Astrometric microlensing with the GAIA satellite

GAIA is the ‘super‐ Hipparcos ’ survey satellite selected as a Cornerstone 6 mission by the European Space Agency. GAIA can measure microlensing by the brightening of source stars. For the broad G ‐band photometer, the all‐sky source‐averaged photometric optical depth is ∼10 −7 . There are ∼1300 photometric microlensing events for which GAIA will measure at least one data point on the amplified light curve. GAIA can also measure microlensing by the small excursions of the light centroid that occur during events. The all‐sky source‐averaged astrometric microlensing optical depth is ∼2.5×10 −5 . Some ∼25 000 sources will have a significant variation of the centroid shift, together with a closest approach, during the lifetime of the mission. This is not the actual number of events that can be extracted from the GAIA data set, as the false detection rate has not been assessed. A covariance analysis is used to study the propagation of errors and the estimation of parameters from realistic sampling of the GAIA data stream of transits in the along‐scan direction during microlensing events. The mass of the lens can be calculated to good accuracy if the lens is nearby so that the angular Einstein radius θ E is large; if the Einstein radius projected on to the observer plane r˜ E is approximately an astronomical unit; or if the duration of the astrometric event is long (≳1 yr) or the source star is bright. Monte Carlo simulations are used to study the ∼2500 events for which the mass can be recovered with an error of <50 per cent. These high‐quality events are dominated by disc lenses within a few tens of parsecs and source stars within a few hundred parsecs. We show that the local mass function can be recovered from the high‐quality sample to good accuracy. GAIA is the first instrument with the capability of measuring the mass locally in very faint objects such as black holes and very cool white and brown dwarfs. For only ∼5 per cent of all astrometric events will GAIA record even one photometric data point. There is a need for a dedicated telescope that densely samples the Galactic Centre and spiral arms, as this can improve the accuracy of parameter estimation by a factor of ∼10. The total number of sources that have an astrometric microlensing variation exceeding the mission target accuracy is ∼10 5 . The positional measurement of one source in every 20 000 is affected by microlensing noise at any instant. We show that microlensing is negligible as an unbiased random error source for GAIA .