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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 seven 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, six "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 five 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, define conventions, summarize all known microlensing degeneracies, and extend a set of parameters to describe full Keplerian motion of the binary lenses.

Because of the development of large-format, wide-field cameras, microlensing surveys are now able to monitor millions of stars with sufficient cadence to detect planets. These new discoveries will span the full range of significance levels including planetary signals too small to be distinguished from the noise. At present, we do not understand where the threshold is for detecting planets. MOA-2011-BLG-293Lb is the first planet to be published from the new surveys, and it also has substantial followup observations. This planet is robustly detected in survey+followup data (∆χ 2 ∼ 5400). The planet/host mass ratio is q = 5.3 ± 0.2 × 10 −3 . The best fit projected separation is s = 0.548 ± 0.005 Einstein radii. However, due to the s ↔ s −1 degeneracy, projected separations of s −1 are only marginally disfavored at ∆χ 2 = 3. A Bayesian estimate of the host mass gives M L = 0.43 +0.27 −0.17 M ⊙ , with a sharp upper limit of M L < 1.2 M ⊙ from upper limits on the lens flux. Hence, the planet mass is m p = 2.4 +1.5 −0.9 M Jup , and the physical projected separation is either r ⊥ ≃ 1.0 AU or r ⊥ ≃ 3.4 AU. We show that survey data alone predict this solution and are able to characterize the planet, but the ∆χ 2 is much smaller (∆χ 2 ∼ 500) than with the followup data. The ∆χ 2 for the survey data alone is smaller than for any other securely detected planet. This event suggests a means to probe the detection threshold, by analyzing a large sample of events like MOA-2011-BLG-293, which have both followup data and high cadence survey data, to provide a guide for the interpretation of pure survey microlensing data.

We present measurements of the microlensing optical depth and event rate toward the Galactic Bulge based on two years of the MOA-II survey. This sample contains ∼ 1000 microlensing events, with an Einstein Radius crossing time of t E ≤ 200 days in 22 bulge fields covering ∼ 42 deg 2 between −5 • < l < 10 • and −7 • < b < −1 • . Our event rate and optical depth analysis uses 474 events with well defined microlensing parameters. In the central fields with |l| < 5 • , we find an event rates of Γ = [2.39 ± 1.1]e [0.60±0.05](3−|b|) × 10 −5 star −1 yr −1 and an optical depth (for events with t E ≤ 200 days) of τ 200 = [2.35 ± 0.18]e [0.51±0.07](3−|b|) × 10 −6