Binary astrometric microlensing with Gaia
  We investigate whether Gaia can specify the binary fractions of massive
stellar populations in the Galactic disk through astrometric microlensing.
Furthermore, we study if some information about their mass distributions can be
inferred via this method. In this regard, we simulate the binary astrometric
microlensing events due to massive stellar populations according to the Gaia
observing strategy by considering (a) stellar-mass black holes, (b) neutron
stars, (c) white dwarfs and (d) main-sequence stars as microlenses. The Gaia
efficiency for detecting the binary signatures in binary astrometric
microlensing events is $\sim 10-20$ per cent. By calculating the optical depth
due to the mentioned stellar populations, the number of the binary astrometric
microlensing events being observed with Gaia with detectable binary signatures,
for the binary fraction about 0.1, is estimated as 6, 11, 77 and 1316
respectively. Consequently, Gaia can potentially specify the binary fractions
of these massive stellar populations. However, the binary fraction of black
holes measured with this method has the large uncertainty owing to a low number
of the estimated events. Knowing the binary fractions in massive stellar
populations helps for studying the gravitational waves. Moreover, we
investigate the number of massive microlenses which Gaia specifies their masses
through astrometric microlensing of single lenses toward the Galactic bulge.
The resulted efficiencies of measuring the mass of mentioned populations are
9.8, 2.9, 1.2 and 0.8 per cent respectively. The number of their astrometric
microlensing events being observed in the Gaia era in which the lens mass can
be inferred with the relative error less than 0.5 toward the Galactic bulge is
estimated as 45, 34, 76 and 786 respectively.
