Two Isolated Microlensing Events Near the Upper Shore of Einstein Desert
The Einstein desert is a deficit in the angular Einstein-radius ($θ_{\rm E}$) distribution of isolated objects over the range $9 {\rm μas} < θ_{\rm E}<26 {\rm μas}$. Although this interval contained no events when the desert was first identified, several subsequent detections have fallen within it, raising questions about its detailed structure and requiring a larger detection sample. In this paper, we report the observations and analyses of two microlensing events possibly caused by isolated giant planets or brown dwarfs whose $ θ_{\rm E}$ lie near the upper shore of the desert. MOA-2021-BLG-145 has $ θ_{\rm E} = 23.1\pm2.0 ~{\rm μas}$, placing it just inside the upper boundary, and KMT-2026-BLG-0357 has $ θ_{\rm E} = 36.5\pm 3.7~{\rm μas}$, placing it above the desert. We also compare the $ θ_{\rm E}$ distributions of isolated objects and bound planetary events. The bound population shows no corresponding deficit over the same range, suggesting that the Einstein desert may be associated with the formation or subsequent evolution of the isolated population. Furthermore, some FFPs may lie above the upper shore of the Einstein desert, indicating that a more complete understanding of the FFP population requires direct lens-mass measurements.