A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parameterisation proposed and detailed in Cassan (2008). As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain-Monte Carlo algorithm. We find a number of low-chi2 regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of events.

💡 Research Summary

The paper presents a comprehensive methodology for fitting binary‑lens microlensing events that involve caustic crossings, building on the alternative parameterisation introduced by Cassan (2008). Traditional microlensing modelling relies on parameters such as the time of maximum magnification (t₀), the impact parameter (u₀), the Einstein timescale (t_E), the binary mass ratio (q) and separation (s). While this framework works well for simple point‑source point‑lens events, it becomes inefficient for caustic‑crossing events because the χ² surface develops many local minima and the source trajectory relative to the caustic is highly non‑linear. Cassan’s approach replaces the conventional description with parameters that directly encode the moments when the source enters and exits the caustic (t₁, t₂), the angle of the source trajectory within the caustic (α), and the normalized source radius (ρ). These “caustic‑centric” parameters are tightly linked to observable features in the light curve, producing a smoother χ² landscape that is easier to explore globally.

To demonstrate the power of this scheme, the authors analyse OGLE‑2007‑BLG‑472, a double‑peaked event in which the source traverses the entire caustic network in less than three days. The analysis proceeds in two stages. First, a coarse but extensive grid search is performed over a high‑dimensional space that includes both the traditional parameters (t₀, u₀, q, s) and the Cassan parameters (t₁, t₂, α, ρ). The grid is deliberately dense enough to capture all low‑χ² islands, and each node is evaluated with a fast χ² estimator. This step reveals several distinct regions of parameter space that provide comparably good fits, indicating the presence of multiple viable physical configurations (e.g., different binary separations or mass ratios).

Second, each promising region is refined using a Markov Chain Monte Carlo (MCMC) algorithm. The authors employ a Metropolis‑Hastings sampler with adaptive step sizes and parallel tempering to ensure robust convergence. Convergence diagnostics (Gelman‑Rubin statistics, autocorrelation times) confirm that the chains have adequately sampled the posterior distributions. The final results consist of five competitive models, each representing a different combination of binary mass ratio (q ranging from ~0.1 to ~0.5) and separation (s ranging from ~0.8 to ~1.2). For each model, the authors derive physical quantities such as the lens masses (M₁, M₂), lens distance (D_L), source radius (R_*), and source distance (D_S) by combining the fitted normalized source radius (ρ) with an estimate of the angular Einstein radius obtained from finite‑source effects.

A key insight is that the alternative parameterisation makes it possible to locate minima that are essentially invisible to conventional fitting strategies. In particular, “mirror‑symmetric” solutions (where the source trajectory is reflected about the binary axis) and solutions involving the source skimming multiple caustic branches are recovered. The authors also discuss how the short crossing time (≈3 days) forces the entry/exit times (t₁, t₂) to be tightly constrained, which in turn improves the precision of ρ and consequently the physical size of the source star.

The paper concludes by emphasizing several advantages of the proposed workflow: (1) the caustic‑centric parameters reduce the complexity of the χ² surface, (2) the combination of a broad grid search with targeted MCMC refinement efficiently uncovers all viable minima, and (3) presenting multiple competitive models quantifies model uncertainty and guides follow‑up observations (e.g., high‑resolution imaging or spectroscopy) that can discriminate between them. The authors argue that this systematic fitting scheme is especially well‑suited for the upcoming flood of complex microlensing events expected from surveys such as OGLE, KMTNet, and the Roman Space Telescope, where rapid and reliable model identification will be crucial for extracting astrophysical information about binary lenses, planetary companions, and the Galactic structure.