The Photometric Precision Floor for Detecting Earth-Mass Companions in Microlensing Events

This paper computes the photometric accuracy and cadence a survey must sustain before an Earth-mass companion, with a mass ratio near one part in one hundred thousand, produces a deviation larger than the noise. 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 Earth-mass sensitivity is a cadence problem as much as a precision problem, because the planetary deviation lasts only hours. 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.