skip to main content

SciTech ConnectSciTech Connect

Title: Two regimes in the regularity of sunspot number

Sunspot numbers WN display quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional λ (an 'irregularity index') that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute λ for the daily WN from 1850 to 2012 within 4 yr sliding windows: λ exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio R of the amplitudes of the main versus secondary peaks. Two regimes have alternated in the past 150 yr, R1 from 1850 to 1915 (large λ and R values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, R values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11 yr cycle and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation a of the model series. The features of the two regimes are stable for model and WN with respect to embedding dimension and delay. Nearmore » the time of the last solar minimum (∼2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.« less
Authors:
;  [1] ; ;  [2]
  1. IEPT RAS, Profsoyuznaya str. 84/32, 117997 Moscow (Russian Federation)
  2. IPGP, 1 rue Jussieu, F-75005, Paris (France)
Publication Date:
OSTI Identifier:
22348470
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 779; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; CHAOS THEORY; LYAPUNOV METHOD; NOISE; PERIODICITY; RANDOMNESS; SUN; SUNSPOTS