We present a study on the determination of rotation periods (P) of solar-like stars from the photometric irregular time-sampling of the ESA Gaia mission, currently scheduled for launch in 2013, taking into account its dependence on ecliptic coordinat
es. We examine the case of solar-twins as well as thousands of synthetic time-series of solar-like stars rotating faster than the Sun. In the case of solar twins we assume that the Gaia unfiltered photometric passband G will mimic the variability of the total solar irradiance (TSI) as measured by the VIRGO experiment. For stars rotating faster than the Sun, light-curves are simulated using synthetic spectra for the quiet atmosphere, the spots, and the faculae combined by applying semi-empirical relationships relating the level of photospheric magnetic activity to the stellar rotation and the Gaia instrumental response. The capabilities of the Deeming, Lomb-Scargle, and Phase Dispersion Minimisation methods in recovering the correct rotation periods are tested and compared. The false alarm probability (FAP) is computed using Monte Carlo simulations and compared with analytical formulae. The Gaia scanning law makes the rate of correct detection of rotation periods strongly dependent on the ecliptic latitude (beta). We find that for P ~ 1 d, the rate of correct detection increases with ecliptic latitude from 20-30 per cent at beta ~ 0{deg} to a peak of 70 per cent at beta=45{deg}, then it abruptly falls below 10 per cent at beta > 45{deg}. For P > 5 d, the rate of correct detection is quite low and for solar twins is only 5 per cent on average.
Rotation and solar-type magnetic activity are closely related to each other in stars of G or later spectral types. Presence and level of magnetic activity depend on stars rotation and rotation itself is strongly influenced by strength and topology of
the magnetic fields. Open clusters represent especially useful targets to investigate the connection between rotation and activity. The open cluster NGC2099 has been studied as a part of the RACE-OC project, which is aimed at exploring the evolution of rotation and magnetic activity in the late-type members of open clusters of different ages. Time series CCD photometric observations of this cluster were collected during January 2004. The relations between activity manifestations, such as the light curve amplitude, and global stellar parameters are investigated. We have discovered 135 periodic variables, 122 of which are candidate cluster members. Determination of rotation periods of G- and K-type stars has allowed us to better explore evolution of angular momentum at an age of about 500 Myr. A comparison with the older Hyades cluster (~625 Myr) shows that the newly determined distribution of rotation periods is consistent with the scenario of rotational braking of main-sequence spotted stars as they age. However, a comparison with the younger M34 cluster (~200 Myr) shows that the G8-K5 members of these clusters have the same rotation period distribution, that is G8-K5 members in NGC2099 seem to have experienced no significant braking in the age range from ~200 to ~500 Myr. Finally, NGC2099 members have a level of photospheric magnetic activity, as measured by light curve amplitude, smaller than in younger stars of same mass and rotation, suggesting that the activity level also depends on some other age-dependent parameters.
