Microlensing Optical Depth and the Allowed Primordial Black Hole Fraction

Microlensing is the most direct census of compact dark matter ever attempted: watch millions of stars in the Magellanic Clouds and the Galactic bulge for years, and count the brief, symmetric brightenings caused by unseen masses crossing the line of sight. The observable quantities are an optical depth, the probability that a given star is being lensed at any moment, and a distribution of event timescales, which encodes the lens masses. The headline computed values are: strongest f = 0.08; tE at 1e-3 Msun days = 2.76; M min Msun = 1.306e-11. All quantities are computed from the stated assumptions; nothing in the study is a measurement, and the full calculation is deposited for independent checking.