Abstract: | We present the first example of binary microlensing for which the parameter
measurements can be verified (or contradicted) by future Doppler observations.
This test is made possible by a confluence of two relatively unusual
circumstances. First, the binary lens is bright enough (I=15.6) to permit
Doppler measurements. Second, we measure not only the usual 7 binary-lens
parameters, but also the ’microlens parallax’ (which yields the binary mass)
and two components of the instantaneous orbital velocity. Thus we measure,
effectively, 6 ’Kepler+1’ parameters (two instantaneous positions, two
instantaneous velocities, the binary total mass, and the mass ratio). Since
Doppler observations of the brighter binary component determine 5 Kepler
parameters (period, velocity amplitude, eccentricity, phase, and position of
periapsis), while the same spectroscopy yields the mass of the primary, the
combined Doppler + microlensing observations would be overconstrained by 6 + (5
+ 1) - (7 + 1) = 4 degrees of freedom. This makes possible an extremely strong
test of the microlensing solution. We also introduce a uniform microlensing
notation for single and binary lenses, we define conventions, summarize all
known microlensing degeneracies and extend a set of parameters to describe full
Keplerian motion of the binary lenses. |