The Gaia-ESO Survey (GES) is a large public spectroscopic survey at the European Southern Observatory Very Large Telescope. A key aim is to provide precise radial velocities (RVs) and projected equatorial velocities (v sin i) for representative sampl
es of Galactic stars, that will complement information obtained by the Gaia astrometry satellite. We present an analysis to empirically quantify the size and distribution of uncertainties in RV and v sin i using spectra from repeated exposures of the same stars. We show that the uncertainties vary as simple scaling functions of signal-to-noise ratio (S/N) and v sin i, that the uncertainties become larger with increasing photospheric temperature, but that the dependence on stellar gravity, metallicity and age is weak. The underlying uncertainty distributions have extended tails that are better represented by Students t-distributions than by normal distributions. Parametrised results are provided, that enable estimates of the RV precision for almost all GES measurements, and estimates of the v sin i precision for stars in young clusters, as a function of S/N, v sin i and stellar temperature. The precision of individual high S/N GES RV measurements is 0.22-0.26 km/s, dependent on instrumental configuration.
At fast rotation rates the coronal activity of G- and K-type stars has been observed to saturate and then decline again at even faster rotation rates -- a phenomenon dubbed super-saturation. In this paper we investigate coronal activity in fast-rotat
ing M-dwarfs using deep XMM-Newton observations of 97 low-mass stars of known rotation period in the young open cluster NGC 2547, and combine these with published X-ray surveys of low-mass field and cluster stars of known rotation period. Like G- and K-dwarfs, we find that M-dwarfs exhibit increasing coronal activity with decreasing Rossby number N_R, the ratio of period to convective turnover time, and that activity saturates at L_x/L_bol ~ 10^-3 for log N_R < -0.8. However, super-saturation is not convincingly displayed by M-dwarfs, despite the presence of many objects in our sample with log N_R < -1.8, where super-saturation is observed to occur in higher mass stars. Instead, it appears that a short rotation period is the primary predictor of super-saturation; P <=0.3d for K-dwarfs and perhaps P <=0.2d for M-dwarfs. These observations favour the centrifugal stripping model for super-saturation, where coronal structures are forced open or become radiatively unstable as the Keplerian co-rotation radius moves inside the X-ray emitting coronal volume.
