Author: Suzana S. A. Silva , Gary Verth, Viktor Fedun The University of Sheffield, Erico L. Rempel Aeronautics Institute of Technology, Sergiy Shelyag Deakin University, Luiz A. C. A. Schiavo Sao Paulo State University.
Photospheric flows play a crucial role in the dynamical evolution of the solar atmospheric as they are inherently coupled to magnetic fields, and this may lead to the generation of strong energetic events such as flares, coronal mass ejections, and solar tornados. The wide variety of photospheric plasma dynamics can create barriers in the plasma flow, impacting the magnetic field distribution, thereby influencing important aspects of energy and mass transport in the solar atmosphere. There is particular interest in studying the twisting of magnetic field lines due to photospheric motions, however, there is actually no universally accepted definition for a twisted magnetic flux tube. This inhibits the development of techniques to automatically identify twisted magnetic flux tubes and here we address this fundamental problem.
Due to their geometry, we can define the twisted magnetic flux tube as a vortex in the magnetic field, the M-vortex. This is illustrated in Figure 1, where we see the geometry of a twisted flux tube from a realistic magneto–convection simulation performed using MURaM .
We performed our analysis on a time frame series of a simulated solar plage , covering 600 km from the solar surface to the lower chromosphere. The vortex boundaries were determined based on the Integrated Averaged Current Deviation (IACD method . The IACD field was calculated by tracing the magnetic field line for each point starting in a selected height level and computing the current density along the line minus the spatial average of the current. The vortex boundary was defined as the outermost convex contour of the IACD field around the local maxima.
The meaning of the vortex boundary defined by IACD is illustrated in Fig. 2 where we can see the following:
- The boundary delimits a region where the vortex boundary lines are twisted and preserve their coherence for the length used to compute the IACD field,
- The magnetic field lines inside the vortex are also twisted, forming a coherent twisted flux tube,
- The lines traced from points inside the M-vortex (green lines) do not cross the vortex boundary (blue lines).
Therefore, IACD provides a proper physical definition for twisted magnetic flux tubes and automatically detects those structures.
We computed the plasma variables across the M-vortices and averaged them along the azimuthal direction, considering a cylindrical coordinate system where the origin is placed at the vortex centre. We found that inside M-vortices mainly downflows are present and that they locally concentrate the vertical magnetic field and current . Based on the ratio of magnetic energy (Em) and kinetic energy (Ek), we classify the M-vortices as: type I M-vortex (Em/Ek >1); and type II M-vortex (Em/Ek ≤1).
Examples of both types of vortices are given in Figure 3, where we see the magnetic field lines of the M-vortex in blue and the surrounding velocity field lines in red. From Figure 3, we see that the different types of M-vortex also present different geometries. Moreover, we see that the M-vortices appear in regions with shear flows.
In order to compare M-vortices and kinetic (plasma flow) vortices, which we denote as K-vortice, we also applied Instantaneous Vorticity Deviation to identify K-vortices for the time interval of the analysis as described in . Figure 4 displays a 3D view of the domain with the detected K- and M- vortices at t= 1424 seconds.
The magnetic field lines of all detected M-vortices are represented by white lines and the red lines show the velocity field streamlines from detected K -vortices. On average, over a time period of 500s, the densities of ~13 and ~28 per Mm2 were detected for M- and K-vortices, respectively. The K-vortices are located in low plasma-β regions and the M -vortices are present in regions of the flow with higher plasma-β. We find that K -vortices and M-vortices have a mean lifetime of 84.7s and 54.1 seconds, respectively, i.e., the plasma supports more K -vortex long-duration structures than M-vortices .
- M-vortices are observed in parts of the intergranular lanes with the plasma-beta >1. K-vortices appear in low plasma-beta intergranular lanes.
- M-vortices locally concentrate the vertical magnetic field due to the gas pressure gradient between the vortex boundary and its centre, forcing a new magnetic field into the M-vortex.
- There are two types of M-vortices: they show differences between their shape, magnetic and kinetic energy ratio.
- M- vortices appear if two conditions are simultaneously present: (i) shear flow, (ii) plasma-beta >1
- Further numerical studies and high-resolution observations at different spatial and temporal scales are essential to correctly describe the interplay between the magnetic field and K-vortices and the interconnectivity between structures at different height levels.