Binary-Lens Caustic Crossings: Crossing Times, Source Sizes and the Information in a Few Hours of Light Curve

This paper computes why the brief caustic-crossing features of a binary lens, lasting hours rather than weeks, encode the source size and the lens proper motion with unusual precision. For a representative lens of 0.6 solar masses at 4.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 0.782 milliarcseconds, the event timescale is 57.1 days at a relative proper motion of 5.0 milliarcseconds per year, the microlensing parallax is 0.16, and the physical Einstein radius projected at the lens is 3.13 astronomical units. The central finding is that the caustic-crossing duration measures the same source-size ratio as a single-lens transit but with a sharper edge, giving a cleaner proper-motion estimate. All quantities are computed from stated assumptions and published survey values used as comparison points; the study is simulated and computed, not measured. Where the computation shows that an inference commonly drawn from such events is not supported at the stated precision, that negative result is reported in full.