Author: Cosima A. Breu at the University of St. Andrews.
From water spiralling into a sink drain to mesmerising giant storms on Jupiter, vortex motions are present throughout the universe on scales from the very small to the very large. On the Sun, hot plasma bubbles up, only to sink back into the darker troughs between the bright granules, braiding and twisting the strong magnetic field that threads the solar atmosphere. Spiralling plasma winding up the magnetic field can generate large rotating flows higher up in the atmosphere, sometimes dubbed “magnetic tornadoes” . Unlike the violent storms raging on Earth, however, these structures are held together by giant twisted magnetic funnels reaching up to low coronal heights, potentially channeling mass and energy into the corona.
Vortex motions on the Sun have been observed as rotational motions of magnetic bright points in the photosphere, as well as bright and dark spiral shapes in the chromosphere and low corona . Furthermore, they have also been inferred from numerical simulations [2-4]. Due to their small scales, these structures are not easy to observe. New ground-based telescopes such as the Daniel K. Inouye Telescope (DKIST) allow us to resolve finer and finer structures on the solar surface down to tens of kilometers, increasing the importance of taking into account the contribution of small-scale motions inside magnetic flux concentrations to accurately estimate the energy flux into the solar atmosphere. Most existing studies focus on the photosphere and chromosphere. Here we present efforts to build a comprehensive model incorporating the energy transfer from the convection zone to the corona.
We use 3D resistive magnetohydrodynamic simulations with the MURaM code  to study vortex motions in the interior of a coronal loop and their influence on energy transport. Computer simulations of the solar atmosphere are faced with competing demands between including regions of sizes of tens or hundreds of Mm with a realistic magnetic field geometry and resolving small-scale structures such as magnetic patches on the surface or current sheets in the atmosphere. To achieve a balance, we model an isolated loop as a straightened out magnetic flux tube in a Cartesian box rooted in a shallow convection zone at each foot point, allowing vortex motions to arise self-consistently from magnetoconvection [6,7]. While we have an intuitive notion of what a vortex is, finding an objective criterion to systematically identify vortices in a complex flow is not trivial. Here we employ the swirling strength criterion  that relies on the eigenvalues of the velocity gradient tensor to detect plasma locally spiralling around a point. Vortices exist on many scales, from a few tens of km to Mm. Since the swirling strength criterion depends on local gradients, we smooth out the velocity field to pick up rotational motions on larger scales.
Do swirls reach the corona?
We find that vortices can form coherent structures that reach far into the corona and funnel energy into the coronal loop, coupling different layers of the solar atmosphere from the photosphere to the corona. An example of a coherent magnetic structure harbouring a vortex is shown in Fig. 1. The coronal heating problem does not only involve the question of how energy is transported into the solar atmosphere, especially past the steep temperature and density gradients in the transition region, but also how it is converted into heat. To investigate general properties of swirls across a large
range of atmospheric heights, we conducted a statistical study of swirl properties in our simulation. Statistics for Poynting flux, density, heating rate and coronal emission are shown in Fig. 2. We find both an increased upward Poynting flux as well as enhanced heating in vortices.
Can we observe this?
We know that energy is dissipated in vortices, therefore this heating should lead to higher temperatures and thus cause the vortex to be brighter than its environment, potentially forming a coronal loop strand. The reality, however, seems to be less straightforward. While we find examples of brightenings at the edges of vortices, as shown in Fig. 3, some vortices are dark and the contrast between swirls and the environment is generally low with only about 5 % enhancement in X-rays (see Fig. 2). In addition to temperature, coronal emission has a strong density dependence and is determined by a complex interplay between the timescales of heating, cooling and chromospheric evaporation. We find the density to be enhanced in vortices in the chromosphere, but not the corona. While vortices are generally short lived, the cooling timescales of coronal plasma are on the order of half an hour, so a vortex causing a heating event might be long gone by the time denser material from the chromosphere evaporates into the corona and the loop brightens up.
Vortices can act as energy channels into the solar corona as well as sites of energy conversion and heat deposition. Spanning from spiralling plasma downflows in the intergranular lanes through the chromosphere up to the corona they connect different atmospheric layers. Vortices are in some cases associated with coronal brightenings and influence the visible coronal loop structure, although there is no one-to-one correspondence between a vortex tube and a bright coronal strand. The role vortices play compared to other mechanisms of energy transport and their dependence on the magnetic topology remains to be explored. Furthermore, observationally studying the 3D structure of vortices and the connectivity between different atmospheric layers poses a huge challenge due to the small spatial snd temporal scales involved, but new missions such as MUSE promise to allow a closer look at the complex plasma flows in the solar atmosphere. Finally, we can look beyond our own solar system and explore the role of vortices on other stars with convection zones and atmospheres different from our Sun.
This work was recently published in Astronomy and Astrophysics .
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