Resolution of the MACHO-LMC-5 Puzzle: The Jerk-Parallax Microlens Degeneracy

By A. Gould. 2003

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By extending the constant-acceleration analysis of Smith, Mao, & Paczyński 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 j = -(3/4) csc βec( ψ βec + ψ)3/2v⊕, where βec 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⊕ = 30 km s-1 is the speed of the Earth. The degeneracy becomes important when the lens projected velocity is of order j. For events toward the Large Magellanic Cloud, 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, 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, tE ≲ yr/2π.

Subfields: Astronomy and Astrophysics

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Citations in the corpus

The OGLE view of microlensing towards the Magellanic Clouds – IV. OGLE-III SMC data and final conclusions on MACHOs (2011, methodology): “…the most likely scenario for OGLE-SMC-03 is that the lens is an M dwarf with mass of about 0.1-0.3 M⊙ located 1-5 kpc from the Earth and belonging to the thick disk of the Galaxy, similar to the event MACHO-LMC-5, e.g. Drake et al. (2004), Gould (2004) and event EROS2-LMC-8 (Tisserand et al. 2007).”
Microlens OGLE-2005-BLG-169 Implies That Cool Neptune-like Planets Are Common (2006, unknown): “…events, the physical parameters (lens mass M , lens-source relative par- allax πrel, and relative proper motion µ) are related to the “observable” event parameters (tE, θE, and the microlens parallax (Gould 2004), πE), by θE = √ κMπrel, πE = √ κM πrel , tE = θE µ , (2) where κ ≡ 4G/(c2AU).”
MOA-2009-BLG-387Lb: a massive planet orbiting an M dwarf (2011, methodology): “This degeneracy was discussed in the context of point lenses in Gould et al. (1994), Smith et al. (2003a), and Gould (2004).”
A Low-Mass Planet with a Possible Sub-Stellar-Mass Host in Microlensing Event MOA-2007-BLG-192 (2008, background): “The second microlensing parallax degeneracy is usually called the “jerk-parallax” degeneracy (Gould 2004) and it is closely related to a continuous degeneracy discussed by Smith et al. (2003).”
Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds (2006, background): “We might note, however, that of these candidates, MACHO-LMC-14 is most likely due to LMC self-lensing and MACHO-LMC-5 is due to lensing by a normal red-dwarf star in the disk of the Milky Way (Alcock et al. 2001d; Gould 2004).”