Angular Radii of Stars via Microlensing

Abstract

We outline a method by which the angular radii of giant and main-sequence stars located in the Galactic bulge can be measured to a few percent accuracy. The method combines comprehensive ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise (~10 μas) astrometric measurements of the lensed star during the event, to measure the angular radius of the source, θ*. Dense photometric coverage of one caustic crossing yields the crossing timescale Δt. Less frequent coverage of the entire event yields the Einstein timescale tE and the angle ϕ of source trajectory with respect to the caustic. The photometric light-curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield θE, the angular Einstein ring radius. Then the angular radius of the source is obtained by θ* = θE(Δt/tE) sin ϕ. We argue that the parameters tE, Δt, ϕ, and θE, and therefore θ*, should all be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1 m class) telescopes, combined with astrometric observations with a precision of ~10 μas to measure θE. We find that a factor of ~50 times fewer photons are required to measure θE to a given precision for binary lens events than for single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), we find that ~7 minutes of SIM time is required to measure θE to ~5% accuracy for giant sources in the bulge. For main-sequence sources, θE can be measured to ~15% accuracy in ~1.4 hr. Thus, with access to a network of 1 m class telescopes, combined with 10 hr of SIM time, it should be possible to measure θ* to 5% for ~80 giant stars, or to 15% for roughly seven main-sequence stars. We also discuss methods by which the distances and spectral types of the source stars can be measured. A by-product of such a campaign is a significant sample of precise binary lens mass measurements.