2004ApJ...606..319G

By extending the constant-acceleration analysis of Smith, Mao, & Paczy{nacute}ski to include jerk, I show that microlens parallax measurements are subject to a four-fold discrete degeneracy. The new degeneracy is characterized by a projected velocity v{d5}_j=-(3/4)cscβ_ec(cos\ul 2ψsin\ul 2β_ec+sin\ul 2ψ)^3/2v_⊕, where β_ecis the ecliptic latitude, ψ is the phase of the Earth's orbit relative to opposition at the time of the event maximum, and v_⊕=30km/s is the speed of the Earth. The degeneracy becomes important when the lens projected velocity v{d5} is of order v{d5}_j. For events toward the Large Magellanic Cloud, v{d5}_j≃(3/4)v_⊕, so this degeneracy is important primarily for lenses in the Milky Way disk. In particular, it solves the puzzle of MACHO-LMC-5, whose microlens parallax measurement had yielded mass and distance determinations for the lens that were inconsistent with photometric estimates. Toward the Galactic bulge, v{d5}_jranges from ∼0.2 km/s at the summer solstice to ∼200 km/s at the equinoxes, so the effect of the degeneracy depends strongly on the peak time of the event. The degeneracy applies mainly to events with Einstein timescales, t_E≲yr/2π.