Author: David MacTaggart at the University of Glasgow, Chris Prior, Breno Raphaldini at Durham University and Paolo Romano, Salvo Guglielmino at INAF Catania.
Solar active regions are the nurseries of the most important dynamical events in the Sun’s atmosphere, including flares and coronal mass ejections. A fundamental constituent that helps to determine the evolution of an active region is the topology of its magnetic field. By this, we mean how the magnetic field lines are connected and twisted. A long-held assumption of active region formation is that they are created by large tubes of magnetic field with a net twist (rather like a large magnetic slinky). This assumption has been popular for two main reasons. The first is that twisted magnetic fields can survive in the solar convection zone better than untwisted fields, and are thus more likely to reach the photosphere and emerge as active regions. The second is that simulations of the emergence of twisted tubes are able to produce a variety of signatures that are found in solar observations, which match well with proxies of magnetic twist found in observations. However, despite many works suggesting the existence of twisted tubes creating active regions, the question of whether or not this is the case has remained open. This is because there exist plausible competing theories which suggest that the twist in active regions can be created in the atmosphere rather than emerge into it. Further, observational proxies used in support of the emergence of pre-twisted tubes can be reproduced by emerging magnetic fields that are not twisted tubes. What is needed is a direct measure of the magnetic topology.
One widely-used measure of magnetic topology is magnetic helicity. The flux of this quantity through the photosphere can be calculated in observations, and many studies of this have been made. No clear signature for twisted tube emergence has been found, however. One reason for this is that magnetic helicity represents a combination of two fundamental quantities, magnetic flux and field line topology, which together can introduce a confound. For example, a highly entangled field with a strong topological measure can have a very weak field strength. Thus, the magnetic helicity of such a field can be small and, therefore, not diagnose the topological complexity of the field clearly. It is not that magnetic helicity is giving an erroneous result, rather it is the interpretation of magnetic helicity as a direct measure of magnetic topology which is not correct in general. In order to find a direct measure, we can renormalize magnetic helicity to produce a quantity called magnetic winding . This quantity is effectively the magnetic helicity with the field strength weighting removed, and thus represents a direct measure of magnetic field line topology.
Signatures in simulations and observations
The flux of magnetic winding can be calculated in both simulations and observations, just like magnetic helicity. The analysis of magnetic winding in simulations of twisted flux tubes emerging through a convective layer and into the solar atmosphere, reveals a consistent “rise and plateau” signature across a range of parameters . This is not the case for magnetic helicity which does not provide a consistent signature, just as in observational studies. An example of the accumulation of magnetic winding in a flux emergence simulation is shown below.
Figure 1(a) shows field lines of an emerging twisted tube below and above the photospheric boundary (shown in red). There is no visible resemblance to a twisted flux tube due to the strong deformations caused by convective motion and the emergence into the atmosphere. That being said, the magnetic winding is robust enough to still detect that the magnetic field has a net twist, and this can be seen in Figure 1(b), which shows the accumulations of the total magnetic winding L, as well as the contributions to magnetic winding due to emergence, Lemerge, and photospheric braiding motions, Lbraid. What this signature is saying is that when the bulk of the twisted tube rises above the photosphere, it remains there. Even though convection drags down part of this field, no more topologically-significant field is passing through the photosphere. Thus, after the rise during emergence, there is a plateau which indicates that the main topological content has passed through the photospheric boundary (where the calculations are performed). Further, Lemerge dominates the contribution to L, which means that the signature is dominated by a pre-twisted magnetic field, rather than one whose twist is generated later by photospheric motions.
This magnetic winding signature for twisted tube emergence has now also been found in observations. As an example, Figure 2 shows the winding accumulations for the bipolar region AR11318.
The “rise and plateau” signature can be found for this region (even despite the period of missing data). AR11318 has been studied extensively  and many signatures had been found which are highly suggestive of twisted tube emergence though not conclusive. The magnetic winding signature is the last piece in the puzzle to confirm that the region is formed by a twisted magnetic flux tube.
Magnetic winding is a robust measure of magnetic topology that can provide different information compared to magnetic helicity. Since it is a direct measure of field line topology, it has been used to show that pre-twisted tubes can emerge to create active regions. Therefore, the assumptions used in many flux emergence simulations now have an observational basis. For many more details and examples, together with a large set of relevant references, please consult . Further developments of magnetic winding for use in flare prediction can be found in .
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-  Raphaldini et al. 2022, Astrophysical Journal, 927, 156