Combining the Einstein Radius and Parallax: A Joint Mass and Distance Solution With a Full Error Budget

This paper computes the complete solution, mass and lens distance together, that becomes available when both the angular Einstein radius and the microlensing parallax are measured for the same event. For a representative lens of 0.8 solar masses at 3.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 1.17 milliarcseconds, the event timescale is 85.1 days at a relative proper motion of 5.0 milliarcseconds per year, the microlensing parallax is 0.179, and the physical Einstein radius projected at the lens is 3.5 astronomical units. The central finding is that mass and distance errors are correlated through the shared parallax measurement, so quoting either alone understates the uncertainty of the other. 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.