Statistics of stellar variability from Kepler I. Revisiting Quarter 1 with an astrophysically robust systematics correction

We investigate the variability properties of main sequence stars in the first month of Kepler data, using a new astrophysically robust systematics correction. We find that the fraction of stars with variability greater than that of the Sun is 60%, which is marginally consistent with previous studies, and confirm the trend of increasing variability with decreasing effective temperatures. We define low and high variability samples, with a cut corresponding to twice the variability level of the active Sun, and compare the properties of the stars belonging to each sample. We show tentative evidence that the more active stars have lower proper motions and may be located closer to the galactic plane. We also investigate the frequency content of the variability, finding clear evidence for periodic or quasi-periodic behaviour in 16% of stars, and showing that there exist significant differences in the nature of variability between spectral types. Of the periodic objects, most A and F stars have short periods (<2 days) and highly sinusoidal variability, suggestive of pulsations, whilst G, K and M stars tend to have longer periods (>5 days, with a trend towards longer periods at later spectral types) and show a mixture of periodic and stochastic variability, indicative of activity. Finally, we use auto-regressive models to characterise the stochastic component of the variability, and show that its typical amplitude and time-scale both increase towards later spectral types, which we interpret as a corresponding increase in the characteristic size and life-time of active regions.