Research
Vortex definition
For a flow, the vortex can be defined as "the collective motion associated with the azimuthal component of a vector field (e.g. true velocity or magnetic field) or its observational counterparts (such as trackable motions of features associated with radiation intensity or magnetic field) about a common centre or axis.” (Tziotziou et al. 2023)
In the solar atmosphere, we have different kind of vortices, as illustrate in the figure below:
Illustration depicting various types of vortex flows and associated phenomena in the solar atmosphere. The granulation pattern is represented schematically in shades of brown, with black arrows illustrating the corresponding convective flow field for the prominent granules. Magnetic field lines are shown as blue lines, while instantaneous streamlines are represented in red. Green arrows indicate the rotation of magnetic flux structures.
Importance of vortices in the Sun
Vortices are key features in any turbulent flows. They help mix the flow and dissipate energy into small scales. In the solar atmosphere, they are believed to influence plasma dynamics, leading to important phenomena.
Jets
Structures such as spicules, fibrils, mottles, rapid blue/red-shifted excursions (RBEs/RREs), and straws are solar jets. They can be observed in various wavelengths, lasting from a few seconds to several minutes. One leading theory for these jet-like features in the chromosphere is that they are thin, dense magnetic fluxtubes. Vortices can help to create overdense thin magnetic fluxtubes in the chromosphere and lead to an overshot of dense plasma material (Kitiashvili 2013, Yadav et al. 2021, Silva et al. 2024)
Snow et al. (2018) studied how magnetic flux tubes expand from the photosphere to the upper solar atmosphere, with vortex motions at their base. These vortex motions twist the magnetic field of the larger flux tube, creating smaller structures within it. These smaller structures act as waveguides to the upper solar atmosphere. The interacting vortex motions cause a mix of merging flux tubes, producing strong upward shocks that drive chromospheric jets.
Wave excitation
Solar vortices have been identified as key potential sources of magnetohydrodynamic (MHD) waves in the solar atmosphere. When the flow is rotating, it carries magnetic field lines with them, disturbing the magnetic field and creating various types of waves.
In a 2011 study, Fedun and colleagues used a vortex-like force at the base of an open magnetic flux tube to create MHD wave modes like sausage, kink, and torsional Alfvén waves. Similarly, Yadav and his team in 2022 used vortex flows to generate MHD waves, finding that these waves play a significant role in transferring energy through the solar corona.
Observations by Jess et al. in 2009 showed that vortex motions in the photosphere can trigger incompressible waves in the solar chromosphere. These Alfvén waves are important for moving energy from the photosphere to the upper chromosphere (Liu et al., 2019). Additionally, the CO5BOLD radiative MHD code has been used to simulate a small part of the solar atmosphere, revealing the Alfvénic nature of chromospheric swirls (Battaglia et al., 2021).
Energy transport and plasma heating
The way energy is created, moved, and used up to keep the solar upper atmosphere hot is still mostly a mystery. One important factor in understanding this heating process is the Poynting flux, Research by Shelyag et al. (2011) and Yadav et al. (2020) found that flow vortices produce enough electromagnetic energy to explain the high temperatures in the chromosphere. However, it was unclear if the energy generated in the photosphere could reach the upper atmosphere. Silva et al. (2024) showed that when kinematic and magnetic vortices interact, they create a channel that lets three times more energy from the photosphere reach the upper chromosphere and lower corona, overcoming existing energy transport barriers. In these situations, magnetic energy moves from the centre of the vortices to their edges and upper parts, where temperatures can reach around a million Kelvin. As these vortices break down, they concentrate some of this energy inside.
Silva et al. (2024) findings also show that the generated magnetic energy follows a swirling motion through the solar atmosphere, creating an energy vortex that matches the kinetic vortex. In areas where these vortices co-exist, their dynamics make it easier for energy to be used up through Ohmic and viscous heating because they naturally create large gradients in magnetic and velocity fields over small areas.
Solar Flares
The mechanisms underlying the formation of significant solar explosive events, such as flares and coronal mass ejections, remain not fully understood (Shibata & Magara 2011). Multiple mechanisms have been proposed to explain the origins of solar flares. Kusano et al. 2020 conclude that the magnetic twist flux density, near a magnetic polarity inversion line on the solar surface, dictates the timing, location, and magnitude of solar flares. Magnetic twist and magnetic vortices can be driven by the action of shear and flow vortices. On the other hand, a flare can induce sunspot rotation, as shown by Bi et al. 2016
Detection methods
The detection methods are based on the definition of vortex. Since mathematically there is no universal definition, see e.g. Haller 2015, there are different methods to detect vortices.
The main detection methods applied in solar physics are:
Gamma method : it is a 2D method based on the velocity field topology and provides the center and the boundary of the vortex (Grafteaux et al. 2001, Silva et al. 2018, Giagkiozis et al. 2018, Yuan et al. 2023). The figure depicts a close view of a photospheric plasma flow. The velocity field direction is indicated by the white arrows and the centers in blue and red and the boundary in orange (Credit: Giagkiozis et al. 2018)
Lagrangian Averaged Vorticity Deviation (Haller 2015): it defines the vortex as the region with local maximum vorticity fluctuations along the particle's pathline. LAVD provides the center and the boundary of the vortex. It can be used to identify vortices in 2 and 3D (Rempel et al 2017, Silva et al. 2018, Alhojani et al. 2022).
SWIRL algorithm: Identifies the region of the vortices in 2D flows based on the morphological properties of the velocity field (Canivete Cuissa et al 2022, 2024).
Swirling Strength: it can be applied to both 2 and 3D flows. The vortices are identified as regions where gradient of the velocity field has a pair of complex conjugate eigenvalues. (Zhou et al. 1999, Moll et al 2011, 2012, Kato & Wedemeyer 2017, Yadav et al. 2020 )
Integrated Averaged Current Deviation): it was developed to identify coherent flux ropes, twisted fluxtubes, aka magnetic vortices. It defines the vortex as the region with local maximum current fluctuations along the along the magnetic field lines. IACD provides the center and the boundary of the vortex. It can be used to identify vortices in 2 and 3D. (Rempel et al 2017, 2019, Silva et al 2021)
