2003/11/30 by Andrew Gould · 1 citation
Physics and Astronomy · #astro-ph
paper · pdf · doi:10.1086/382782
published as Astrophys.J. 606 (2004) 319-325 · 19 Pages, 5 figures, 1 table, ApJ 2004, in press
arxiv created 2004/03/14 · arxiv updated 2009/12/01
By extending the constant-acceleration analysis of Smith, Mao, & Paczynski 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 vj = -(3/4)\cscβ_\ec(cos2ψsin2β_\ec+sin2ψ)3/2vearth, where β_\ec is the ecliptic latitude, ψis the phase of the Earth's orbit relative to opposition at the time of the event maximum, and vearth=30 km/s is the speed of the Earth. The degeneracy becomes important when the lens projected velocity v is of order vj. For events toward the Large Magellanic Cloud, vj≃ (3/4)vearth, 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, vj ranges from about 0.2 km/s at the solstice to about 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, tE < yr/2pi.