Comparison of Chaotic and Fractal Properties of Polar Faculae With Sunspot Activity

Abstract

The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.

Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

“…Uritsky and Davila (2012) however studied the spatio-temporal evolution of unipolar and bipolar photospheric regions to analyze the fractal dimensions' multiscale behavior. Furthermore, fractal dimensions have also been determined for the distribution in the number of sunspots appearing on the solar disk (Deng, 2016a) showed that there is a correlation among the different measures of fractal dimensions of number of sunspots and time series determinations. These different determinations quantify the phenomena they measure which behave fractally and therefore obey a power law.…”

“…Deng et al (2016aDeng et al ( , 2016b suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields produces the complexity and the relationships between the polar faculae and sunspot numbers and areas. They used a time series to investigate the fractal and chaotic properties of high and low-latitude solar activity by use of the fractal dimension, Hurst exponent and Lyapunov exponent and thereby were able to establish a predictability timescales in years for these three measures.…”

“…They used a time series to investigate the fractal and chaotic properties of high and low-latitude solar activity by use of the fractal dimension, Hurst exponent and Lyapunov exponent and thereby were able to establish a predictability timescales in years for these three measures. They determined values of the fractal dimension as approximately 1.2 and the Hurst exponent of approximately 0.8 showed long range persistence (Deng et al 2016a). The fractal dimension for sunspots determined at a point in time differs from the value determined through time series, that is, spatial and temporal determinations yield different values (Georgoulis 2005).…”

Multi-scale Oscillation Modes and Secular Trend Analysis of Astronomical Historic Archives

“…Solar magnetic fields are formed below the surface atmosphere and extend put into the corona which owns high temperature. An obvious feature of sunspot areas or sunspot numbers, which are the key indicators of solar magnetic activity, is the approximate 11-year cycle (sometime, from 9.5 years to 12.5 years) [10]. To this day, sunspot observations remain the one of the best indicators of strong magnetic fields with a few gausses, and they have been become an important subject of extensive research [11].…”

Spatial Inhomogeneity in Solar Faculae

“…Valid and very interesting questions that should be answered are, such as e.g. (i) do faculae show indeed the butterfly distribution; (ii) how to account for the high-latitude distribution of faculae (Deng et al 2016); (iii) is there a longitudinal pattern, supporting the mounting evidence of active longitudes (AL), of solar faculae; (iv) are all faculae the result of the global 11-year cycle dynamo, or, could there be a second dynamo operating (e.g. a local, surface one); (v) could actually the statistical analysis of spatio-temporal properties of faculae provide evidence towards the coupling of global and local dynamos; -just to raise a few questions that may justify why to pay so much attention to faculea.…”