Characterizing Vortex-Driven Dynamics in the Solar Atmosphere Using Information Theory

TL;DR

This work addresses how solar vortices reorganize their local atmosphere and heating beyond mere co-location, by applying information theory to a 3D Bifrost MHD simulation. Using Shannon entropy $H$ and normalized mutual information $\mathrm{NMI}$, the authors track entropy-driven complexity and cross-variable coupling within a dynamically tracked vortex core, contrasting with a nearby non-vortical flux tube and employing surrogate tests to establish significance. They find that magnetic complexity $H(E_{\text{mag}})$ rises during vortex formation, temperature becomes strongly linked to magnetic shear and current dissipation in the upper atmosphere, and the usual temperature–density adiabatic coupling weakens, indicating non-adiabatic heating pathways. The approach provides a scalable, model-agnostic framework for diagnosing energy transport in nonlinear solar plasmas, with potential extension to high-resolution observations of vortices, swirls, and flux ropes.

Abstract

Solar vortex regions show enhanced Poynting flux and favourable heating conditions, but how the vortices reorganize and influence their surroundings remains unclear. Here we apply information-theoretic diagnostics to a Bifrost simulation to quantify the dynamics of a long-lived vortex. By combining Shannon Entropy and Normalized Mutual Information, we track how the vortex reshapes plasma-magnetic couplings and modifies local thermodynamics. The vortex originates in the upper photosphere and extends into the chromosphere, where it suppresses the background p-mode-like organisation seen in the neighbouring magnetic flux tube. Shannon Entropy analysis shows that magnetic complexity rises sharply as the vortex develops, which is consistent with the build-up of currents and stored energy. At the same time, temperature becomes more strongly linked to magnetic shear, pointing to heating associated with current dissipation. The way temperature responds to different heating processes also changes with height: in the photosphere and lower chromosphere, it follows local compressional and expansion motions, while in the upper atmosphere, it is influenced mainly by viscous and current-driven effects. During this phase, the usual temperature-density relationship weakens, indicating that the plasma departs from purely adiabatic behaviour. Applying the same diagnostics to a nearby non-vortical flux tube yields only weak, uniform couplings, which confirms that the enhanced links are vortex-driven. Together, these results demonstrate that a coherent solar vortex not only drives heating but also reconfigures the local atmosphere, replacing periodic pressure-driven behaviour with magnetically dominated dynamics.

Figures (11)

• Figure 1: Central panel: Horizontal extent of the Bifrost simulation domain at $t = 500$ s, showing the synthetic H$\alpha$ core line. The two analyzed subregions are marked by the red and black squares, respectively. Left panel: 3D view of the region without large-scale vortical activity. Red lines indicate selected magnetic field lines seeded near the centre of the subdomain. The horizontal slice at $z = 2$ Mm is colored by $B_z$, with line-integrated convolution (LIC) patterns overplotted to reveal the horizontal velocity field. The bottom slice at the photosphere ($z = 0$ Mm) also shows $B_z$ for context. Right panel: Same as left, but for the region containing the dynamically tracked large-scale kinetic vortex. The LIC texture highlights the coherent rotational motion, and the magnetic field lines reveal a twisted, vertically extended structure anchored in the vortex core.
• Figure 2: Magnetic field strength $|\mathbf{B}|$ (grayscale, in Gauss) with unit velocity vectors (red) shown inside the circular mask (black contour) that automatically identifies the magnetic flux region at $z=3$ Mm and $t=500$ s.
• Figure 3: Temporal evolution of the SE computed from the $\log_{10}$ of the plasma temperature within the masked region of the magnetic flux tube, at a height of 2.52 Mm, where a vortex develops. The upper circular panels display snapshots of the temperature gradient magnitude, $|\nabla \log_{10} T|$, at selected times along the entropy curve.
• Figure 4: Temporal and vertical evolution of the spatially averaged plasma quantities within the dynamically tracked magnetic flux core. Each panel corresponds to a different physical variable: a) kinetic energy $Ek$, b) vorticity of horizontal velocity $\nabla \times \mathbf{v}_h$, c) vertical velocity $v_z$, (d) magnetic energy density $E_{\text{mag}}$, e) magnitude of magnetic shear $\left| \nabla \times \mathbf{B}_h \right|$ of the transverse magnetic field, f) vertical magnetic field $B_z$, g) mass density $\rho$, h) gas pressure $P$, i) temperature $T$, and j) plasma-$\beta$. All variables are shown in base-10 logarithmic scale, except for the vorticity $\nabla \times \mathbf{v}_h$ of horizontal plasma flows and the vertical velocity $v_z$. Blue stars mark the onset of the main large-scale vortex, solar tornado, at each height, while orange stars indicate its decay. Green stars denote the termination of smaller secondary vortices that form after the decay of the primary structure. All times and locations were identified using the $\Gamma$-method with $\Gamma>1$.
• Figure 5: Same as Figure \ref{['fig:variables']}, but for the magnetic flux tube without coherent rotational motion.