Gaia predicted brown dwarf detection rates around FGK stars in
  astrometry, radial velocity, and photometric transits
  Context: The current sample of known brown dwarfs (BDs) around FGK-stars is
only of the order of a hundred. The ongoing ESA mission Gaia has already
collected its nominal 5 yr of mission data and might operate up to 10 yr.
  Aims: Using detailed simulations, we estimate the number of BDs that could be
discovered by Gaia astrometry, radial velocity, and photometric transits around
main sequence (V) and subgiants (IV) FGK host stars for a 5 and 10-yr mission.
  Methods: Using a robust $\Delta \chi^2$ statistic we analyse the BD companion
detectability from the Besan\c{c}on Galaxy population synthesis model
complemented by Gaia DR2 data for the bright end, using the latest Gaia
performance and scanning law, and literature-based BD-parameter distributions.
  Results: We report here reliable detection numbers ($\Delta \chi^2$>50) for a
5-yr [10-yr] mission. Astrometry alone yields 28,000-42,000 [45,000-55,000]
detections out to several hundred pc [>kiloparsec], with the majority around G
magnitude 14-15 [14-16] and P>200 d. Gaia radial velocity time series allow
detection of 830-1100 [1500-1900] mainly massive BDs (55-80 M_J), most having P
<10 d. Systems with at least 3 photometric transits (S/N>3) are expected for
720-1100 [1400-2300] BDs, averaging at 4-5 [5-6] transits per source. Overlap
of astrometric and radial velocity detection yield 370-410 [870-950]
candidates, transit and radial velocity 17-27 [35-56], and transit and
astrometric detection 1-3 [4-6].
  Conclusions: Though above numbers have +/- 50% uncertainty due to the
uncertain occurrence rate and period distribution of BDs around FGK host stars,
Gaia detections will number in the tens-of-thousands, enlarging the current
sample by at least two orders of magnitude, allowing to investigate the BD
fraction and orbital architectures as a function of host stellar parameters in
greater detail than every before.
