11institutetext:  Department of Physics, Chungbuk National University,
Cheongju 28644, Republic of Korea 22institutetext: Korea Astronomy and Space
Science Institute, Daejon 34055, Republic of Korea 33institutetext: Korea
University of Science and Technology, Korea, (UST), 217 Gajeong-ro, Yuseong-
gu, Daejeon, 34113, Republic of Korea 44institutetext: Institute of Natural
and Mathematical Science, Massey University, Auckland 0745, New Zealand
55institutetext: Max-Planck-Institute for Astronomy, Königstuhl 17, 69117
Heidelberg, Germany 66institutetext: Department of Astronomy, Ohio State
University, 140 W. 18th Ave., Columbus, OH 43210, USA 77institutetext:
University of Canterbury, Department of Physics and Astronomy, Private Bag
4800, Christchurch 8020, New Zealand 88institutetext: Center for Astrophysics
$|$ Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
99institutetext: Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, Rehovot 76100, Israel 1010institutetext: Department of
Astronomy, Tsinghua University, Beijing 100084, China 1111institutetext:
School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104,
Republic of Korea 1212institutetext: Institute for Space-Earth Environmental
Research, Nagoya University, Nagoya 464-8601, Japan 1313institutetext: Code
667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
1414institutetext: Department of Astronomy, University of Maryland, College
Park, MD 20742, USA 1515institutetext: Department of Earth and Planetary
Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan 1616institutetext: Instituto de Astrofísica
de Canarias, Vía Láctea s/n, E-38205 La Laguna, Tenerife, Spain
1717institutetext: Department of Earth and Space Science, Graduate School of
Science, Osaka University, Toyonaka, Osaka 560-0043, Japan 1818institutetext:
Department of Physics, The Catholic University of America, Washington, DC
20064, USA 1919institutetext: Institute of Space and Astronautical Science,
Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara,
Kanagawa 252-5210, Japan 2020institutetext: Sorbonne Université, CNRS, UMR
7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France
2121institutetext: Department of Physics, University of Auckland, Private Bag
92019, Auckland, New Zealand 2222institutetext: University of Canterbury Mt.
John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand

# MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planets

Cheongho Han MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planets Youn Kil Jung MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Ian A. Bond MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Andrew Gould
(Leading authors)
Michael D. Albrow MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Sun-Ju Chung MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Kyu-Ha
Hwang MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Chung-Uk
Lee MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yoon-Hyun
Ryu MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets In-Gu Shin
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yossi
Shvartzvald MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planets Hongjing Yang MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Jennifer C. Yee MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Weicheng Zang
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Sang-Mok
Cha MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Doeon Kim
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Dong-Jin Kim
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Seung-Lee Kim
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Dong-Joo Lee
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yongseok Lee
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Byeong-Gon
Park MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Richard W.
Pogge
(The KMTNet collaboration)
Fumio Abe MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Richard Barry MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets David P.
Bennett MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Aparna Bhattacharya MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Hirosame
Fujii MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Akihiko
Fukui MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Ryusei
Hamada MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yuki Hirao
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Stela Ishitani
Silva MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yoshitaka
Itow MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Rintaro
Kirikawa MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planets Naoki Koshimoto MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Yutaka Matsubara MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Shota Miyazaki
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Yasushi Muraki
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Greg Olmschenk
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Clément Ranc
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Nicholas J.
Rattenbury MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planets Yuki Satoh MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planets Takahiro Sumi MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Daisuke Suzuki
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Mio Tomoyoshi
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Paul J.
Tristram MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb:
Three sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planets Aikaterini Vandorou MOA-2022-BLG-563Lb,
KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass
microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing
planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Hibiki
Yama MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three
sub-Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb,
and KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets Kansuke
Yamashita
(The MOA Collaboration)
MOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and KMT-2023-BLG-0735Lb: Three sub-
Jovian-mass microlensing planetsMOA-2022-BLG-563Lb, KMT-2023-BLG-0469Lb, and
KMT-2023-BLG-0735Lb: Three sub-Jovian-mass microlensing planets

###### Abstract

Aims.  We analyze the anomalies appearing in the light curves of the three
microlensing events MOA-2022-BLG-563, KMT-2023-BLG-0469, and
KMT-2023-BLG-0735. The anomalies exhibit common short-term dip features that
appear near the peak.

Methods.  From the detailed analyses of the light curves, we find that the
anomalies were produced by planets accompanied by the lenses of the events.
For all three events, the estimated mass ratios between the planet and host
are on the order of $10^{-4}$: $q\sim 8\times 10^{-4}$ for MOA-2022-BLG-563L,
$q\sim 2.5\times 10^{-4}$ for KMT-2023-BLG-0469L, and $q\sim 1.9\times
10^{-4}$ for KMT-2023-BLG-0735L. The interpretations of the anomalies are
subject to a common inner-outer degeneracy, which causes ambiguity when
estimating the projected planet-host separation.

Results.  We estimated the planet mass, $M_{\rm p}$, host mass, $M_{\rm h}$,
and distance, $D_{\rm L}$, to the planetary system by conducting Bayesian
analyses using the observables of the events. The estimated physical
parameters of the planetary systems are $(M_{\rm h}/M_{\odot},M_{\rm p}/M_{\rm
J},D_{\rm L}/{\rm
kpc})=(0.48^{+0.36}_{-0.30},0.40^{+0.31}_{-0.25},6.53^{+1.12}_{-1.57})$ for
MOA-2022-BLG-563L,
$(0.47^{+0.35}_{-0.26},0.124^{+0.092}_{-0.067},7.07^{+1.03}_{-1.19})$ for
KMT-2023-BLG-0469L, and
$(0.62^{+0.34}_{-0.35},0.125^{+0.068}_{-0.070},6.26^{+1.27}_{-1.67})$ for
KMT-2023-BLG-0735L. According to the estimated parameters, all planets are
cold planets with projected separations that are greater than the snow lines
of the planetary systems, they have masses that lie between the masses of
Uranus and Jupiter of the Solar System, and the hosts of the planets are main-
sequence stars that are less massive than the Sun. In all cases, the planetary
systems are more likely to be in the bulge with probabilities $P_{\rm
bulge}=64\%$, 73%, and 56% for MOA-2022-BLG-563, KMT-2023-BLG-0469, and
KMT-2023-BLG-0735, respectively.

###### Key Words.:

planets and satellites: detection – gravitational lensing: micro

##  1 Introduction

Because of its trait that does not depend on the luminosity of a lensing
object, microlensing provides an important tool to detect extrasolar planets.
Planetary microlensing (Mao & Paczyński, 1991; Gould & Loeb, 1992) was
proposed before the first discoveries of an exoplanet belonging to a pulsar
(Wolszczan & Frail, 1992) and a planet belonging to a normal stellar system
(Mayor & Queloz, 1995), but the first microlensing planet was only discovered
in 2004 (Bond et al., 2004), that is, 12 years after the operation of the
first-generation microlensing surveys, for example, Massive Compact Halo
Objects (MACHO: Alcock et al., 1993), Optical Gravitational Lensing Experiment
(OGLE: Udalski et al., 1994), and Expérience pour la Recherche d’Objets
Sombres (EROS: Aubourg et al., 1993). The difficulty of finding planets from
these early microlensing surveys was mostly ascribed to the low cadence of the
surveys, which were typically carried out with a 1 day cadence, while the
duration of a planet-induced lensing signal is several hours for terrestrial
planets and several days even for giant planets. In order to increase the
observational cadence, planetary microlensing experiments during the time from
the mid 1990s to mid 2010s had been carried out in a hybrid mode (Gould &
Loeb, 1992; Albrow et al., 1998), in which survey experiments with a low
observational cadence mainly focused on detecting lensing events, and follow-
up groups conducted high-cadence observations for a fraction of events
detected by the survey experiments.

Table 1: Coordinates, baseline magnitude, and extinction.  Event |  (RA, DEC)J2000 | $(l,b)$ | $I_{\rm base}$ | $A_{I}$
---|---|---|---|---
MOA-2022-BLG-563 | (18:01:12.05, -27:50:08.99) | $(2^{\circ}\hskip-2.0pt.687,-2^{\circ}\hskip-2.0pt.395)$ | 18.12 | 1.25
KMT-2023-BLG-0469 | (17:57:37.63, -28:42:54.22) | $(1^{\circ}\hskip-2.0pt.533,-2^{\circ}\hskip-2.0pt.149)$ | 18.45 | 1.50
KMT-2023-BLG-0735 | (17:50:18.23, -29:12:10.51) | $(0^{\circ}\hskip-2.0pt.301,-1^{\circ}\hskip-2.0pt.014)$ | 19.79 | 5.97

Planetary microlensing experiments entered a new phase in the mid 2010s by
dramatically increasing the observational cadence of lensing surveys with the
employment of globally distributed multiple telescopes that are equipped with
very wide-field cameras. With the upgraded instrument, the current lensing
surveys achieve observational cadences down to 0.25 hr, which is two orders of
magnitude shorter than the cadence of the early experiments. The operation of
the high-cadence surveys has led to the great increase in the event detection
rate, and the number of lensing events that are annually detected by the
current lensing surveys is more than 3000, which is nearly two orders of
magnitude higher than the rate of the early surveys. Being able to monitor a
large number of lensing events with enhanced cadences, the detection rate of
planets has also greatly increased. According to the NASA Exoplanet
Archive111exoplanetarchive.ipac.caltech.edu, the number of microlensing
planets that have been detected since the full operation of the high-cadence
surveys in 2016 is 137, and this is more than two times the 64 planets found
from the previous experiments that had been conducted for 24 years from the
year 1992 to 2015. Considering that the high-cadence surveys were partially
operated in 2020 due to the COVID pandemic and the data collected in the 2022
and 2023 season are under analysis, the current surveys are annually detecting
about 30 planets on average (Gould et al., 2022; Jung et al., 2022).

The growing number of microlensing planets reveals similar anomaly patterns in
certain planetary signals. Han et al. (2021a) outlined instances of planetary
signals emerging via a non-caustic-crossing channel in their analysis of two
lensing events KMT-2022-BLG-0475 and KMT-2022-BLG-1480. Similarly, Han et al.
(2021a) depicted analogous occurrences of non-caustic-crossing signals in
their study of the three planetary lensing events KMT-2018-BLG-1976,
KMT-2018-BLG-1996, and OGLE-2019-BLG-0954. In their examination of the the
three planetary events KMT-2017-BLG-2509, OGLE-2017-BLG-1099, and
OGLE-2019-BLG-0299, Han et al. (2021a) presented various instances where
planetary signals emerged from source crossings over resonant caustics formed
by giant planets near the Einstein rings of host stars. Jung et al. (2021)
demonstrated planetary signals arising from perturbations by peripheral
caustics induced by planets in their analyses of two lensing events
OGLE-2018-BLG-0567 and OGLE-2018-BLG-0962. Moreover, in the cases of
KMT-2018-BLG-1743 and KMT-2021-BLG-1898, Han et al. (2021a) and Han et al.
(2021a), respectively, highlighted two microlensing planets with signals
deformed by companions to the source stars. Additionally, Han et al. (2017)
presented an exemplary case of a planetary signal arising through a repeating
channel from the analysis of the microlensing planet OGLE-2016-BLG-0263Lb.
These various studies collectively underscore the diverse mechanisms and
complexities observed in detecting microlensing planets.

Microlensing planets are found from detailed analyses of anomalous signals
appearing in numerous lensing light curves. These analyses are done via a
complex procedure and require heavy computations in order to identify the
planetary origin of signals by distinguishing them from signals of other
origins. Therefore, morphological studies by classifying lensing events with
similar anomalies and investigating the origins for the individual classes of
anomalies are important not only for the diagnosis of anomalies before
detailed analysis but also for the accurate characterization of lens systems
for future lensing events with similar anomaly structures.

In this work, we conduct analyses of the three compiled planetary microlensing
events that were detected from short-term signals exhibiting similar anomaly
features, including MOA-2022-BLG-563 KMT-2023-BLG-0469 and KMT-2023-BLG-0735.
These events share similar characteristics, in which the anomalies showed up
near the peaks of the lensing light curves and they exhibit similar dip
features surrounded by peaks on both sides of the dips. We present the common
characteristics of the planetary systems that are found from the detailed
analyses of the anomalies.

We present the analyses of the lensing events according to the following
organization. In Sect. 2, we describe the observations conducted to acquire
the data used in the analyses, and mention the instruments used for the
observations and the procedure of data reduction and error-bar normalization.
In Sect. 3, we begin by briefly mentioning planetary lensing properties and
introducing parameters used in the modeling of the lensing light curves. In
the subsequent subsections, we present detailed analyses conducted for the
individual events: in Sect. 3.1 for MOA-2022-BLG-563, in Sect. 3.2 for
KMT-2023-BLG-0469, and in Sect. 3.3 for KMT-2023-BLG-0735. In Sect. 4, we
characterize the source stars of the events and estimate the angular Einstein
radii. In Sect. 5, we determine the physical parameters of the planetary
system by conducting Bayesian analyses for the individual events. We summarize
the results found from the analyses and conclude in Sect. 6.

##  2 Observations and data

The anomalous nature of the three lensing events MOA-2022-BLG-563,
KMT-2023-BLG-0469, and KMT-2023-BLG-0735 were found from the inspection of the
data obtained from the two high-cadence lensing surveys conducted toward the
Galactic bulge field by the Korea Microlensing Telescope Network (KMTNet: Kim
et al., 2016) group and the Microlensing Observations in Astrophysics (MOA:
Bond et al., 2001) group. Among these events, KMT-2023-BLG-0469 and
KMT-2023-BLG-0735 were observed solely by the KMTNet group, and
MOA-2022-BLG-563 was observed by both survey groups. The KMTNet ID reference
corresponding to the event MOA-2022-BLG-563 is KMT-2022-BLG-2681, and,
hereafter, we use the MOA ID reference because the event was first discovered
by the MOA group. In Table 1, we list the equatorial and galactic coordinates
of the events together with the $I$-band baseline magnitudes, $I_{\rm base}$,
and extinction, $A_{I}$, toward the source stars. The $I$-band extinction is
estimated as $A_{I}=7\,A_{K}$, where the $K$-band extinction $A_{K}$ is
adopted from Gonzalez et al. (2012).

The KMTNet observations of the events were carried out using three identical
1.6 m telescopes, which are globally distributed in the three continents of
the Southern Hemisphere: at the Cerro Tololo Inter-American Observatory in
Chile, the South African Astronomical Observatory in South Africa, and the
Siding Spring Observatory in Australia. We designate the individual KMTNet
telescopes as KMTC, KMTS, and KMTA using the initials of the countries in
which the telescopes are located. The MOA observations were done using the 1.8
m telescope of the Mt. John Observatory located in New Zealand. The fields of
view of the cameras mounted on the KMTNet telescopes and the MOA telescope are
4 deg2 and 2.2 deg2, respectively. We describe details of the observations
conducted for the individual events in the following section.

Reduction of images and photometry of the source stars were carried out using
the photometry codes of the individual groups, which were developed by Albrow
et al. (2009) for the KMTNet survey and by Bond et al. (2001) for the MOA
survey. For a fraction of the KMTC data set, additional photometry using the
pyDIA code (Albrow et al., 2017) was done to construct color-magnitude diagram
(CMD) of stars lying near the source stars and to determine the source colors.
For the data used in the analyses, the error bars estimated from the
photometry pipelines were readjusted so that they are consistent with the
scatter of the data and $\chi^{2}$ per degree of freedom (dof) for each data
set becomes unity. This error-bar normalization process was done following the
routine depicted in detail by Yee et al. (2012).

##  3 Anomaly analysis

The image of a microlensed source star is split into two, in which the
brighter one (major image) appears outside of the Einstein ring, and the
fainter one (minor image) appears inside the ring. Planet-induced anomalies in
a lensing light curve arise when a planet lies close to one of these two
source images. The ”major-image perturbation” refers to the case in which the
planet perturbs the major image, and the ”minor-image perturbation” indicates
the case in which the planet perturbs the minor image (Gaudi & Gould, 1997).
When the planet perturbs the major image, the image is further magnified by
the planet, and this results in a bump feature (positive deviations) of the
anomaly. When the planet disturbs the minor image, by contrast, the image is
demagnified, and this results in a dip feature (negative deviations) of the
anomaly. Because the major image lies outside the Einstein ring, the bump
feature of a planetary anomaly is generally produced by a ”wide planet”, for
which the projected planet-host separation is greater than the Einstein
radius. By contrast, the dip feature of an anomaly is generated by a ”close
planet”, for which the separation is smaller than the Einstein radius, because
the minor image lies inside the Einstein ring. See the appendix of Han et al.
(2018) for more detailed discussion on the types of planetary perturbations.

As viewed on the source plane, planet-induced anomalies arise when the source
approaches the planet-induced caustics. Caustics refer to the source positions
at which the lensing magnifications of a point source are infinite. Planet-
induced caustics form two sets of caustics, in which the ”central caustic”
forms near the position of the planet host, and the ”planetary caustic” forms
away from the host at the position $\sim(1-1/s^{2}){\bf s}$. Here ${\bf s}$
denotes the position vector of the planet from the host with a length
normalized to the angular Einstein radius $\theta_{\rm E}$ of the planetary
lens system. For detailed descriptions on the position, size, and shape of the
central and planetary caustics, see Chung et al. (2005) and Han (2006).

There exist multiple known channels that can produce short-term anomalies in
lensing light curves. Besides the planetary channel, it is known that bump-
featured anomalies can be produced via a 1L2S channel, in which the lens
system is composed of a single-mass lens and binary source, and the bump
feature can be generated by the close approach of the faint source companion
to the lens (Gaudi et al., 1998). Dip-featured anomalies can be produced not
only by a planet but also by a binary companion to the lens, although the two
features can be usually distinguished from the shape of the dip feature (Han &
Gaudi, 2008).

The events analyzed in this work share a common characteristics that short-
term anomalies with dip features appear near the peaks of the lensing light
curves. Considering that a dip-featured anomaly is produced by a lens with
either a binary companion or a planet, we conduct a binary-lens single-source
(2L1S) modeling of the light curves for the interpretations of the observed
anomalies. For each lensing event, the modeling was done in search of a
lensing solution, which refers to a set of the lensing parameters that define
the light curve of the event. Under the approximation of the rectilinear
relative motion between the lens and source, the light curve of a 2L1S event
is characterized by 7 lensing parameters. The first set of the three
parameters $(t_{0},u_{0},t_{\rm E})$ define the source approach to the lens,
and the individual parameters denote the time of the closest lens-source
approach, the separation at that time (impact parameter), and the event time
scale, respectively. The second set of the three parameters $(s,q,\alpha)$
define the binary lens, and the first two parameters represent the projected
separation and mass ratio between the binary-lens components ($M_{1}$ and
$M_{2}$), respectively, and the other parameter denotes the angle (source
trajectory angle) between the direction of the relative lens-source proper
motion vector $\mu$ and the $M_{1}$–$M_{2}$ axis. The lengths of $u_{0}$ and
$s$ are scaled to the Einstein radius. The last parameter $\rho$ is defined as
the ratio of the angular source radius $\theta_{*}$ to the Einstein radius,
that is, $\rho=\theta_{*}/\theta_{\rm E}$ (normalized source radius), and it
describes the deformation of a lensing light curve by finite-source effects
during source crossings over caustics or close approaches to caustics.

Among the lensing parameters, we search for the binary parameters $s$ and $q$
via a grid approach with multiple starting values of $\alpha$, and find the
other parameters via a downhill approach. In the downhill approach, $\chi^{2}$
is minimized using the Markov Chain Monte Carlo (MCMC) method with an adaptive
step size Gaussian sampler (Doran & Mueller, 2004). We then refine the local
solutions appearing in the $\Delta\chi^{2}$ map on the plane of the grid
parameters, and then find a global solution by comparing the $\chi^{2}$ values
of the individual local solutions. The anomalies of the all analyzed events
appear near the peaks of the lensing light curves. Such central anomalies are
known to be produced by a planetary companion lying around the Einstein ring
of the planet host or a very close or wide binary companion to the primary
lens. In order to check both the planetary and binary origins of the
anomalies, we set the ranges of the grid wide enough to check both possible
origins of the anomalies: $-1.0<\log s\leq 1.0$ and $-5.0<\log q\leq 1.0$. For
the case that multiple solutions with similar $\chi^{2}$ values exist, we
present all degenerate solutions.

In the following subsections, we present the analyses conducted for the
individual events. We describe in detail the features of the anomalies
residing in the light curves and present the results found from the modeling.
For events with multiple identified solutions, we explain the cause of the
degeneracy among the solutions.

Figure 1:  Light curve of MOA-2022-BLG-563. The top panel shows the whole
view, and the lower panels show the zoom-in view around the anomaly and the
residuals from the 2L1S and 1L1S models. The solid and dashed curves drawn
over the data points are the 2L1S and 1L1S models, respectively. The colors of
data points are set to match the labels of the observatories in the legend.

###  3.1 MOA-2022-BLG-563

The lensing event MOA-2022-BLG-563 was first found on 2022 October 14, which
corresponds to the abridged Heliocentric Julian day ${\rm
HJD}^{\prime}\equiv{\rm HJD}-2450000\sim 9866$, by the MOA group, and was
later identified by the KMTNet group from the post-season analysis of the 2022
season data (Kim et al., 2018). The source position of the event corresponds
to the KMTNet prime fields of BLG03 and BLG43, toward which observations were
conducted with a 0.5 hr cadence for each field and a 0.25 hr cadence in
combination. The MOA observations were conducted with a similar cadence. The
event occurred during the late stage of the 2022 bulge season, and thus the
declining part of the light curve after ${\rm HJD}^{\prime}\sim 9878$ could
not be covered. The source brightness returned to the baseline in the
beginning of the 2023 season, and thus we do not include the 2023 season data
in the analysis. We included the KMTC $V$-band data in the analysis because
one data point lies in the region of the anomaly. Although the event lies in
the field that usually is observed frequently, there are gaps among the data
sets because of the short duration of observation time at the late stage of
the bulge season.

The lensing light curve of MOA-2022-BLG-563 is shown in Figure 1. The event
reached a moderate magnification of $A_{\rm max}\sim 5.5$ at the peak. From
the inspection of the light curve, we find that the peak region of the light
curve displays a short-term deviation from a single-lens single-source (1L1S)
model. The anomaly is characterized by a dip feature centered at ${\rm
HJD}^{\prime}\sim 9871.5$ and double peaks lying on both sides of the dip. The
time gap between the peaks is about $0.8$ day. The dip part of the anomaly was
covered by the KMTC data, and the peaks were covered by the MOA data. Besides
these main features, the data before and after the peaks show weak positive
deviations from the 1L1S model.

Figure 2:  $\Delta\chi^{2}$ maps on the $(\log s,\log q)$ parameter plane for
the events MOA-2022-BLG-563 (top panel), KMT-2023-BLG-0469 (middle panel), and
KMT-2023-BLG-0735 (bottom panel). Color coding is set to indicate points with
$\Delta\chi^{2}\leq 1^{2}n$ (red), $\leq 2^{2}n$ (yellow), $\leq 3^{2}n$
(green), $\leq 4^{2}n$ (cyan), and $\leq 5^{2}n$ (blue), where $n=2$. The
dashed vertical line in each panel represents the geometric mean, $(s_{\rm
in}\times s_{\rm out})^{1/2}$, of the planet separations of the inner and
outer solutions.  Figure 3:  Lens-system configurations of MOA-2022-BLG-563.
The configurations of the inner and outer solutions are shown in the upper and
lower panels, respectively. In each panel, the red figures represent the
caustics, and the arrowed line is the source trajectory. Gray contours
encompassing the caustics represent equi-magnification contours. The
coordinates are centered at the center of mass of the planetary lens system,
and the lengths are scaled to the Einstein radius.  Table 2: Model parameters
of MOA-2022-BLG-563.

Parameter | Inner | Outer
---|---|---
$\chi^{2}$/dof | $5535.7/5355$ | $5536.7/5355$
$t_{0}$ (HJD′) | $9872.226\pm 0.041$ | $9872.214\pm 0.040$
$u_{0}$ | $0.123\pm 0.009$ | $0.124\pm 0.009$
$t_{\rm E}$ (days) | $19.72\pm 0.92$ | $19.58\pm 0.97$
$s$ | $0.886\pm 0.009$ | $0.986\pm 0.010$
$q$ ($10^{-4}$) | $8.06\pm 1.55$ | $7.41\pm 1.79$
$\alpha$ (rad) | $1.896\pm 0.022$ | $1.905\pm 0.025$
$\rho$ ($10^{-3}$) | – | –

222 ${\rm HJD}^{\prime}={\rm HJD}-2450000$.

From the modeling of the light curve, it was found that the anomaly was
produced by a planetary companion to the lens. We identified a pair of
degenerate solutions with binary parameters $(\log s,\log q)_{\rm
in}\sim(-0.050,-3.1)$ and $(\log s,\log q)_{\rm out}\sim(-0.005,-3.1)$. The
top panel of Figure 2 shows the positions of the two local solutions in the
$\Delta\chi^{2}$ map on the $(\log s,\log q)$ parameter plane. For the reason
discussed below, we designate the former and latter solutions as ”inner” and
”outer” solutions, respectively. In Table 2, we list the full lensing
parameters of the inner and outer solutions together with $\chi^{2}$ values of
the fits and degrees of freedom (dof). The two solutions are very degenerate,
and the inner solution is favored over the outer solution by only
$\Delta\chi^{2}=1.0$. The model curve of the inner solution is drawn over the
data points in Figure 1, and the residuals from the inner 2L1S and 1L1S
solutions in the region around the anomaly are shown in the lower two panels.

The upper and lower panels of Figure 3 show the lens-system configurations of
the inner and outer solutions, respectively. The configurations show that the
source passed the region between the central and planetary caustics according
to the inner solution, while the source passed the region outside the caustic
according to the outer solution. The planetary and central caustics of the
inner solution are well separated, while the two sets of caustics of the outer
solution merge together and form a single resonant caustic. The dip feature of
the anomaly was produced when the source passed through the negative deviation
region on the back-end side of the caustic, and the bump features were
produced when the source went through the positive deviation region extending
from the strong cusps of the caustic. The normalized source radius $\rho$
could have been measured if the event had occurred in mid-season, so that
there would be dense coverage over the cusp approach, but the large gaps among
the data sets together with the non-caustic-crossing nature of the anomaly
features made it difficult to measure $\rho$.

We find that the degeneracy between the two solutions originates from the
”inner-outer” degeneracy. This degeneracy was originally introduced by Gaudi &
Gould (1997) to point out the similarity between the planetary signals
resulting from the source passages through the near (inner) and far (outer)
sides of the planetary caustic. Yee et al. (2021) pointed out the continuous
transition between the inner-outer and close-wide degeneracies, where the
latter degeneracy originates from the similarity between the central caustics
induced by a pair of planets with separation $s$ and $1/s$ (Griest &
Safizadeh, 1998; Dominik, 1999; An, 2005). While the planetary separations of
the pair of solutions that are subject to the close-wide degeneracy follows
the relation $s_{\rm close}\times s_{\rm wide}=1$, the planetary separations
of the pair of solutions that are subject to the inner-outer degeneracy,
$s_{\rm in}$ and $s_{\rm out}$, follow the relation

$s_{\pm}^{\dagger}=(s_{\rm in}\times s_{\rm out})^{1/2}={\sqrt{u_{\rm
anom}^{2}+4}\pm u_{\rm anom}\over 2},$ (1)

where $u_{\rm anom}=(\tau_{\rm anom}^{2}+u_{0}^{2})^{1/2}$, $\tau_{\rm
anom}=(t_{\rm anom}-t_{0})/t_{\rm E}$, $t_{\rm anom}$ indicates the time of
the anomaly, and the signs in the right term are ”+” and ”$-$” for the
anomalies that are generated by the major and minor images perturbations,
respectively (Hwang et al., 2022; Gould et al., 2022). We note that for
$u_{\rm anom}\rightarrow 0$, we have $s^{\dagger}_{\pm}\rightarrow 1$, which
recovers the high-magnification limit of Griest & Safizadeh (1998). In the
case of MOA-2022-BLG-563, the sign is ”$-$” because the anomaly displayed a
dip feature produced by the minor-image perturbation. With the lensing
parameters $(t_{0},u_{0},t_{\rm E},t_{\rm
anom})\sim(9872.226,0.123,19.6,9871.3)$, we find $s^{\dagger}\sim 0.936$, and
this matches very well the geometric mean $(s_{\rm in}\times s_{\rm
out})^{1/2}\sim 0.935$. In the top panel of Figure 2, we mark the
$s^{\dagger}$ as a dashed vertical line.

Table 3: Model parameters of KMT-2023-BLG-0469.  Parameter | Inner | Intermediate | Outer
---|---|---|---
$\chi^{2}$/dof | $6664.6/6668$ | $6676.6/6668$ | $6652.3/6668$
$t_{0}$ (HJD′) | $10052.069\pm 0.005$ | $10052.080\pm 0.005$ | $10052.081\pm 0.005$
$u_{0}$ ($10^{-3}$) | $8.42\pm 0.20$ | $8.24\pm 0.22$ | $8.24\pm 0.21$
$t_{\rm E}$ (days) | $44.59\pm 1.03$ | $44.35\pm 0.93$ | $45.38\pm 1.09$
$s$ | $0.9501\pm 0.0016$ | $0.9831\pm 0.0009$ | $1.0285\pm 0.0014$
$q$ ($10^{-4}$) | $2.630\pm 0.088$ | $2.073\pm 0.078$ | $2.507\pm 0.087$
$\alpha$ (rad) | $0.521\pm 0.008$ | $0.522\pm 0.008$ | $0.521\pm 0.007$
$\rho$ ($10^{-3}$) | $0.765\pm 0.046$ | $0.692\pm 0.038$ | $0.674\pm 0.038$
Figure 4:  Light curve of KMT-2023-BLG-0469. The solid, dotted, and dashed
curves on the data points represent the models of the outer, intermediate, and
inner 2L1S solutions, respectively.

###  3.2 KMT-2023-BLG-0469

The lensing event KMT-2023-BLG-0469 was discovered by the KMTNet group on 2023
April 18 (${\rm HJD}^{\prime}\sim 10052$), near which the event reached its
maximum magnification of $A_{\rm max}\sim 120$. The source of the event lies
in a small (0.8 deg2) region that is covered by the four KMTNet prime fields
BLG02, BLG03, BLG42, and BLG43, and thus the event was observed very densely
with a combined cadence of 0.125 hr. See the layout of the KMTNet fields
presented in Figure 12 of Kim et al. (2018). As we discuss in Sect. 4, the
source is very faint and the baseline flux is heavily blended. As a result,
the source at the peak was brighter than the baseline by only $\sim 1.1$ mag
despite the high magnification of the event.

Figure 5:  Lens-system configurations of the inner (top panel), intermediate
(middle panel), and outer (bottom panel) solutions for the lensing event
KMT-2023-BLG-0469. Notations are same as those in Fig. 3.

The lensing light curve of KMT-2023-BLG-0469 is shown in Figure 4, in which
the top panel shows the whole view, and the second panel shows the zoom-in
view of the anomaly region appearing near the peak. Similar to the case of
MOA-2022-BLG-563, the anomaly is characterized by a dip feature and the
positive peaks appearing before and after the dip. The anomaly is centered at
$t_{\rm anom}\sim 10052.8$ in HJD′, and the time gap between the two peaks is
$\sim 1.2$ days. The second half of the first peak, which was covered by the
KMTS data sets, exhibits a sharply declining feature, indicating that the peak
was produced by the caustic crossing of the source. On the other hand, the
second peak exhibits a smoothly varying feature, suggesting that the peak was
produced by the cusp approach of the source.

From the analysis of the lensing light curve, we find that KMT-2023-BLG-0469
share common properties to those of the event MOA-2022-BLG-563 in the sense
that the anomaly was produced by a low-mass planetary companion and the
solution is subject to the inner-outer degeneracy. The planetary parameters of
the inner and outer solutions are $(s,q)_{\rm in}\sim(0.95,2.6\times 10^{-4})$
and $(s,q)_{\rm out}\sim(1.03,2.5\times 10^{-4})$, respectively. Regardless of
the solutions, the estimated planet-to-host mass ratio is much smaller than
the Jupiter/Sun mass ratio of $\sim 10^{-3}$, and this suggests that the
planet is less massive than Jupiter. We list the full lensing parameters of
the two solutions in Table 3. With the lensing parameters $(t_{0},u_{0},t_{\rm
E},t_{\rm anom})\sim(10052.07,8.42\times 10^{-3},44.6,10052.8)$, we find
$s^{\dagger}=0.991$, which matches well the geometric mean $(s_{\rm in}\times
s_{\rm out})^{1/2}\sim 0.989$, and this indicates that the degeneracy between
the two solutions is caused by the inner-outer degeneracy. We mark the
position of $s^{\dagger}$ on the $\Delta\chi^{2}$ map presented in the middle
panel of Figure 2.

Besides the two solutions resulting from the inner-outer degeneracy, we found
an additional degenerate solution. The $\Delta\chi^{2}$ map presented in the
middle panel of Figure 2 shows the three local solutions. The additional
solution has binary parameters $(s,q)_{\rm int}\sim(0.98,2.1\times 10^{-4})$.
We designate this solution as ”intermediate” solution because the planet
separation of the solution approximately corresponds to the mean of the inner
and outer solutions. We list the full lensing parameters of the intermediate
solution in Table 3. Among the three degenerate solutions, the outer solution
is preferred over the inner and intermediate solutions by
$\Delta\chi^{2}=12.3$ and 24.3, respectively. In Figure 4, we plot the model
curves and residuals of the outer (solid curve), intermediate (dotted curve),
and inner (dashed curve) solutions.

In Figure 5, we present the lens-system configurations corresponding to the
three degenerate solutions. The configurations of the pair of the inner and
outer solutions have similar characteristic to those of the event
MOA-2022-BLG-563: the source passed through the inner region between the
central and planetary caustics for the inner solution, and the source passed
through the region outside the caustic for the outer solution. For the
intermediate solution, on the other hand, the source passed through the two
caustic prongs that extend from the two back-end cusps of a resonant caustic.
According to this solution, the source crossed the caustic four times during
the anomaly. The first pair of crossings occurred when the source passed
through the lower prong, and the other pair of crossings occurred when the
source passed through the upper prong. The individual caustic crossings
produced caustic spikes, but the one produced when the source entered the
lower caustic prong and the one generated when the source exited the upper
caustic prong do not exhibit obvious features due to the combination of the
weakness of the caustic folds and finite-source effects. From the resolved
caustic-crossing part of the anomaly, the normalized source radius,
$\rho=(0.674\pm 0.038)\times 10^{-3}$, is precisely measured.

Figure 6:  Light curve of KMT-2023-BLG-0735.

###  3.3 KMT-2023-BLG-0735

The KMTNet group found the event KMT-2023-BLG-0735 on 2023 May 08 (${\rm
HJD}^{\prime}\sim 10072$), which was about two days after the peak of the
lensing light curve. The event reached a moderately high magnification of
$A_{\rm max}\sim 60$ at the peak. The extinction toward the source,
$A_{I}=5.97$, is very high because of the closeness of the source to the
Galactic center. The source lies near the edge of the KMTNet prime fields
BLG02 and BLG42. The KMTC data were recovered from the images of both fields,
but the KMTS and KMTA data in the BLG42 field were not recovered. As a result,
the observational cadence varies depending on the field: 0.25 hr for the KMTC
data set and 0.5 hr for the KMTS and KMTA data sets.

We present the lensing light curve of KMT-2023-BLG-0735 in Figure 6. The light
curve exhibits similar characteristics to those of the previous two events in
various aspects. First, an anomaly occurred near the peak of the light curve.
Second, the anomaly exhibits a dip feature, which is centered at $t_{\rm
anom}\sim 10070.84$ in HJD′, and two positive peaks on both sides of the dip.
The time gap between the two peak is $\Delta t\sim 0.6$ day. The anomaly was
covered mostly by the combination of KMTC02 and KMTC42 data sets

Table 4: Model parameters of KMT-2023-BLG-0735. Parameter | Inner | Outer
---|---|---
$\chi^{2}$/dof | $2901.8/2908$ | $2901.0/2908$
$t_{0}$ (HJD′) | $10070.611\pm 0.009$ | $10070.602\pm 0.011$
$u_{0}$ ($10^{-2}$) |  -$1.83432\pm 0.25$ |  -$1.68\pm 0.283$
$t_{\rm E}$ (days) | $17.93\pm 2.38$ | $19.31\pm 2.28$
$s$ | $0.935\pm 0.009$ | $1.041\pm 0.009$
$q$ ($10^{-4}$) | $2.26\pm 0.39$ | $1.92\pm 0.46$
$\alpha$ (rad) | $5.311\pm 0.029$ | $5.334\pm 0.034$
$\rho$ ($10^{-3}$) | $1.64\pm 0.54$ | $1.63\pm 0.49$
Figure 7:  Lens-system configurations of the inner (upper panel) and outer (lower panel) solutions for the lensing event KMT-2023-BLG-0735. Notations are same as those in Fig. 3.  Figure 8:  Locations of the source, blend, and RGC centroid in the instrumental color-magnitude diagrams (CMDs) of the lensing events MOA-2022-BLG-563, KMT-2023-BLG-0469, and KMT-2023-BLG-0735. For KMT-2023-BLG-0735, the CMD is constructed by combining the KMTC data (gray dots) and HST (brown dots) data.  Table 5: Source parameters.  Quantity | MOA-2022-BLG-563 | KMT-2023-BLG-0469 | KMT-2023-BLG-0735
---|---|---|---
$(V-I,I)$ | $(1.825\pm 0.100,19.764\pm 0.068)$ | $(2.246\pm 0.091,23.056\pm 0.011)$ | $(2.419\pm 0.117,23.127\pm 0.036)$
$(V-I,I)_{\rm RGC}$ | $(2.282,15.967)$ | $(2.446,16.131)$ | $(2.70,20.10)$
$(V-I,I)_{{\rm RGC},0}$ | $(1.060,14.357)$ | $(1.060,14.384)$ | $(1.060,14.429)$
$(V-I,I)_{0}$ | $(0.604\pm 0.108,18.154\pm 0.071)$ | $(0.860\pm 0.100,21.308\pm 0.023)$ | $(0.779\pm 0.117,17.455\pm 0.036)$
Spectral type | F8V | K0V | G8 turnoff
Table 6: Angular source radius, Einstein radius, and relative lens-source proper motion.  Quantity | MOA-2022-BLG-563 | KMT-2023-BLG-0469 | KMT-2023-BLG-0735
---|---|---|---
$\theta_{*}$ ($\mu$as) | $0.656\pm 0.084$ | $0.204\pm 0.024$ | $1.135\pm 0.155$
$\theta_{\rm E}$ (mas) | – | $0.302\pm 0.040$ | $0.697\pm 0.225$
$\mu$ (mas/yr) | – | $2.43\pm 0.33$ | $13.17\pm 4.54$

As expected from the similar pattern of the anomaly to those of
MOA-2022-BLG-563 and KMT-2023-BLG-0469, we find a pair of inner and outer
planetary solutions describing the observed anomaly. The planetary parameters
are $(s,q)_{\rm in}\sim(0.95,2.6\times 10^{-4})$ for the inner solution and
$(s,q)_{\rm out}\sim(1.03,2.5\times 10^{-4})$ for the outer solution, and the
estimated mass ratio indicates that the planet is likely to be substantially
less massive than Jupiter of the Solar System. The positions of the two
degenerate solutions in the $\log s$–$\log q$ parameter plane are shown on the
$\Delta\chi^{2}$ map presented in the bottom panel of Figure 2, and the full
lensing parameters of both solutions are listed in Table 4. The two solutions
are very degenerate, and the outer solution is preferred over the inner
solution only by $\Delta\chi^{2}=0.8$. From the lensing parameters
$(t_{0},u_{0},t_{\rm E},t_{\rm anom})\sim(10070.61,1.75\times
10^{-2},18.5,10070.84)$, we find $s^{\dagger}\sim 0.98$ compared to the
geometric mean $(s_{\rm in}\times s_{\rm out})^{1/2}\sim 0.97$, indicating
that the degeneracy between the solutions is caused by the inner-outer
degeneracy. The model curve of the outer solution and the residual are shown
in Figure 6.

Figure 7 shows the lens-system configurations corresponding to the inner and
outer solutions of KMT-2023-BLG-0735. According to the configurations, the
anomaly was produced by the passage of the source through the negative
deviation region on the back-end side of the caustic. The configurations are
very similar to those of the MOA-2022-BLG-563 in the senses that the ambiguity
between the two solutions originates from the inner-outer degeneracy, and the
central and planetary caustics of the inner solution are well separated, while
the caustics of the outer solution form a single resonant caustic. Although
the source did not cross the caustic, the normalized source radius,
$\rho=(1.64\pm 0.53)\times 10^{-3}$, is measured because of the large
magnification gradient of the anomaly region extending from the strong cusp of
the caustic.

##  4 Source star and Einstein radius

In this section, we characterize the source stars of the events and estimate
the angular Einstein radii. The Einstein radius is estimated from the relation

$\theta_{\rm E}={\theta_{*}\over\rho},$ (2)

where the normalized source radius $\rho$ is measured from the light curve
modeling, and the angular source radius $\theta_{*}$ is deduced from the type
of the source determined from its extinction and reddening-corrected
(dereddened) color and magnitude. Although the angular Einstein radius cannot
be estimated for MOA-2022-BLG-563 because the normalized source radius could
not not measured, we specify the source star for the complete characterization
of the event.

For each event, the dereddened color and magnitude of the source,
$(V-I,I)_{0}$, were estimated using the Yoo et al. (2004) method. In this
method, the instrumental color and magnitude, $(V-I,I)$, of the source are
measured, and then they are calibrated using the centroid of red giant clump
(RGC), for which its dereddened values, $(V-I,I)_{{\rm RGC},0}$, are known, as
a reference, that is,

$(V-I,I)_{0}=(V-I,I)_{{\rm RGC},0}+\Delta(V-I,I).$ (3)

Here $\Delta(V-I,I)$ represents the offsets in color and magnitude between the
source and RGC centroid. The instrumental $V$ and $I$-band magnitudes of the
source were measured by regressing the light curves of the individual
passbands constructed using the pyDIA photometry code (Albrow et al., 2017)
with respect to the model.

For KMT-2023-BLG-0735, the photometry quality of the $V$-band data is not good
because of the very high extinction toward the field, and this makes it
difficult to directly measure the source color. In this case, we adopted the
median color of stars lying within the range of the measured $I$-band
magnitude on the main-sequence or giant branches of the combined CMD, which is
constructed by aligning the CMD constructed using the KMTC data and the CMD of
bulge stars lying toward the Baade’s window constructed from the observations
using the Hubble Space Telescope (HST) by Holtzman et al. (1998). For the
alignment of the KMTC and HST CMDs, we used $I$-band magnitudes the RGC
centroids in the individual CMDs as registration marks. The RGC centroid was
chosen as the median position of stars in the clump of red giants. The
position of the RGC centroid in the $(I-V)$–$I$ KMTC CMD was somewhat
uncertain, and thus we determined the $I$-band magnitude of the RGC centroid
from the $(I-K)$–$I$ CMD, which clearly shows the RGC centroid. The
$(I-K)$–$I$ CMD was constructed by matching stars in the KMTC image and those
in the catalog of VISTA Variables in the Via Lactea (VVV) survey (Minniti et
al., 2010).

In Figure 8, we mark the positions of the source stars (blue dots) and the RGC
centroids (red dots) of the individual events in the instrumental CMDs of
stars lying in the vicinity of the source stars. Also marked in the CMDs are
the positions of the blended objects (green dots). We found that the source
flux is heavily blended by the flux from a nearby giant star in all cases of
the events.

With the measured instrumental colors and magnitudes together with the de-
reddened values of the RGC centroid adopted respectively from Bensby et al.
(2013) and Nataf et al. (2013), we then estimated the calibrated source colors
and magnitudes using the relation in Eq. (3). In Table 5, we list the values
of $(V-I,I)$, $(V-I,I)_{\rm RGC}$, $(V-I,I)_{{\rm RGC},0}$, and $(V-I,I)_{0}$
for the individual events. According to the estimated color and magnitude, the
source star is a late F-type main-sequence star for MOA-2022-BLG-563, an early
K-type main-sequence star for KMT-2023-BLG-0469, and a late G-type turn-off
star for KMT-2023-BLG-0735.

The angular source radius is derived from the measured $(V-I,I)_{0}$ by first
converting the $V-I$ color into $V-K$ color using the color-color relation of
Bessell & Brett (1988), and then deducing $\theta_{*}$ from the
$(V-K,I)$–$\theta_{*}$ relation of Kervella et al. (2004). With the estimated
the source radius, the angular Einstein radius is then estimated using the
relation in Eq. (2), and the relative lens-source proper motion is estimated
as

$\mu={\theta_{\rm E}\over t_{\rm E}}.$ (4)

In Table 6, we list the estimated values of $\theta_{*}$, $\theta_{\rm E}$,
and $\mu$ for the individual lensing events.

Table 7: Physical lens parameters.  Parameter | MOA-2022-BLG-563 | KMT-2023-BLG-0469 | KMT-2023-BLG-0735
---|---|---|---
$M_{\rm h}$ ($M_{\odot}$) | $0.48^{+0.36}_{-0.30}$ | $0.47^{+0.35}_{-0.26}$ | $0.61^{+0.34}_{-0.34}$
$M_{\rm p}$ ($M_{\rm J}$) | $0.40^{+0.31}_{-0.25}$ | $0.124^{+0.092}_{-0.067}$ | $0.122^{+0.068}_{-0.068}$
$D_{\rm L}$ (kpc) | $6.53^{+1.12}_{-1.57}$ | $7.07^{+1.03}_{-1.19}$ | $6.39^{+1.21}_{-1.60}$
$a_{\perp,{\rm in}}$ (AU) | $2.15^{+0.37}_{-0.52}$ | $2.32^{+0.33}_{-0.38}$ | $2.66^{+0.50}_{-0.66}$
$a_{\perp,{\rm out}}$ (AU) | $2.40^{+0.41}_{-0.58}$ | $2.42^{+0.35}_{-0.41}$ | $2.96^{+0.56}_{-0.74}$
$a_{\perp,{\rm int}}$ (AU) | – | $2.31^{+0.34}_{-0.39}$ | –
$a_{\rm snow}$ (AU) | 1.3 | 1.3 | 1.67
$P_{\rm disk}$ | 36% | 27% | 42%
$P_{\rm bulge}$ | 64% | 73% | 58%
Figure 9:  Bayesian posteriors of the planet masses. The three dotted vertical
lines represent the masses of Earth ($M_{\rm E}$), Uranus ($M_{\rm U}$), and
Jupiter ($M_{\rm J}$) of the Solar System. The curves drawn in red and blue
indicate the contributions by the disk and bulge lens populations,
respectively, and the black curve represents the sum of the contributions by
the two lens populations.

##  5 Physical lens parameters

The physical parameters of the individual planetary systems were estimated
from Bayesian analyses, which were conducted using the constraints given by
the measured lensing observables. In the first step of the analysis, we
produced a large number of artificial lensing events from a Monte Carlo
simulation. For each simulated event, we assigned the mass $M$ of the lens,
which was derived from a model mass function, and the distances to the lens
$D_{\rm L}$ and source $D_{\rm S}$, and their relative proper motion $\mu$,
which were derived from a Galaxy model. In the simulation, we adopted the Jung
et al. (2021) model for the mass function, and the Jung et al. (2021) model
for the Galaxy model. In the second step, we calculated the lensing
observables of the event time scale and Einstein radius corresponding to the
physical parameters $(M,D_{\rm L},D_{\rm S},\mu)$ of each simulated event from
the relations

$t_{\rm E}={\theta_{\rm E}\over\mu};\qquad\theta_{\rm E}=(\kappa M\pi_{\rm
rel})^{1/2},$ (5)

where $\kappa=4G/(c^{2}{\rm AU})\simeq 8.14\leavevmode\nobreak\ {\rm
mas}/M_{\odot}$, and $\pi_{\rm rel}=\pi_{\rm L}-\pi_{\rm S}={\rm AU}(1/D_{\rm
L}-1/D_{\rm S})$ denotes the relative lens-source parallax. For all three
events, the extra lensing observable of the microlens parallax $\pi_{\rm E}$
could not be constrained, because either the event time scale was not long
enough or the photometric precision of data was not high enough to detect the
subtle deviations induced by the higher-order effects. In the third step, we
constructed the posteriors of the lens mass and distance by imposing a weight
to each event of

$w_{i}=\exp\left(-{\chi_{i}^{2}\over 2}\right);\qquad\chi_{i}^{2}={(t_{{\rm
E},i}-t_{\rm E})^{2}\over\sigma^{2}(t_{\rm E})}+{(\theta_{{\rm
E},i}-\theta_{\rm E})^{2}\over\sigma^{2}(\theta_{\rm E})},$ (6)

where $(t_{\rm E},\theta_{\rm E})$ denote the measured values of the lensing
observables, and $[\sigma(t_{\rm E}),\sigma(\theta_{\rm E})]$ represent their
uncertainties. Besides the lensing observables $t_{\rm E}$ and $\theta_{\rm
E}$, the blended flux can often provide a constraint on the lens system from
the fact that the flux from the lens contributes to the blended light, and
thus it should be less than the measured blended flux. We found that the
blending constraint has little effects on the lens parameters, because the
blended flux was high in all cases of the events.

Figure 10:  Bayesian posteriors of the distances to the planetary systems.
Notations are the same as those in Fig. 9.

We present the posterior distributions of the planet mass and distance to the
planetary lens system for the individual events in Figures 9 and 10,
respectively. In each panel, the distributions drawn in blue and red represent
the contributions by the disk and bulge lens populations, respectively, and
the distribution drawn in black represents the sum of contributions by the two
lens populations. In the panels of the planet-mass posteriors, we draw three
dotted vertical lines corresponding to the masses of Jupiter ($M_{\rm J}$),
Uranus ($M_{\rm U}$), and Earth ($M_{\rm E}$) of the Solar System.

In Table 7, we list the physical parameters the host mass, $M_{\rm h}$, planet
mass, $M_{\rm p}$, distance to the planetary system, $D_{\rm L}$, and the
projected planet-host separation, $a_{\perp}$. For the planetary separation,
we present the values corresponding to the inner ($a_{\perp,{\rm in}}$) and
outer ($a_{\perp,{\rm out}}$) solutions, and additionally present the value
corresponding to the intermediate solution ($a_{\perp,{\rm int}}$) for
KMT-2023-BLG-0469. For each lens parameter, the median of the Bayesian
posterior distribution is chosen as the representative value, and the 16% and
84% of the posterior distribution are set as the upper and lower limits,
respectively. Also presented are the snow line distances estimated as $a_{\rm
snow}\sim 2.7{\rm AU}(M/M_{\odot})$ (Kennedy & Kenyon, 2008), and the
probabilities for the lenses to be in the disk, $P_{\rm disk}$, and bulge,
$P_{\rm bulge}$.

It is found that all three planets have masses lying between those of Jupiter
and Uranus. For all planetary systems, the hosts of planets are main-sequence
stars that are less massive than the Sun, and the planets lie well beyond the
snow lines of the planetary systems. For the planet MOA-2022-BLG-563Lb, the
estimated mass is 1.3 times of the mass of Saturn, and thus it is likely to be
a giant planet. On the other hand, the masses of the planets
KMT-2023-BLG-0469Lb and KMT-2023-BLG-0735Lb are approximately 2.7 times of the
mass of Uranus, and thus they are more likely to be ice giants. In all cases,
the planetary systems are more likely to be in the bulge with probabilities
$P_{\rm bulge}=64\%$, 73%, and 58% for MOA-2022-BLG-563, KMT-2023-BLG-0469,
and KMT-2023-BLG-0735, respectively.

##  6 Summary and conclusion

We conducted analyses of the three microlensing events MOA-2022-BLG-563,
KMT-2023-BLG-0469, and KMT-2023-BLG-0735, for which the lensing light curves
exhibit short-term anomalies with dip features appearing near the peaks of the
lensing light curves. From the detailed analyses of the anomalies, we found
that the anomalies were produced by planets, for which the mass ratios between
the planet and host are on the order of $10^{-4}$. All planetary systems share
common properties that planets have masses lying between those of Jupiter and
Uranus, the hosts of planets are main-sequence stars that are less massive
than the Sun, and the planets lie beyond the snow lines of the planetary
systems. We found that interpreting the anomalies was subject to a common
inner-outer degeneracy, which causes ambiguity in estimating the projected
planet-host separation, and identified an extra local solution resulting from
an accidental degeneracy in the case of KMT-2023-BLG-0469.

Conducting morphological studies to classify lensing events based on similar
anomalies and exploring the specific origins of each anomaly class is crucial.
This not only aids in promptly diagnosing anomalies before in-depth analysis
but also facilitates an accurate characterization of lens systems for future
events sharing similar anomaly structures. The anomalies observed in the
analyzed events share a distinctive trait, characterized by a brief dip
surrounded by subtle bumps near the peak of the light curve. This particular
feature strongly suggests a planetary origin for the anomaly.

###### Acknowledgements.

Work by C.H. was supported by the grants of National Research Foundation of
Korea (2019R1A2C2085965). This research has made use of the KMTNet system
operated by the Korea Astronomy and Space Science Institute (KASI) at three
host sites of CTIO in Chile, SAAO in South Africa, and SSO in Australia. Data
transfer from the host site to KASI was supported by the Korea Research
Environment Open NETwork (KREONET). This research was supported by the Korea
Astronomy and Space Science Institute under the R&D program (Project No.
2023-1-832-03) supervised by the Ministry of Science and ICT. The MOA project
is supported by JSPS KAKENHI Grant Number JP24253004, JP26247023, JP23340064,
JP15H00781, JP16H06287, JP17H02871 and JP22H00153. J.C.Y., I.G.S., and S.J.C.
acknowledge support from NSF Grant No. AST-2108414. Y.S. acknowledges support
from NSF Grant No. 2020740. C.R. was supported by the Research fellowship of
the Alexander von Humboldt Foundation.

## References

  * Adams et al. (2018) Adams, A. D., Boyajian, T. S., & von Braun, K., 2018, MNRAS, 473, 3608
  * Albrow et al. (1998) Albrow, M., Beaulieu, J. -P.m Birch, P., et al. 1998, ApJ, 509, 687
  * Albrow et al. (2009) Albrow, M., Horne, K., Bramich, D. M., et al. 2009, MNRAS, 397, 2099
  * Albrow et al. (2017) Albrow, M. 2017, MichaelDAlbrow/pyDIA: Initial Release on Github,Versionv1.0.0, Zenodo, doi:10.5281/zenodo.268049
  * Alcock et al. (1993) Alcock, C., Akerlof, C. W., Allsman, R. A., et al. 1993, Nature, 365, 621
  * An (2005) An, J. H. 2005, MNRAS, 356, 1409
  * Aubourg et al. (1993) Aubourg, E., Bareyre, P., Bréhin, S., et al. 1993, Nature, 365, 623
  * Bensby et al. (2013) Bensby, T. Yee, J.C., Feltzing, S. et al. 2013, A&A, 549, A147
  * Bessell & Brett (1988) Bessell, M. S., & Brett, J. M. 1988, PASP, 100, 1134
  * Bond et al. (2001) Bond, I. A., Abe, F., Dodd, R. J., et al. 2001, MNRAS, 327, 868
  * Bond et al. (2004) Bond, I. A., Udalski, A., Jaroszyński, M., et al. 2004, ApJ, 606, L155
  * Chung et al. (2005) Chung, S.-J., Han, C., Park, B.-G., et al. 2005, ApJ, 630, 535
  * Dominik (1999) Dominik, M. 1999, A&A, 349, 108
  * Doran & Mueller (2004) Doran, M., & Mueller, C. M. 2004, J. Cosmology Astropart. Phys., 09, 003
  * Gaudi & Gould (1997) Gaudi, B. S., & Gould, A. 1997, ApJ, 486, 85
  * Gonzalez et al. (2012) Gonzalez, O. A., Rejkuba, M., Localize, M., et al. 2012, A&A, 543, A13
  * Gaudi et al. (1998) Gaudi, B. S. 1998, ApJ, 506, 533
  * Gould & Loeb (1992) Gould, A., & Loeb, L. 1992, ApJ, 396, 104
  * Gould et al. (2022) Gould, A., Han, C., Weicheng, Z., et al. 2022, A&A, 664, A13
  * Griest & Safizadeh (1998) Griest, K., & Safizadeh, N. 1998, ApJ, 500, 37
  * Han (2006) Han, C. 2006, ApJ, 638, 1080
  * Han et al. (2017) Han, C., Udalski, A., Gould, A., et al. 2017, AJ, 154, 133
  * Han & Gaudi (2008) Han, C., & Gaudi, B. S. 2008, ApJ, 689, 53
  * Han et al. (2018) Han, C., Bond, I. A., Gould, A., et al. 2018, AJ, 156, 226
  * Han et al. (2021a) Han, C., Udalski, A., Kim, D., et al. 2021a, A&A, 650, A89
  * Han et al. (2021a) Han, C., Albrow, M. D., Chung, S.-J., et al. 2021b, A&A, 652, A145
  * Han et al. (2021a) Han, C., Udalski, A., Kim, D., et al. 2021c, A&A, 655, A21
  * Han et al. (2021a) Han, C., Gould, A., Kim, D., et al. 2022, A&A, 663, A145
  * Han et al. (2021a) Han, C., Lee, C.-U., Bond, I. A., et al. 2023, A&A, 676, A97
  * Holtzman et al. (1998) Holtzman, J. A., Watson, A. M., Baum, W. A., et al. 1998, AJ115, 1946
  * Hwang et al. (2022) Hwang, K.-H., Zang, W., Gould, A., et al. 2022, AJ, 163, 43
  * Jung et al. (2021) Jung, Y. K., Udalski, A., Gould, A., et al. 2018, AJ, 155, 219
  * Jung et al. (2021) Jung, Y. K., Han, C., Udalski, A., et al. 2021, AJ, 161, 293
  * Jung et al. (2022) Jung, Y. K., Zang, W., Han, C., et al. 2022, AJ, 164, 262
  * Kennedy & Kenyon (2008) Kennedy, G. M., & Kenyon, S. J. 2008, ApJ, 673, 502
  * Kervella et al. (2004) Kervella, P., Thévenin, F., Di Folco, E., & Ségransan, D. 2004, A&A, 426, 29
  * Kim et al. (2018) Kim, D. -J., Kim, H. -W., Hwang, K. -H., et al. 2018, AJ, 155, 76
  * Kim et al. (2016) Kim, S.-L., Lee, C.-U., Park, B.-G., et al. 2016, JKAS, 49, 37
  * Mayor & Queloz (1995) Mayor, M., & Queloz, D. 1995, Nature, 378, 355
  * Mao & Paczyński (1991) Mao, S., & Paczyński, B. 1991, ApJ, 374, 37
  * Minniti et al. (2010) Minniti, D., Lucas, P. W., Emerson, J. P., et al. 2010, New Astronomy, 15, 433
  * Nataf et al. (2013) Nataf, D. M., Gould, A., Fouqué, P. et al. 2013, ApJ, 769, 88
  * Udalski et al. (1994) Udalski, A., Szymanski, M., Kałużny, J., et al. 1994, Acta Astron., 44, 1
  * Wolszczan & Frail (1992) Wolszczan, A., & Frail, D. A 1992, Nature, 355, 145
  * Yee et al. (2012) Yee, J. C., Shvartzvald, Y., Gal-Yam, A., et al. 2012, ApJ, 755, 102
  * Yee et al. (2021) Yee, J. C., Zang, W., Udalski, A., et al. 2021, AJ, 162, 180
  * Yoo et al. (2004) Yoo, J., DePoy, D.L., Gal-Yam, A. et al. 2004, ApJ, 603, 139