Optical Depth and Event Rate Toward the Galactic Bulge: A Computed Check Against Survey Counts

This paper computes whether the observed rate of bulge microlensing events is consistent with the stellar mass along the line of sight, computed from the optical depth and the mean timescale. 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 event rate follows from the optical depth divided by the mean timescale, and the published bulge values sit where ordinary stellar populations predict, leaving little room for a dominant exotic lens population. 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.