Exoplanet Sensitivity in Microlensing: The Mass-Ratio and Separation Window Where Planets Announce Themselves

This paper computes the region of planet mass ratio and projected separation in which a planetary companion produces a detectable deviation on a stellar microlensing light curve. 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 sensitivity peaks near the Einstein ring and falls steeply inside and outside it, so microlensing surveys are naturally tuned to planets at a few astronomical units. 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.