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Regular version of the site

Article

Stochastic Description of the High-Frequency Content of Daily Sunspots and Evidence for Regime Changes

Astrophysical Journal. 2015. Vol. 799. P. 56-65.
A. Shapoval, Le Mouël J., Shnirman M., Courtillot V.

The irregularity index λ is applied to the high-frequency content of daily sunspot numbers ISSN. This λ is
a modification of the standard maximal Lyapunov exponent. It is here computed as a function of embedding
dimension m, within four-year time windows centered at the maxima of Schwabe cycles. The λ(m) curves form
separate clusters (pre-1923 and post-1933). This supports a regime transition and narrows its occurrence to cycle
16, preceding the growth of activity leading to the Modern Maximum. The two regimes are reproduced by a simple
autoregressive process AR(1), with the mean of Poisson noise undergoing 11 yr modulation. The autocorrelation
a of the process (linked to sunspot lifetime) is a ≈ 0.8 for 18501923 and ≈0.95 for 19332013. The AR(1) model
suggests that groups of spots appear with a Poisson rate and disappear at a constant rate. We further applied the
irregularity index to the daily sunspot group number series for the northern and southern hemispheres, provided
by the Greenwich Royal Observatory (RGO), in order to study a possible desynchronization. Correlations between
the north and south λ(m) curves vary quite strongly with time and indeed show desynchronization. This may
reflect a slow change in the dimension of an underlying dynamical system. The ISSN and RGO series of group
numbers do not imply an identical mechanism, but both uncover a regime change at a similar time. Computation
of the irregularity index near the maximum of cycle 24 will help in checking whether yet another regime change is
under way.