Astrometric Gravitational Microlensing

Andy Gould (Ohio State University)

Abstract:

I review the essential elements and main applications of astrometric microlensing. I first show geometrically how the 3 astrometric and photometric observables of a microlensing event (Einstein timescale: tE, angular Einstein radius: qE, and projected Einstein radius: ~ rE) relate to the 3 underlying physical parameters (lens-source relative proper motion: µrel, relative parallax: ¹rel, and lens mass: M). I then show how the observables can all be measured by SIM, and discuss what can be learned about the Galaxy from a set of such measurements. Next, I turn to the topic of microlensing of nearby stars, which can be used to make precision measurements of the masses of stars. Here, all observable effects are astrometric, and therefore the mathematical description of this effect is extremely simple. The biggest difficulty is just to be able to locate the events, but there are also significant technical challenges for the interferometer. I close with some general remarks on the prospects for astrometric microlensing.

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Suggested Reading (in order of importance)

• Theory of Microlensing
  Gould, A. 2000, astro-ph/0004042 [Mainly sections 1-3] "Theory of Microlensing"

• Microlensing and the Stellar Mass Function
  Gould, A. 1996, PASP, 108, 465 (astro-ph/9604014) [FIGURE 5 ONLY]

• Astrometric Observation of MACHO Gravitational Microlensing
  Boden, A.F., Shao, M., & Van Buren, D. 1998, apj, 502, 538

• Photometric Microlens Parallaxes with the Space Interferometry Mission
  Gould, A. & Salim, S. 1999, ApJ, 524, 794

• Nearby Microlensing Events - Identification of the Candidates for SIM
  Salim, S. & Gould, A. 2000, ApJ, in press, astro-ph/9909455