Binary-lens Microlensing Degeneracy: Impact on Planetary Sensitivity and Mass-ratio Function

Abstract Gravitational microlensing is a unique method for discovering cold planets across a broad mass range. Reliable statistics of the microlensing planets require accurate sensitivity estimates. However, the impact of the degeneracies in binary-lens single-source (2L1S) models that affect many actual planet detections is often omitted in sensitivity estimates, leading to potential self-inconsistency of the statistics studies. In this work, we evaluate the effect of the 2L1S degeneracies on planetary sensitivity by simulating a series of typical microlensing events and comprehensively replicating a realistic planet detection pipeline, including the anomaly identification, global 2L1S model search, and degenerate model comparison. We find that for a pure-survey statistical sample, the 2L1S degeneracies reduce the overall planetary sensitivity by 5%–10%, with the effect increasing at higher planet-host mass ratios. This bias leads to an underestimation of planet occurrence rates and a flattening of the inferred mass-ratio function slope. This effect will be critical for upcoming space-based microlensing surveys like the Roman or Earth 2.0 missions, which are expected to discover <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> planets. We also discuss the computational challenges and propose potential approaches for future applications.