The continuous period search method and its application to the young solar analogue HD 116956

We formulate an improved time series analysis method for the analysis of photometry of active stars. This new Continuous Period Search (CPS) method is applied to 12 years of V band photometry of the young solar analogue HD 116956 (NQ UMa). The new method is developed from the previous Three Stage Period Analysis (TSPA) method. Our improvements are the use of a sliding window in choosing the modelled datasets, a criterion applied to select the best model for each dataset and the computation of the time scale of change of the light curve. We test the performance of CPS with simulated and real data. The CPS has a much improved time resolution which allows us to better investigate fast evolution of stellar light curves. We can also separate between the cases when the data is best described by periodic and aperiodic (e.g. constant brightness) models. We find, however, that the performance of the CPS has certain limitations. It does not determine the correct model complexity in all cases, especially when the underlying light curve is constant and the number of observations too small. Also the sensitivity in detecting two close light curve minima is limited and it has a certain amount of intrinsic instability in its period estimation. Using the CPS, we find persistent active longitudes in the star HD 116956 and a "flip-flop" event that occurred during the year 1999. Assuming that the surface differential rotation of the star causes observable period variations in the stellar light curve, we determine the differential rotation coefficient to be |k|>0.11. The mean timescale of change of the light curve during the whole 12 year observing period was T_C=44.1 d, which is of the same order as the predicted convective turnover time of the star. We also investigate the presence of activity cycles on the star, but do not find any conclusive evidence supporting them.