yoo et al. (2004), i.e., the CMD analysis. The θ* measurement is important. If we measure ρ* from the finite-source effect, we can determine θE= θ*/ρ*. Furthermore, even if we cannot measure ρ*, θ* is required to apply the ρ* distributions as constraints on the Bayesian analysis. We proceed with this analysis based on multiband observa- tions (I and V bands) taken from the KMTNet survey (i.e., KMTC). We align the KMTNet instrumental color and magnitudes to the OGLE-III scales using cross-matching of field stars. We note that the position of the red giant clump centroid (RGC) is determined based on the OGLE-III CMD (Szymański et al. 2011). In Figure 16, we present CMDs of the five planetary events for the best-fit cases with the positions of the RGC, source, and blend. We also present all information from the CMD analysis, including θ*, θE, and μrel, in Table 10. We note that the intrinsic color of the RGC is adopted from Bensby et al. (2011). The dereddened magnitude of the RGC is adopted from Nataf et al. (2013). The dereddened colors and magnitudes of the source and blend are determined by assuming they experienced the same amount of stellar extinction of the RGC. Lastly, we determine θ* using the surface brightness–color relation adopted from Kervella et al. (2004). Note that we proceed differently for the special case of the putative second source in the 1L2S solution for KMT-2016- BLG-0625. We find IS,0= 19.345± 0.010 using the method of Yoo et al. (2004). Then, we derive I 25.112 0.231S ,02 =  based on the qflux value of the 1L2S model. We convert the dereddened I-band magnitude of the second source to its absolute I-band magnitude (MI) by adopting MI,RGC= −0.12± 0.09 and IRGC,0= 14.335 from Nataf et al. (2013): Figure 12. Caustic geometry of each solution of KMT-2016-BLG-1751. The color of the caustic is identical to the color of the light curve shown in Figure 10. 15 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. M 10.656 0.248I,S2 =  . We can estimate the radius of the second source, R R0.208S2 ~ , based on studies of stellar properties (Pecaut et al. 2012; Pecaut & Mamajek 2013). Thus, we find that the angular radius of the second source is * 0.128 asS, 2q m~ , which yields 0.83 0.22 mas yrrel,S 1 2 m =  - . Note that we adopt the distance to the second source (D 7.59 kpcS2 ~ ) from Nataf et al. (2013). For KMT-2016-BLG-1855, the field is highly extincted (AI= 5.97; Gonzalez et al. 2012), so it is not possible to measure the source color in the V band from the KMTNet data. We construct an I−H CMD for this event by cross-matching the OGLE-III catalog (Szymański et al. 2011) to the VVV DR2 (Minniti et al. 2017), and we convert the KMT pyDIA I magnitude of the source to the OGLE-III system. This suggests Figure 13. Light curve of KMT-2016-BLG-1855 with the best-fit model. 16 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. that the source is a red clump giant. However, the clump is extended in both color and magnitude in the CMD. Both the lack of a color measurement and the uncertainty in the clump magnitude would make θå highly uncertain. However, there are no meaningful constraints on ρå, so we do not calculate a value for θå because it has no bearing on the analysis. We also measure the astrometric offsets between baseline objects and sources. Because we can use the blend light as a constraint for the Bayesian analysis if the blend light is associated with the lens. For all planetary events, we find that the blend is separated by >0 3, so it is dominated by a star that is not the lens. 5. Planet Properties 5.1. Bayesian Formalism To determine the lens properties, two additional observables are simultaneously required. They are the angular Einstein ring radius (θE) and the amplitude of the microlens parallax vector (|πE|), which are measured from the effects of the finite source and microlens parallax, respectively. However, the events for which both observables are simultaneously measured are relatively rare. Indeed, we can measure only one of these observables out of five planetary events presented in this work. Thus, we estimate the lens properties using the Bayesian analysis. We follow the Bayesian formalism described in Shin et al. (2023) to generate the Galactic prior. Then, we apply the measured observable as a constraint on the Galactic prior. In Table 11, we present the applied constraints and lens properties for each event. For the notation of the constraint, tE indicates a Gaussian weight function constructed based on the best-fit value of the tE parameter and its uncertainty, θE indicates the Gaussian weight adopted from the measured θE if ρ* is certainly measured, and ρ* indicates a weight function built based on the Δχ2 distribution as a function of ρ* if the ρ* measurement is uncertain. Lastly, πE indicates a constraint using the 2D APRX distributions described in Ryu et al. (2019). In Table 11, we present various lens properties for each event because each event has degenerate solutions, which yield different lens properties. For ease of cataloging, we present “adopted” values for each property by adopting the method described in Jung et al. (2023), i.e., weighted average values. Table 8 Model Parameters of KMT-2016-BLG-1855 Parameter A: Best Fit A′: 3(π/2) B: 2(π/2) B′: 2(π/2) χ2/Ndata 7734.217/7735 7749.828/7735 7758.514/7735 7757.884/7735 Δχ2 (full data) L 15.611 24.297 23.667 Δχ2 (HJD 7600¢ < ) L 13.196 8.055 8.821 t0 HJD[ ]¢ 7,454.015 ± 0.080 7,455.619 ± 0.078 7,453.981 ± 0.104 7,455.694 ± 0.086 u0 0.041 ± 0.007 0.040 ± 0.006 0.001 ± 0.001 −0.001 ± 0.001 tE [days] 94.156 ± 17.078 103.244 ± 18.364 2889.644 ± 493.547 2924.318 ± 120.251 tE¢ [days] 14.424 ± 0.908 15.331 ± 0.904 13.282 ± 0.984 13.321 ± 0.945 s 3.798 ± 0.108 3.780 ± 0.088 3.598 ± 0.132 3.708 ± 0.121 q 42.614 ± 21.193 45.352 ± 24.063 (47.334 ± 11.658) × 103 (48.189 ± 5.978) × 103 q 1 0.023 ± 0.012 0.022 ± 0.009 (0.211 ± 0.419) × 10−4 (0.208 ± 0.042) × 10−4 log q10 1á ñ −1.605 ± 0.196 −1.666 ± 0.173 −4.249 ± 0.248 −4.574 ± 0.068 α [rad] 0.657 ± 0.012 5.603 ± 0.016 3.812 ± 0.016 3.803 ± 0.015 ρ*,limit <0.023 <0.024 <0.002 <0.0006 Note. HJD′ = HJD–2,450,000.0. Bold indicates the best-fit solution. Table 9 Model Parameters of KMT-2016-BLG-1855 (Continued) Parameter C: s ¢- C′: s ¢+ D: 1(π/2) Parameter E: 1L2S χ2/Ndata 7751.738/7735 7750.972/7735 7755.555/7735 χ2/Ndata 7752.925/7735 Δχ2 (full data) 17.521 16.775 21.338 Δχ2 (full data) 18.708 Δχ2 (HJD 7600¢ < ) 2.269 1.414 5.727 Δχ2 (HJD 7600¢ < ) 3.060 t0 HJD[ ]¢ 7,454.864 ± 0.061 7,454.893 ± 0.090 7,455.816 ± 0.102 t S0, 1 HJD[ ]¢ 7,451.870 ± 0.112 u0 0.226 ± 0.049 0.531 ± 0.066 0.148 ± 0.024 u S0, 1 0.124 ± 0.015 tE [days] 15.382 ± 1.392 15.408 ± 1.392 24.015 ± 4.242 tE [days] 17.409 ± 1.362 tE¢ [days] L L 14.176 ± 1.999 t S0, 2 HJD[ ]¢ 7457.697 ± 0.106 s 0.687 ± 0.025 1.161 ± 0.042 3.392 ± 0.162 u S0, 1 0.133 ± 0.018 q 18.911 ± 3.028 16.223 ± 2.143 2.870 ± 1.418 qflux 1.146 ± 0.181 q 1 0.053 ± 0.006 0.062 ± 0.007 0.348 ± 0.215 L L log q10 1á ñ −1.328 ± 0.059 −1.229 ± 0.053 −0.389 ± 0.203 L L α [rad] 1.582 ± 0.013 1.578 ± 0.012 2.544 ± 0.014 L L ρ*,limit <0.168 <0.178 <0.101 L L Note. HJD′ = HJD–2,450,000.0. 17 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. 5.2. OGLE-2016-BLG-1635 For the Bayesian analysis of this event, we apply constraints obtained from tE (i.e., the Gaussian weight) and ρ* weight functions on the Galactic prior because the ρ* measurements are uncertain and the APRX is not measured. Note that we can evaluate the effect of the ρ* weight on the posterior before conducting the Bayesian analysis. If the lower limit on the relative lens-source proper motion μrel,+3σ≡ θ*/(ρ*,+3σtE) 1mas yr−1, the effect is minor. As expected (see the μrel column of Table 10), the effects of ρ* are minor for both solutions. The Bayesian results indicate that the lens system of this event consists of an M dwarf host star (Mhost∼ 0.4Me) and a super-Jupiter-mass planet with a mass of Mplanet∼ 11.5MJ, which is close to the limit of planetary objects. The planet orbits the host with a projected separation of a⊥∼ 1.31 or ∼3.82 au, which is beyond its snow line. The planetary system is located in the Galactic bulge at a distance of ∼6.6 kpc from us. Hence, this event is caused by a typical microlensing planetary system, which is a giant planet orbiting an M dwarf host beyond the snow line (Ida & Lin 2005; Kennedy & Kenyon 2008). 5.3. MOA-2016-BLG-532 For this event, the ρ* values are measured. Thus, we apply tE and θE constraints on the Bayesian analyses. The lens system of this event consists of a late-type M dwarf host star (Mhost∼ 0.1Me) and a super-Neptune-mass planet (Mplanet∼ 7.2MN) orbiting with a projected separation of a⊥ ∼ 0.56 or ∼1.36 au. The planetary system is located at a distance of DL∼ 7.4 kpc from us. Similar to OGLE-2016- BLG-1635, this event is also caused by a typical microlensing planet. Figure 14. Light curve of KMT-2016-BLG-1855 with the best-fit (A) and degenerate (A¢, B, and B¢) models. 18 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. 5.4. KMT-2016-BLG-0625 Despite the nonoptimal coverage, we can measure ρ* for this event. Thus, we apply tE and θE constraints on the Bayesian analyses. For this event, the Bayesian results for the lens system span a wide range of properties because of the degenerate solutions (i.e., due to different q and ρ* for each solution; see Table 5). The host star is an M dwarf with a mass range of Mhost∼ 0.2–0.3Me. For the s− case (the best-fit solution), the planet could be a Neptune-mass planet with a mass of Mplanet∼ 1.36MN orbiting the host with a projected separation of a⊥∼ 1.3 au. For the remaining cases, the planet could be a super-Earth-mass planet with a mass range of Mplanet∼ 2.0–9.0M⊕ orbiting the host with a projected separation range of a⊥∼ 0.9–1.9 au. The planetary system belongs to the Galactic bulge with a distance range of DL∼ 6.1–6.7 kpc. 5.5. OGLE-2016-BLG-1850 For this event, we find the APRX effect on the light curve. However, the ρ* measurements are uncertain. Thus, we apply tE, ρ* weights, and πE constraints on the Bayesian analyses. The πE constraints have major effects on the posteriors, while the ρ* constraints have only minor effects as expected from μrel,+3σ 1 mas yr−1 (see Table 10). The planetary system of this event consists of an M dwarf host star (Mhost∼ 0.2–0.3Me) and a super-Earth-mass planet. We find that the planet mass of the inner cases (Mplanet ∼ 9M⊕) is smaller than that of the outer cases (Mplanet ∼ 11M⊕). The planet orbits the host with a projected separation of a⊥ ∼ 1.4–1.5 au beyond its snow line. The system is located at a distance of DL∼ 2 kpc from us, i.e., in the disk, which is expected by considering the strong microlens parallax effect. Figure 15. Light curve of KMT-2016-BLG-1855 with degenerate models C, C¢, D, and E. 19 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. 5.6. KMT-2016-BLG-1751 For this event, we conduct Bayesian analyses for the s± and s ¢ solutions by applying tE and ρ* weights as constraints. We find that the lens system consists of an M dwarf host (Mhost∼ 0.18Me) and a Jupiter-class planet (Mplanet∼ 0.7– 1.2MJ), which is located at a distance of ∼7.05 kpc from us. The planet orbits the host with a projected separation of a⊥∼ 1.2–1.4 au. We note that, as mentioned in Section 3.6, the s - case is removed from our fiducial solutions. Thus, although we conduct the Bayesian analysis for this case, we do not include its lens properties in Table 11. However, for completeness, we present the lens properties of this case. The Bayesian analysis result using the tE constraint indicates that the lens system consists of a M dwarf host star (M M0.18host 0.11 0.28 = - + ) and a super-Neptune-mass planet (M M2.5planet 1.57 4.25 N= - + ) with a projected separation of 1.28 0.44 0.54 - + au. The system is located at a distance of 7.04 1.38 0.54 - + kpc, and the relative lens-source proper motion is 7.56 mas yrrel 2.68 3.45 1m = - + - . The results are similar to the lens properties of our fiducial solutions because the tE value of s - is similar to them, except for the planet mass, which is caused by the smallest q value of the s - model. On the other hand, the Bayesian analysis applying tE and ρ*weights shows an extreme lens system caused by the unusually small θE. That is, the lens system could consist of a very low mass host (M M0.02host 0.01 0.05 = - + ) and sub- Neptune-mass planet (M M0.31planet 0.19 0.71 N= - ) with a projected separation of 0.31 0.07 0.06 - + . The system could be located at a distance Figure 16. The CMDs of the five planetary events. 20 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. of 8.17 1.04 1.05 - + kpc. The relative lens-source proper motion is relm = 1.59 mas yr0.34 0.21 1 - + - , which is inconsistent with the typical value of the bulge-lens/bulge-source microlensing event (5–10mas yr−1). If the lens star were resolved by future adaptive optics imaging, this could definitively rule out the s - solution. 6. Summary We found five new planetary systems and one planet candidate through a systematic anomaly search for the 2016 prime fields of the KMTNet data archive. These “buried” planets have various properties. For OGLE-2016-BLG-1635, the planetary system consists of an M dwarf host (Mhost∼ 0.4Me) and a super-Jupiter- mass planet (Mplanet∼ 11.5MJ) that orbits the host with a projected separation of 1.3 or 3.8 au. The system is located at a distance of ∼6.6 kpc from us. For MOA-2016-BLG-532, the lens system indicates that a super-Neptune-mass planet (Mplanet∼ 7.2MN) orbits a late M dwarf host star (Mhost∼ 0.1Me) with a projected separation of 0.6 or 1.4 au. The planetary system is located at a distance of ∼7.4 kpc from us. For KMT-2016-BLG- 0625, because of the degenerate solutions, the planetary system consists of an M dwarf host star with mass in the range 0.1–0.3Me and a planet with mass in the range 2.0M⊕–1.4MN. The system is located at a distance of 6.1–6.7 kpc. For OGLE- 2016-BLG-1850, the planetary system consists of an M dwarf host star (Mhost∼ 0.3Me) and a super-Earth-mass planet (Mplanet= 9–11M⊕) with a projected separation of ∼1.5 au. The system is located at a distance of 2 kpc. For KMT-2016-BLG- 1751, we adopt the lens properties of the s± and s†  cases, which indicate that a Jupiter-class planet (Mplanet= 0.7–1.2MJ) orbits an Table 10 CMD Analyses of Planetary Events Event Case (V − I)RGC (V − I)0,RGC (V − I)S (V − I)0,S (V − I)B θ* θE μrel IRGC I0,RGC IS I0,S IB (μas) (mas) (mas yr−1) OB161635 s− 2.763 1.060 2.441 ± 0.136 0.738 ± 0.145 2.503 ± 0.005 0.315 ± 0.050 >0.085 >1.49 16.519 14.482 22.121 ± 0.015 20.084 ± 0.015 16.872 ± 0.001 s+ 2.763 1.060 2.442 ± 0.137 0.739 ± 0.145 2.503 ± 0.005 0.311 ± 0.050 >0.076 >1.26 16.519 14.482 22.153 ± 0.015 20.116 ± 0.015 16.872 ± 0.001 MB16532 s− 2.313 1.060 2.952 ± 0.150 1.699 ± 0.158 2.135 ± 0.002 0.529 ± 0.035 0.113 ± 0.015 1.98 ± 0.26 15.995 14.391 22.200 ± 0.008 20.596 ± 0.008 16.998 ± 0.001 s+ 2.313 1.060 2.958 ± 0.150 1.705 ± 0.158 2.135 ± 0.002 0.534 ± 0.036 0.112 ± 0.016 1.99 ± 0.29 15.995 14.391 22.188 ± 0.008 20.584 ± 0.008 16.997 ± 0.001 KB160625 s− 1.892 1.060 1.427 ± 0.044 0.595 ± 0.066 1.584 ± 0.005 0.364 ± 0.025 0.297 ± 0.029 9.44 ± 0.93 15.331 14.335 20.412 ± 0.010 19.416 ± 0.010 17.363 ± 0.001 s ¢- 1.892 1.060 1.429 ± 0.044 0.597 ± 0.066 1.583 ± 0.005 0.363 ± 0.025 0.173 ± 0.017 5.46 ± 0.54 15.331 14.335 20.423 ± 0.010 19.427 ± 0.010 17.362 ± 0.001 s+ 1.892 1.060 1.429 ± 0.043 0.597 ± 0.066 1.584 ± 0.005 0.368 ± 0.026 0.210 ± 0.021 6.78 ± 0.67 15.331 14.335 20.390 ± 0.010 19.394 ± 0.010 17.364 ± 0.001 s ¢+ 1.892 1.060 1.429 ± 0.043 0.597 ± 0.066 1.584 ± 0.005 0.372 ± 0.026 0.210 ± 0.021 6.85 ± 0.68 15.331 14.335 20.371 ± 0.010 19.375 ± 0.010 17.366 ± 0.001 OB161850 APRX inner u0 + 2.552 1.060 2.106 ± 0.048 0.614 ± 0.069 1.738 ± 0.031 0.880 ± 0.064 >0.126 >0.73 16.502 14.558 19.488 ± 0.007 17.544 ± 0.007 18.868 ± 0.007 APRX outer u0 + 2.552 1.060 2.108 ± 0.048 0.616 ± 0.069 1.740 ± 0.030 0.874 ± 0.064 >0.097 >0.56 16.502 14.558 19.508 ± 0.007 17.564 ± 0.007 18.854 ± 0.006 APRX inner u0 − 2.552 1.060 2.106 ± 0.048 0.614 ± 0.069 1.743 ± 0.030 0.871 ± 0.064 >0.124 >0.76 16.502 14.558 19.510 ± 0.007 17.565 ± 0.007 18.848 ± 0.006 APRX outer u0 − 2.552 1.060 2.108 ± 0.048 0.616 ± 0.069 1.743 ± 0.030 0.873 ± 0.064 >0.097 >0.58 16.502 14.558 9.511 ± 0.007 17.566 ± 0.007 18.847 ± 0.006 KB161751 s+ 2.664 1.060 2.083 ± 0.056 0.479 ± 0.075 3.034 ± 0.068 0.543 ± 0.038 0.039 ± 0.010 >1.06 16.657 14.548 20.407 ± 0.007 18.299 ± 0.007 19.431 ± 0.004 s ¢+ 2.664 1.060 2.083 ± 0.057 0.479 ± 0.076 3.059 ± 0.073 0.554 ± 0.039 0.040 ± 0.011 >1.06 16.657 14.548 20.366 ± 0.007 18.258 ± 0.007 19.448 ± 0.004 s− 2.664 1.060 2.084 ± 0.057 0.480 ± 0.076 2.998 ± 0.062 0.527 ± 0.037 0.041 ± 0.014 >0.94 16.657 14.548 20.477 ± 0.007 18.368 ± 0.007 19.404 ± 0.004 s ¢- 2.664 1.060 2.084 ± 0.057 0.480 ± 0.076 3.052 ± 0.072 0.551 ± 0.039 0.044 ± 0.015 >1.05 16.657 14.548 20.375 ± 0.007 18.267 ± 0.007 19.444 ± 0.004 s - 2.664 1.060 2.084 ± 0.057 0.480 ± 0.075 3.047 ± 0.071 0.549 ± 0.039 0.029 ± 0.004 1.09 ± 0.17 16.657 14.548 20.387 ± 0.007 18.279 ± 0.007 19.439 ± 0.004 Note. We use abbreviations for event names; e.g., OGLE-2016-BLG-1635 is abbreviated as OB161635. 21 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. Table 11 Lens Properties of Planetary Events Event Constraints Case Mhost Mplanet DL a⊥ μrel Gal. Mod. χ2 (Me) (MJ/MN/M⊕) (kpc) (au) (mas yr−1) OB161635 tE + ρ* s− 0.43 0.27 0.33 - + M11.49 7.25 8.91 J- + 6.62 1.68 1.15 - + 1.31 0.47 0.50 - + 6.32 2.25 2.89 - + 1.000 1.000 s+ 0.44 0.27 0.33 - + M11.48 7.28 8.57 J- + 6.60 1.71 1.15 - + 3.82 1.37 1.43 - + 6.14 2.20 2.82 - + 0.723 0.021 Adopted 0.43 ± 0.29 11.49 ± 7.96 MJ 6.62 ± 1.39 1.34 ± 0.47 6.32 ± 2.53 MB16532 tE + θE s− 0.09 0.05 0.14 - + M7.18 3.90 11.35 N- + 7.38 1.02 0.97 - + 0.56 0.10 0.10 - + 2.10 0.28 0.30 - + 1.000 0.520 s+ 0.09 0.05 0.15 - + M7.23 4.05 11.46 N- + 7.37 1.02 0.97 - + 1.36 0.25 0.26 - + 2.14 0.31 0.34 - + 0.997 1.000 Adopted 0.09 ± 0.07 7.21 ± 5.73 MN 7.37 ± 0.74 1.09 ± 0.17 2.13 ± 0.23 KB160625 tE + θE s− 0.30 0.16 0.30 - + M1.36 0.73 1.90 N- + 6.14 1.28 0.95 - + 1.31 0.28 0.24 - + 9.25 0.97 0.98 - + 1.000 1.000 s ¢- 0.15 0.08 0.21 - + M8.98 5.20 17.84 - + Å 6.68 1.04 0.94 - + 0.86 0.15 0.15 - + 5.53 0.57 0.58 - + 0.365 0.603 s+ 0.19 0.10 0.26 - + M4.68 2.92 6.42 - + Å 6.52 1.11 0.94 - + 1.85 0.35 0.33 - + 6.80 0.70 0.72 - + 0.556 0.612 s ¢+ 0.19 0.10 0.26 - + M2.03 1.06 3.53 - + Å 6.51 1.11 0.94 - + 1.84 0.34 0.33 - + 6.85 0.69 0.71 - + 0.574 0.193 Adopted 0.25 ± 0.14 0.94 ± 0.80 MN 6.31 ± 0.71 1.40 ± 0.17 8.10 ± 0.61 OB161850 tE + ρ* + πE APRX inner u0 + 0.26 0.12 0.20 - + M8.85 4.19 7.03 - + Å 2.12 0.80 1.17 - + 1.46 0.26 0.22 - + 5.09 2.30 3.94 - + 0.905 1.000 APRX outer u0 + 0.26 0.12 0.20 - + M10.73 5.36 8.59 - + Å 2.14 0.82 1.19 - + 1.49 0.27 0.22 - + 4.95 2.28 3.94 - + 0.914 0.306 APRX inner u0 − 0.24 0.11 0.20 - + M8.70 3.98 7.20 - + Å 2.09 0.79 1.13 - + 1.41 0.24 0.20 - + 5.17 2.32 4.09 - + 0.923 0.190 APRX outer u0 − 0.26 0.12 0.20 - + M11.47 5.70 9.05 - + Å 2.22 0.83 1.19 - + 1.50 0.28 0.26 - + 5.17 2.37 3.94 - + 1.000 0.070 Adopted 0.26 ± 0.11 9.33 ± 3.88 M⊕ 2.12 ± 0.67 1.46 ± 0.16 5.07 ± 2.11 KB161751 tE + ρ* s+ 0.18 0.11 0.28 - + M1.21 0.76 1.88 J- + 7.05 1.38 1.16 - + 1.40 0.49 0.60 - + 7.49 2.70 3.46 - + 0.835 1.000 s ¢+ 0.17 0.11 0.27 - + M0.73 0.48 1.14 J- + 7.05 1.38 1.16 - + 1.36 0.48 0.58 - + 7.51 2.71 3.48 - + 0.719 0.014 s− 0.18 0.12 0.28 - + M1.18 0.74 1.82 J- + 7.05 1.38 1.15 - + 1.16 0.41 0.50 - + 7.37 2.66 3.42 - + 1.000 0.058 s ¢- 0.17 0.11 0.27 - + M0.69 0.48 1.08 J- + 7.05 1.37 1.16 - + 1.15 0.41 0.49 - + 7.49 2.70 3.47 - + 0.696 0.012 Adopted 0.18 ± 0.18 1.20 ± 1.21 MJ 7.05 ± 1.17 1.39 ± 0.50 7.49 ± 2.83 Note. For the planet mass, we present the value in Jupiter (MJ), Neptune (MN), or Earth (M⊕) masses as appropriate. Table 12 Planetary Events Discovered on KMTNet Prime Fields in 2016 Event Name KMT Name qlog10( ) s Degeneracy References OB160007 KB161991 −5.17 2.83 W. Zang et al. (2023, in preparation) OB161195a KB160372 −4.34 0.99 c/w, ecliptic Gould et al. (2023) OB161850 KB161307 −4.00 0.80 i/o, ecliptic This work MB16319 KB161816 −2.41 0.82 i/o Han et al. (2018) MB16532 KB160506 −2.39 0.65 c/w This work KB161836 −2.35 1.30 c/w, ecliptic Yang et al. (2020) MB16227 KB160622 −2.03 0.93 Koshimoto et al. (2017) OB160596 KB161677 −1.93 1.08 Mróz et al. (2017) KB162605 −1.92 0.94 Ryu et al. (2021) OB161190 KB160113 −1.84 0.60 Ecliptic Ryu et al. (2018) OB161635 KB160269 −1.59 0.59 c/w This work KB160625 −3.63 0.74 c/w This work OB160613b KB160017 −2.26 1.06 c/w Han et al. (2017) KB161751 −2.19 1.05 c/w This work KB161855c −1.61 3.80 c/w, α, offset, 1L2S This work KB160212 −1.43 0.83 c/w Hwang et al. (2018) KB161820 −0.95 1.40 Jung et al. (2018) KB162142c −0.69 0.97 c/w Jung et al. (2018) Notes. a The properties of the planetary system OB161195 were reported by Shvartzvald et al. (2017) and Bond et al. (2017). However, we adopt qlog10( ) and s values from Gould et al. (2023), who reanalyzed the event and measured a more precise mass ratio. b For OB160613, the event was caused by a lens system consisting of a planet and binary host stars. c For KB161855 and KB162142, these are planet candidates. In the Degeneracy column, we present the types of degeneracy for the solutions; “c/w,” “i/o,” “ecliptic,” “offset,” “α,” and “1L2S” indicate the close/wide, inner/outer, ecliptic of the microlens parallax effect, offset, α (see Section 3.7), and 2L1S/1L2S degeneracies, respectively. 22 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. M dwarf host (Mhost∼ 0.18Me). The system is located at a distance of ∼7.05 kpc. Our goal in the series, including this work, is to build a complete planet sample discovered by the microlensing method for the 2016–2021 KMTNet data archive. As discussed in Zang et al. (2021) and Hwang et al. (2022), such a sample can be used to study the mass-ratio function of microlensing planets. Hence, this work is part of the process of constructing such a sample from the AnomalyFinder candidates. In Table 12, we present all microlensing planets discovered on the KMTNet prime fields in 2016, which are published planets that are recovered by the AnomalyFinder and the five newly discovered in this work. The horizontal line separates the planets expected to be part of the final statistical sample and those whose mass ratios are likely too uncertain or large to be included. As discussed in Clanton & Gaudi (2014a, 2014b) and Shin et al. (2019), each planet detection method has a different detection sensitivity, which provides complementary planet samples for studying planet demographics and frequency in our Galaxy. Our works are important for a complete microlensing planet sample. Indeed, although the sample size of microlen- sing planets is relatively small compared to other methods, such as radial velocity and transits, the microlensing planet sample is less biased to host mass because, in principle, the microlensing method can detect any foreground objects regardless of their host brightness. Thus, a complete microlen- sing planet sample can help us to obtain a better understanding of planet demographics in our Galaxy. Acknowledgments This research has made use of the KMTNet system operated by the Korea Astronomy and Space Science Institute (KASI), and the data were obtained at three host sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia. I.-G.S., S.-J.C., and J.C.Y. acknowledge support from NSF grant No. AST- 2108414. Work by C.H. was supported by grants of the National Research Foundation of Korea (2017R1A4A1015178 and 2019R1A2C2085965). Y.S. acknowledges support from BSF grant No. 2020740. W.Z. and H.Y. acknowledge support by the National Science Foundation of China (grant No. 12133005). The MOA project is supported by JSPS KAKENHI grant Nos. JP24253004, JP26247023, JP23340064, JP15H00781, JP16H06287, JP17H02871, and JP22H00153. The computations in this paper were conducted on the Smithsonian High Performance Cluster (SI/HPC), Smithsonian Institution (https://doi.org/10.25572/SIHPC). Appendix A Nonplanetary Events We report on the analysis of binary lens events that are found by AnomalyFinder as candidate planetary events. From the initial analyses, we find that the light curves of these events could be describing both binary and planet lens interpretations. However, based on analyses using TLC reductions, we find that these events disfavor planetary solutions (q< 0.03) by Δχ2> 10. Thus, we cannot claim certain detection of the planets. In Table 2, we present observational information on these events. A.1. OGLE-2016-BLG-0987 The light curve of OGLE-2016-BLG-0987 (which we identified as KMT-2016-BLG-0020) shows deviations from the 1L1S interpretation ( 159.681L1S 2L1S 2cD =- ). From the 2L1S modeling, we find several 2L1S solutions that can explain the deviations. Among the solutions, four are binary lens cases, and three are planet lens cases. The best-fit solution is the binary lens case with (s, q)= (0.492± 0.013, 0.108± 0.005). However, the lowest χ2 planetary solution ((s, q(× 10−4)= (0.702± 0.081, 59.198± 49.265)) shows Δχ2= 26.60 compared to the best-fit solution. The Δχ2 cannot satisfy our criterion to claim the planet detection. Also, the planetary solutions cannot describe the subtle bump feature at HJD′∼ 7,528. Thus, we conclude that OGLE-2016-BLG- 0987 should be removed from the planet sample. We note that, although this event is not likely to be caused by a planetary lens system, the best-fit solution indicates that the companion could be a low-mass object such as a brown dwarf. A.2. MOA-2016-BLG-123 For this event (which we identified as KMT-2016-BLG- 0106), we find seven local solutions based on analysis using the TLC reductions. However, not all local minima satisfy our q criterion (i.e., q< 0.03) for claiming a planet detection. The best-fit solution indicates that the event was caused by a binary lens system, i.e., (s, q)= (2.671± 0.089, 1.113± 0.099). Among the local minima, the model showing the lowest q value (q= 0.052± 0.003) is disfavored by Δχ2= 122.70 compared to the best-fit solution. Thus, we conclude that this event should be removed from the planet sample. A.3. OGLE-2016-BLG-0558 For this event (which we identified as KMT-2016-BLG- 0157), we found two solutions that showed a planet-like mass ratio (q∼ 0.03) from the initial analysis. We therefore refine the solutions based on the TLC reductions. The analysis using the TLC reductions clearly shows localized solutions (i.e., s± cases) with (s, q)= (0.580± 0.009, 0.048± 0.003) and (2.158± 0.027, 0.057± 0.003) for the s− and s+ cases, respectively. However, the mass ratios do not satisfy our criterion (q< 0.03) to claim the planet detection, although the companion is likely to be a low-mass object such as a brown dwarf. Hence, we remove this event from the planet sample. A.4. KMT-2016-BLG-0374 We find plausible solutions within the planetary regime (q< 0.03) from the initial analysis. However, based on the analysis using TLC reductions, we find that the best-fit solutions are binary lens cases with (s, q)= (6.89, 0.55) and (0.20, 0.22) for the s+ and s− cases, respectively. We also find that the planet-like models are disfavored by Δχ2= 19.74 and 18.60 for the s+ and s− cases, respectively. The planet-like solutions cannot satisfy the criterion for the planet detection. Thus, we remove this event from our planet samples. A.5. KMT-2016-BLG-0446 The AnomalyFinder detects a subtle deviation of the light curve at HJD′∼ 7,631.0–7,636.0 based on the pipeline data. The anomaly can be explained by planetary models. However, the TLC reductions reveal that the anomaly is a false positive. 23 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. https://doi.org/10.25572/SIHPC Then, we find that the light curve can be explained by the 1L1S interpretation rather than any 2L1S interpretations. Thus, we remove KMT-2016-BLG-0446 from our sample. A.6. OGLE-2016-BLG-1722 We find that the best-fit solution of OGLE-2016-BLG-1722 (which we identified as KMT-2016-BLG-1716) is caused by a binary lens with the mass ratio q= 1.247± 0.204 (i.e., q∼ 0.80) for the s− case (the competing s+ solution also exists). The best-fit light curves are caused by approaching a diamond-shaped caustic. Thus, a fourfold degeneracy exists (i.e., four solutions with different source trajectories for different α values). We also find alternative planetary solutions with the mass ratio q= (26.095± 8.013)× 10−4 for the s− case. However, 29.23planet binary 2 ( )cD =- . The Δχ2 cannot satisfy our criterion (Δχ2< 10) to claim a planet detection. Indeed, these planetary models clearly show worse fits in their residuals. Hence, we decide to remove OGLE-2016-BLG-1722 from our planet candidate sample for full analysis. A.7. OGLE-2016-BLG-0974 The best-fit solution of OGLE-2016-BLG-0974 (which we identified as KMT-2016-BLG-1863) is a binary lens model with (s, q)= (0.277± 0.005, 0.306± 0.031). There is an s+ solution, (s, q)= (5.626± 0.215, 0.782± 0.133), with Δχ2= 6.96 caused by the close/wide degeneracy. We find that the solutions having the lowest χ2 in the planetary regime (q< 0.03) are disfavored by Δχ2= 78.89 and 73.52 for the s−: [s, q]= [0.576± 0.007, (161.679± 8.552)× 10−4] and s+: [s, q]= [1.657± 0.025, (176.374± 10.013)× 10−4] cases, respectively. Thus, we conclude that OGLE-2016-BLG-0974 is caused by a binary rather than a planetary lens system. Appendix B OGLE-2016-BLG-0185 We also present the analysis of OGLE-2016-BLG-0185, which was identified by eye as a planet candidate but not selected as anomalous in the AnomalyFinder process. We conduct a detailed analysis based on TLC reductions for this event. We find that the best-fit solution is a binary lens case Figure 17. Comparison of light curves between AnomalyFinder (1L1S) and the best fit (2L1S) for OGLE-2016-BLG-0185. Note that the data sets shown in this figure are produced by the KMTNet pipeline, which is actually used for the AnomalyFinder process. 24 The Astronomical Journal, 166:104 (26pp), 2023 September Shin et al. with (s, q)= (4.834± 0.201, 3.480± 1.110). This is equivalent to 0.287 0.085 q 1 =  , which clearly implies a binary lens origin. We also search for a planetary model. The best planetary model that satisfies our mass-ratio criterion has (s, q)= (0.724± 0.037, 0.013± 0.004) but is disfavored by Δχ2= 46 compared to the best-fit model. Thus, we conclude that this event was caused by a binary lens system. Although OGLE-2016-BLG-0185 turned out to be a binary lens event, it is still an important test case for verifying the AnomalyFinder process and assessing possible failure modes. In fact, the AnomalyFinder algorithm did identify a series of possible anomalies in this event, but the human operator rejected them as “fake.” In OGLE-2016-BLG-0185, the anomaly occurs over the peak of the event, but because the event occurs early in the microlensing season, it is only sparsely covered, and the primary deviation from a point lens only occurs in the KMTA data sets. In addition, the event has a short timescale. Hence, due to the χ2 likelihood estimation, a point lens fit is biased toward the points at the peak (which have the smallest error bars) and the baseline points (which dominate the numbers), so it normalized the flux levels of the KMTA data so that the peak points (due to the anomaly) lay on the point lens light curve. As a result, the “anomalies” identified by the AnomalyFinder were in the rising and falling parts of the light curve and caused by the bad flux normalization rather than the actual anomaly (see Figure 17). OGLE-2016-BLG-0185 is qualitatively similar to KMT- 2021-BLG-2294, which was also missed by the Anomaly- Finder process (Shin et al. 2023). They are both short-timescale events (tE= 10.8± 1.3 and 7.1± 0.3 days, respectively) and had anomalies that occurred at the peak of the events. On the other hand, the reasons the anomalies were missed are distinctly different: in OGLE-2016-BLG-0185, the wrong anomaly was identified, but in KMT-2021-BLG-2294, the anomaly did not meet the detection threshold. The latter case is acceptable from the perspective of constructing a statistical sample of events. However, the failure for OGLE-2016-BLG- 0185 is more concerning but could be compensated for by adding an additional criterion to the AnomalyFinder algorithm to check for outliers in flux normalization. ORCID iDs In-Gu Shin https://orcid.org/0000-0002-4355-9838 Jennifer C. Yee https://orcid.org/0000-0001-9481-7123 Weicheng Zang https://orcid.org/0000-0001-6000-3463 Hongjing Yang https://orcid.org/0000-0003-0626-8465 Kyu-Ha Hwang https://orcid.org/0000-0002-9241-4117 Cheongho Han https://orcid.org/0000-0002-2641-9964 Andrzej Udalski https://orcid.org/0000-0001-5207-5619 Michael D. Albrow https://orcid.org/0000-0003-3316-4012 Sun-Ju Chung https://orcid.org/0000-0001-6285-4528 Yoon-Hyun Ryu https://orcid.org/0000-0001-9823-2907 Yossi Shvartzvald https://orcid.org/0000-0003-1525-5041 Seung-Lee Kim https://orcid.org/0000-0003-0562-5643 Chung-Uk Lee https://orcid.org/0000-0003-0043-3925 Byeong-Gon Park https://orcid.org/0000-0002-6982-7722 Richard W. Pogge https://orcid.org/0000-0003-1435-3053 Michał K. Szymański https://orcid.org/0000-0002- 0548-8995 Jan Skowron https://orcid.org/0000-0002-2335-1730 Radosław Poleski https://orcid.org/0000-0002-9245-6368 Igor Soszyński https://orcid.org/0000-0002-7777-0842 Paweł Pietrukowicz https://orcid.org/0000-0002-2339-5899 Szymon Kozłowski https://orcid.org/0000-0003- 4084-880X Patryk Iwanek https://orcid.org/0000-0002-6212-7221 Krzysztof Ulaczyk https://orcid.org/0000-0001-6364-408X Marcin Wrona https://orcid.org/0000-0002-3051-274X Mariusz Gromadzki https://orcid.org/0000-0002-1650-1518 Richard Barry https://orcid.org/0000-0003-4916-0892 David P. 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