2020/02/03 by Andrew Gould · 1 citation
Physics and Astronomy · #astro-ph.IM #astro-ph.EP #astro-ph.GA #astro-ph.SR
paper · pdf · doi:10.5303/jkas.2020.53.5.99
4 pages, submitted to JKAS
arxiv created 2020/02/03 · arxiv updated 2020/12/02
I show that when the observables ( π\rm E,t\rm E,θ\rm E,πs, μs) are well measured up to a discrete degeneracy in the microlensing parallax vector π\rm E, the relative likelihood of the different solutions can be written in closed form Pi = K Hi Bi, 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. 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. Here t\rm E is the Einstein timescale, θ\rm E is the angular Einstein radius, and (πs, μs) are the (parallax, proper motion) of the microlensed source. I also discuss how this analytic expression degrades in the presence of finite errors in the measured observables.