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

TL;DR

This study demonstrates that 2L1S microlensing degeneracies systematically bias planetary sensitivity estimates by about 5–10%, especially at higher mass ratios $q$, leading to underestimates of planet occurrence rates and a shallower inferred mass-ratio function. By simulating five representative microlensing groups and processing a full detection pipeline, the authors reveal concrete degeneracy classes (planet–binary, close–wide planetary caustics, and central–resonant caustics) that yield discrepant $q$ values or non-unique solutions, thereby reducing the ability to uniquely characterize planets in affected events. The work provides a rigorous framework for quantifying these biases, including a detailed pipeline ( anomaly detection, global 2L1S search on a $(k,h)$ grid, local minima refinement, and model comparison) and a quantitative assessment of sensitivity loss across parameter space. The findings have practical implications for upcoming space-based surveys (e.g., Roman, Earth 2.0) expected to find many thousands of planets, highlighting the need for computationally efficient strategies (GPU acceleration, selective sampling, or ML surrogates) and potential degeneracy-breaking observations (parallax, orbital motion, or space-based follow-up) to ensure robust statistical inferences.

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 $5\sim10\%$, 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 $\mathcal{O}(10^3)$ planets. We also discuss the computational challenges and propose potential approaches for future applications.

Figures (9)

• Figure 1: Flow chart of the sensitivity calculation procedure.
• Figure 2: The SNR curve used in the light curve generation, obtained from applying the Qian2025_KMTFFP1 pipeline to the KMTNet-SAAO 2018 observations.
• Figure 3: An example of a simulated $\textcolor{black}{\varepsilon_{\rm uniq}}=0$ event from the GSHM group, affected by the "planet-binary" degeneracy. Left panels show the grid search results projected onto the$(h,k)$, $(h,\alpha)$, and $(\log s, \log q)$ planes, with identified local minima labeled. The top right panel displays the full simulated light curve, and the middle right panels show a zoomed-in view of the anomalous region along with several selected optimized models and residuals relative to the 1L1S model. The bottom right panels present the source-lens trajectories and the caustic geometries for each selected model. Dashed circles indicate the source sizes, and the $\Delta\chi^2=\chi^2-\chi^2_{\rm best}$ value for each model is labeled in "[ ]" brackets. In this case, Models (A, B), (C, D), (E, F), and (G, H) form "close-wide" degenerate pairs; thus, only the "close" models are shown for clarity. The central caustics of Models A and G are visually indistinguishable and are therefore shown together in one panel. Although models G, H, and I are excluded in this example due to their large $\Delta\chi^2$, they could survive under the conditions of lower effective cadence or lower SNR.
• Figure 4: Same as Figure \ref{['fig:lc_exp1']}, but for an example $\textcolor{black}{\varepsilon_{\rm uniq}}=0$ event from the DSHM group that is affected by the planetary caustic "close-wide" degeneracy. Models A and B are visually indistinguishable on the grid search plots but represent different geometries.
• Figure 5: Same as Figure \ref{['fig:lc_exp1']}, but for an example $\textcolor{black}{\varepsilon_{\rm uniq}}=0$ event from the DSEM group that affected by the "central-resonant" degeneracy.