Einstein Radius and Event Timescale Across the Stellar Lens Mass Range: A Computed Grid Tested Against Typical Bulge Event Durations

This paper computes how the two most basic microlensing scales, the angular Einstein radius and the event timescale, move together as lens mass, distance and relative proper motion change. For a representative lens of 0.3 solar masses at 4.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 0.553 milliarcseconds, the event timescale is 40.4 days at a relative proper motion of 5.0 milliarcseconds per year, the microlensing parallax is 0.226, and the physical Einstein radius projected at the lens is 2.21 astronomical units. The central finding is that the timescale grows only as the square root of mass, so a factor of one hundred in mass buys only a factor of ten in duration. 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.