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Observing cycles and active longitudes on young sunlike stars from photometry and spectroscopy
In this study, we aim at investigating the properties of the active longitude system of the young solar analogue HD 116956 in detail, especially concentrating on determining the rotation period of the spot-generating mechanism with respect to the photometric rotation period of the star itself. Because the nonparametric approach, like the Kuiper method, can only give the period of active longitudes, we formulate a new method that can determine the parameters the active longitude distribution uniquely. For this purpose, we have developed an analysis method, based on Bayesian statistics using Markov chain Monte Carlo, presented in this manuscript. One of the advantages of this method is that an estimate of the active longitude system rotation period, as well as the parameters of the shape and location of the active longitudes together with their respective error estimates. This allows us to compare the active longitude and mean photospheric rotation periods of the star. Our analysis confirms previous results of the object having two stable active longitudes with a phase difference of Delta phi = 0.5, the other longitude having dominated over the other one during almost the entire span of the time series. Our method gives the rotation period of the active longitude system P_al = 7.8412 +- 0.00002 d, which is significantly different from the mean photospheric rotation period of the star P_rot = 7.817 +- 0.003 d. Our analysis indicates that the spot-generating mechanism, manifesting itself as a system of two active longitudes, is lagging behind the overall rotation of the star. This behaviour may be interpreted as a nonaxisymmetric dynamo wave propagating in the rotational reference frame of the stellar surface.