RIGOROUS "RICH ARGUMENT" IN MICROLENSING PARALLAX

• Published in: Journal of the Korean astronomical society Vol. 53; no. 5; pp. 99 - 102
• Main Author: Gould, Andrew
• Format: Journal Article
• Language: Korean
• Published: 2020
• Subjects: gravitational microlensing
• ISSN: 1225-4614; 2288-890X

I show that when the observables (πE, tE, θE, πs, µs) are well measured up to a discrete degeneracy in the microlensing parallax vector πE, the relative likelihood of the different solutions can be written in closed form Pi = KHiBi, where Hi is the number of stars (potential lenses) having the mass and kinematics of the inferred parameters of solution i and Bi is an additional factor that is formally derived from the Jacobian of the transformation from Galactic to microlensing parameters. Here tE is the Einstein timescale, θE is the angular Einstein radius, and (πs, µs) are the (parallax, proper motion) of the microlensed source. The Jacobian term Bi constitutes an explicit evaluation of the "Rich Argument", i.e., that there is an extra geometric factor disfavoring large-parallax solutions in addition to the reduced frequency of lenses given by Hi. I also discuss how this analytic expression degrades in the presence of finite errors in the measured observables.