[abridged] We carry out numerical simulations to gauge the Gaia potential for precision astrometry of exoplanets orbiting a sample of known dM stars within 30 pc from the Sun. (1) It will be possible to accurately determine orbits and masses for Jupi
ter-mass planets with orbital periods in the range 0.2<P<6.0 yr and with an astrometric signal-to-noise ratio > 10. Given present-day estimates of the planet fraction f_p around M dwarfs, 100 giant planets could be found by Gaia around the sample. Comprehensive screening by Gaia of the reservoir of 4x10^5 M dwarfs within 100 pc could result in 2600 detections and as many as 500 accurate orbit determinations. The value of f_p could then be determined with an accuracy of 2%, an improvement by over an order of magnitude with respect to the most precise values available to-date; (2) in the same period range, inclination angles corresponding to quasi-edge-on configurations will be determined with enough precision (a few percent) so that it will be possible to identify intermediate-separation planets which are potentially transiting within the errors. Gaia could alert us of the existence of 10 such systems. More than 250 candidates could be identified assuming solutions compatible with transit configurations within 10% accuracy, although a large fraction of these (85%) could be false positives; (3) for well-sampled orbits, the uncertainties on planetary ephemerides, separation and position angle, will degrade at typical rates of < 1 mas/yr and < 2 deg/yr, respectively; (4) planetary phases will be measured with typical uncertainties of several degrees, resulting (under the assumption of purely scattering atmospheres) in phase-averaged errors on the phase function of 0.05, and expected uncertainties in the determination of the emergent flux of intermediate-separation (0.3<a<2.0 AU) giant planets of 20%. [abridged]
[ABRIDGED] In this study, we set out to a) demonstrate the sensitivity to <4 R_E transiting planets with periods of a few days around our program stars, and b) improve our knowledge of some astrophysical properties(e.g., activity, rotation) of our ta
rgets by combining spectroscopic information and our differential photometric measurements. We achieve a typical nightly RMS photometric precision of ~5 mmag, with little or no dependence on the instrumentation used or on the details of the adopted methods for differential photometry. The presence of correlated (red) noise in our data degrades the precision by a factor ~1.3 with respect to a pure white noise regime. Based on a detailed stellar variability analysis, a) we detected no transit-like events; b) we determined photometric rotation periods of ~0.47 days and ~0.22 days for LHS 3445 and GJ 1167A, respectively; c) these values agree with the large projected rotational velocities (~25 km/s and ~33 km/s, respectively) inferred for both stars based on the analysis of archival spectra; d) the estimated inclinations of the stellar rotation axes for LHS 3445 and GJ 1167A are consistent with those derived using a simple spot model; e) short-term, low-amplitude flaring events were recorded for LHS 3445 and LHS 2686. Finally, based on simulations of transit signals of given period and amplitude injected in the actual (nightly reduced) photometric data for our sample, we derive a relationship between transit detection probability and phase coverage. We find that, using the BLS search algorithm, even when phase coverage approaches 100%, there is a limit to the detection probability of ~90%. Around program stars with phase coverage >50% we would have had >80% chances of detecting planets with P<1 day inducing fractional transit depths >0.5%, corresponding to minimum detectable radii in the range 1.0-2.2 R_E. [ABRIDGED]
