We have derived the Galactic bulge initial mass function of the SWEEPS field in the mass range 0.15 $< M/M_{odot}<$ 1.0, using deep photometry collected with the Advanced Camera for Surveys on the Hubble Space Telescope. Observations at several epoch
s, spread over 9 years, allowed us to separate the disk and bulge stars down to very faint magnitudes, F814W $sim$ 26 mag, with a proper-motion accuracy better than 0.5 mas/yr. This allowed us to determine the initial mass function of the pure bulge component uncontaminated by disk stars for this low-reddening field in the Sagittarius window. In deriving the mass function, we took into account the presence of unresolved binaries, errors in photometry, distance modulus and reddening, as well as the metallicity dispersion and the uncertainties caused by adopting different theoretical color-temperature relations. We found that the Galactic bulge initial mass function can be fitted with two power laws with a break at M $sim$ 0.56 $M_{odot}$, the slope being steeper ($alpha$ = -2.41$pm$0.50) for the higher masses, and shallower ($alpha$ = -1.25$pm$0.20) for the lower masses. In the high-mass range, our derived mass function agrees well with the mass function derived for other regions of the bulge. In the low-mass range however, our mass function is slightly shallower, which suggests that separating the disk and bulge components is particularly important in the low-mass range. The slope of the bulge mass function is also similar to the slope of the mass function derived for the disk in the high-mass regime, but the bulge mass function is slightly steeper in the low-mass regime. We used our new mass function to derive stellar M/L values for the Galactic bulge and we obtained 2.1 $<M/L_{F814W}<$ 2.4 and 3.1 $< M/L_{F606W}<$ 3.6 according to different assumptions on the slope of the IMF for masses larger than 1 $M_{odot}$.
We use detailed simulations of the Gaia observations of synthetic planetary systems and develop and utilize independent software codes in double-blind mode to analyze the data, including statistical tools for planet detection and different algorithms
for single and multiple Keplerian orbit fitting that use no a priori knowledge of the true orbital parameters of the systems. 1) Planets with astrometric signatures $alphasimeq 3$ times the single-measurement error $sigma_psi$ and period $Pleq 5$ yr can be detected reliably, with a very small number of false positives. 2) At twice the detection limit, uncertainties in orbital parameters and masses are typically $15%-20%$. 3) Over 70% of two-planet systems with well-separated periods in the range $0.2leq Pleq 9$ yr, $2leqalpha/sigma_psileq 50$, and eccentricity $eleq 0.6$ are correctly identified. 4) Favorable orbital configurations have orbital elements measured to better than 10% accuracy $> 90%$ of the time, and the value of the mutual inclination angle determined with uncertainties $leq 10^{degr}$. 5) Finally, uncertainties obtained from the fitting procedures are a good estimate of the actual errors. Extrapolating from the present-day statistical properties of the exoplanet sample, the results imply that a Gaia with $sigma_psi$ = 8 $mu$as, in its unbiased and complete magnitude-limited census of planetary systems, will measure several thousand giant planets out to 3-4 AUs from stars within 200 pc, and will characterize hundreds of multiple-planet systems, including meaningful coplanarity tests. Finally, we put Gaia into context, identifying several areas of planetary-system science in which Gaia can be expected to have a relevant impact, when combined with data coming from other ongoing and future planet search programs.
In this paper, we first summarize the results of a large-scale double-blind tests campaign carried out for the realistic estimation of the Gaia potential in detecting and measuring planetary systems. Then, we put the identified capabilities in contex
t by highlighting the unique contribution that the Gaia exoplanet discoveries will be able to bring to the science of extrasolar planets during the next decade.
