Multiscale Aspects of the Solar Indexes Mg II, F10.7 and Sunspot Number

The Sun is a major source of energy for the planetary system in our solar system. The solar output shows variations in timescales from a few days (Bartel’s 27-day solar rotation cycle) to several years (the 11-year solar cycle and longer timescales). This variability can be seen in the magnetic field, particle flux, and electromagnetic radiation flux behavior. Several indicators, such as the sunspot number and the Mg II index, have been used as solar activity proxies. Further, direct measurements in radio at centimeter wavelengths have been conducted since 1947 (the F10.7 index). This work uses multiscale techniques to study the relations between these solar indexes and their long-term variations through multiscale techniques. The monthly averages of these indexes from 1979 to 2022 are analyzed using wavelet scalogram, global wavelet spectrum, wavelet cross-correlation, and wavelet entropy techniques. As a result, some nonlinear multiscale aspects in the long-term variations of these solar indexes are identified. The major scales at which these indexes vary are found to be, in order of decreasing energy: sunspots (130.1, 253.9, 11.7, 5.0, and 2.0 months); F10.7 (130.1, 253.9, 39.1, 10.9, 9.9, and 5.4 months), and Mg II (132.9, 39.0, and 10.3 months). Thus, all three indexes present the nearly 11-year solar cycle period as the strongest signal. The three indexes are correlated with a coefficient higher than 0.85 and vary in phase for scales near the 11-year solar cycle, with slight and large deviations from it for longer and shorter scales, respectively. The wavelet entropy analysis shows that the F10.7 and sunspot number values are comparable, while Mg II entropy values are much lower. The entropy also indicates that the minimum values for all the indexes occur close to the solar minimum. However, after the last solar maximum in 2014, the entropy increased even in the declining phase of the cycle, during the 2015 – 2020.