  Context. Astrometric gravitational microlensing can be used to determine the
mass of a single star (the lens) with an accuracy of a few percent. To do so,
precise measurements of the angular separations between lens and background
star with an accuracy below 1 milli-arcsecond at different epochs are needed.
Hence only the most accurate instruments can be used. However, since the
timescale is in the order of months to years, the astrometric deflection might
be detected by Gaia, even though each star is only observed on a low cadence.
Aims. We want to show how accurately Gaia can determine the mass of the lensing
star. Methods. Using conservative assumptions based on the results of the
second Gaia Data release, we simulated the individual Gaia measurements for 501
predicted astrometric microlensing events during the Gaia era (2014.5 -
2026.5). For this purpose we use the astrometric parameters of Gaia DR2, as
well as an approximative mass based on the absolute G magnitude. By fitting the
motion of lens and source simultaneously we then reconstruct the 11 parameters
of the lensing event. For lenses passing by multiple background sources, we
also fit the motion of all background sources and the lens simultaneously.
Using a Monte-Carlo simulation we determine the achievable precision of the
mass determination. Results. We find that Gaia can detect the astrometric
deflection for 114 events. Further, for 13 events Gaia can determine the mass
of the lens with a precision better than 15% and for 13 + 21 = 34 events with a
precision of 30% or better.
