Complexity-entropy analysis of solar photospheric turbulence: Hinode images of magnetic and Poynting fluxes

TL;DR

The paper addresses how solar photospheric turbulence evolves during a supergranular vortex expansion and how energy organizes across scales. It applies a complexity-entropy analysis, based on ordinal-pattern statistics, to Hinode images of the line-of-sight magnetic field $B_z$ and horizontal Poynting flux $S$, extracting the measures $H$ and $C$. The main finding is a monotonic rise in $C$ concurrent with a drop in $H$ for both $B_z$ and $S$, accompanying the merger of plasmoids into a large coherent magnetic structure within the vortex and indicating an inverse cascade toward larger scales. This supports theories of slow-to-fast turbulent magnetic reconnection and demonstrates the utility of complexity-entropy analysis on astrophysical images, providing a path for incorporating velocity-field analyses in future work.

Abstract

The spatiotemporal inhomogeneous-homogeneous transition in the dynamics and structures of solar photospheric turbulence is studied by applying the complexity-entropy analysis to Hinode images of a vortical region of supergranular junctions in the quiet Sun. During a period of supergranular vortex expansion of 37.5 min, the spatiotemporal dynamics of the line-of-sight magnetic field and the horizontal electromagnetic energy flux display the characteristics of inverse turbulent cascade, evidenced by the formation of a large magnetic coherent structure via the merger of two small magnetic elements trapped by a long-duration vortex. Both magnetic and Poynting fluxes exhibit an admixture of chaos and stochasticity in the complexity-entropy plane, involving a temporal transition from low to high complexity and a temporal transition from high to low entropy during the period of vortex expansion, consistent with Hinode observations.

Figures (5)

• Figure 1: Spatiotemporal inhomogeneous-homogeneous transition of the line-of-sight magnetic field (in $G$) images superposed by the LIC maps of the horizontal electric current density at a supergranular vertex during a period of vortex expansion of 37.5 min. The white line denotes the objective vortex boundary; the arrows denote the merging plasmoids 1 and 2; the magenta crosses denote the centers of plasmoid 1 and 2.
• Figure 2: Spatiotemporal inhomogeneous-homogeneous transition of the horizontal electromagnetic energy flux (in ergs cm$^{-2}$ s$^{-1}$) images superposed by the LIC maps of the horizontal photospheric velocity field at a supergranular vertex during a period of vortex expansion of 37.5 min. The white line denotes the objective vortex boundary; the arrows denote the merging plasmoids 1 and 2; the magenta crosses denote the centers of plasmoid 1 and 2.
• Figure 3: Complexity-entropy plane for the line-of-sight magnetic field $B_z$ (a) and the horizontal electromagnetic energy flux $S$ (b) during a period of supergranular vortex expansion of 37.5 min. The timings of Frames 175, 183, 191, and 200 are indicated by the four respective symbols. The dashed line shows the values of $C$ and $H$ obtained from two-dimensional fractional Brownian motions (2D FBM) with Hurst exponent $h$ ranging from $h\approx0$ (lower right corner) to $h\approx1$; the crescent-shaped curves denote the minimum and maximum values of the complexity, respectively, for a given value of the entropy. Error bars in the insets indicate one-standard-deviation uncertainties of $H$ and $C$ estimated by bootstrapping ordinal patterns and their distributions from the $B_z$ and $S$ images.
• Figure 4: The original non-interpolated Hinode images of the line-of-sight magnetic field of Fig. \ref{['fig1']}, with the horizontal electric current density in the background. The white line denotes the objective vortex boundary; the arrows denote the merging plasmoids 1 and 2; the magenta crosses denote the centers of plasmoid 1 and 2.
• Figure 5: The original non-interpolated images of the horizontal electromagnetic energy flux of Fig. \ref{['fig2']}, with the horizontal photospheric velocity field in the background. The white line denotes the objective vortex boundary; the arrows denote the merging plasmoids 1 and 2; the magenta crosses denote the centers of plasmoid 1 and 2.