KMT-2021-BLG-0171Lb and KMT-2021-BLG-1689Lb: two microlensing planets in the KMTNet high-cadence fields with followup observations

Follow-up observations of high-magnification gravitational microlensing events can fully exploit their intrinsic sensitivity to detect extrasolar planets, especially those with small mass ratios. To make followup observations more uniform and efficient, we develop a system, HighMagFinder, to automatically alert possible ongoing high-magnification events based on the real-time data from the Korea Microlensing Telescope Network (KMTNet). We started a new phase of follow-up observations with the help of HighMagFinder in 2021. Here we report the discovery of two planets in high-magnification microlensing events, KMT-2021-BLG-0171 and KMT-2021-BLG-1689, which were identified by the HighMagFinder. We find that both events suffer the 'central-resonant' caustic degeneracy. The planet-host mass-ratio is q similar to 4.7 x 10(-5) or q similar to 2.2 x 10(-5) for KMT-2021-BLG-0171, and q similar to 2.5 x 10(-4) or q similar to 1.8 x 10(-4) for KMT-2021-BLG-1689. Together with two other events, four cases that suffer such degeneracy have been discovered in the 2021 season alone, indicating that the degenerate solutions may have been missed in some previous studies. We also propose a quantitative factor to weight the probability of each solution from the phase space. The resonant interpretations for the two events are disfavoured under this consideration. This factor can be included in future statistical studies to weight degenerate solutions.