Short Events and Free-Floating Planets: The Finite-Source Ceiling on Timescale as a Mass Diagnostic

This paper computes whether the shortest microlensing events, attributed to unbound planetary-mass objects, can be assigned masses at all when their Einstein radii are smaller than the source stars they magnify. For a representative lens of 0.001 solar masses at 4.0 kiloparsecs, in front of a source at 8.0 kiloparsecs, the angular Einstein radius is 0.0319 milliarcseconds, the event timescale is 1.66 days at a relative proper motion of 7.0 milliarcseconds per year, the microlensing parallax is 3.92, and the physical Einstein radius projected at the lens is 0.128 astronomical units. The central finding is that for planetary-mass lenses the event is governed by the source crossing time rather than the Einstein time, which caps the magnification and changes what a short event can prove. 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.