Resolution of the MACHOLMC5 Puzzle: The JerkParallax Microlens Degeneracy
Abstract
By extending the constantacceleration analysis of Smith, Mao, & Paczyński to include jerk, I show that microlens parallax measurements are subject to a fourfold discrete degeneracy. The new degeneracy is characterized by a projected velocity v_{j}=(3/4)cscβ_{ec}(cos2ψsin2β_{ec}+sin2ψ)^{3/2}v_{⊕}, where β_{ec} is the ecliptic latitude, ψ is the phase of the Earth's orbit relative to opposition at the time of the event maximum, and v_{⊕}=30kms^{1} is the speed of the Earth. The degeneracy becomes important when the lens projected velocity v is of order v_{j}. For events toward the Large Magellanic Cloud, v_{j}~=(3/4)v_{⊕}, so this degeneracy is important primarily for lenses in the Milky Way disk. In particular, it solves the puzzle of MACHOLMC5, whose microlens parallax measurement had yielded mass and distance determinations for the lens that were inconsistent with photometric estimates. Toward the Galactic bulge, v_{j} ranges from ~0.2 km s^{ 1} at the summer solstice to ~200 km s^{ 1} 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 2004
 DOI:
 10.1086/382782
 arXiv:
 arXiv:astroph/0311548
 Bibcode:
 2004ApJ...606..319G
 Keywords:

 Cosmology: Gravitational Lensing;
 Stars: LowMass;
 Brown Dwarfs;
 Astrophysics
 EPrint:
 19 Pages, 5 figures, 1 table, ApJ 2004, in press