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.
Comment: 24 pages, 17 figures. Updates in this version 2: rewritten Eq. 2, added references Sarro et al. 2013 and Reyl\'e 2018 regarding free floating BDs in introduction, fixed reference to correct Kiefer et al. 2019 paper, expanded funding acknowledgement, added note about G_RVS in DR2 to end of Appendix H, and a few spelling improvements