Multicomponent Activity Cycles Using Hilbert–Huang Analysis

The temporal analysis of stellar activity evolution is usually dominated by a complex trade-off between model complexity and interpretability, often by neglecting the nonstationary nature of the process. Recent studies appear to indicate that the presence of multiple coexisting cycles in a single star is more common than previously thought. The correct identification of physically meaningful cyclic components in spectroscopic time series is therefore a crucial task, which cannot overlook local behaviors. Here we propose a decomposition technique that adaptively recovers amplitude- and frequency-varying components. We present our results for the solar activity as measured both by the sunspot number and the K -line emission index, and we consistently recover the Schwabe and Gleissberg cycles as well as the Gnevyshev–Ohl pattern probably related to the Hale cycle. We also recover the known 8 yr cycle for 61 Cygni A, in addition to evidence of a three-cycles-long pattern reminiscent of the Gnevyshev–Ohl rule. This is particularly interesting as we cannot discard the possibility of a relationship between the measured field polarity reversals and this Hale-like periodicity.