Papers: Generating Buoyant Magnetic Flux Ropes in Solar-like Convective Dynamos

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• Nelson, Nicholas J. and Miesch, Mark S., 2014, "Generating Buoyant Magnetic Flux Ropes in Solar-like Convective Dynamos", Plasma Physics and Controlled Fusion, 56, 064004

This paper was the result of an invitation to submit a paper as part of a special issue of Plasma Physics and Controlled Fusion which focused on self-organization in magnetic flux ropes across a variety of physical regimes from tokamaks to the Earth's magnetosphere to the solar interior. In our paper we revisited case S3 in order to examine how exactly the buoyant magnetic loops we found and characterized in previous papers are generated. In many models of the flux emergence, strong magnetic fields slowly build up over time through the Omega-effect and then destabilize and buoyantly rise to the solar surface, emerging as sunspots. The purpose of this paper was to test that idea by looking at what physical mechanisms generate the magnetic energy which buoyantly rises and reaches the top of our simulation.

To do this we first developed a more sophisticated tracking algorithm than we had used previously in order to track our buoyant loops as far back in time as possible. This algorithm is capable of following a cross-section of the loop from backward in time from near the top of the domain until well before it begins to rise. Previously our tracking only extended about 15 days.  With this new method we were able to track for as long as 25 days in some cases. The image below shows the magnetic field lines that make up one of our loops (a) at the earliest time we could track and (b) near maximum radial extent 22 days later.

The result of this tracking is that we know the volume which will become our loop and so we can look at the physical processes in that volume over time which generate or dissipate magnetic energy. We find that our tracking cover two distinct phases - the "rise phase" where the loop is moving upward in radius and losing magnetic energy and the "formation phase" where the loop is essentially stationary in radius and growing in magnetic energy. The image below shows the movement of one loop over both phases.

In this case the rise phase lasts about 10 days and the formation phase covers the first 14 days.

If our buoyant loops behaved as assumed in many 2D models of the solar dynamo we should see a slow growth of the magnetic energy with most of the magnetic energy already present at the earliest time we track. We should also expect that the main physical process putting energy into the loop during the formation phase is the Omega-effect in which axisymmetric shearing motions turn axisymmetric poloidal field into axisymmetric toroidal field.

If we compute the average contribution from all of the possible mechanism which can add or remove magnetic energy from our loops, average them in time and space, and plot them for the 5 loops which we can track, we get the figure below.

You can check out the paper for more details, but the important thing is that the brown line which represents the Omega-effect is not the dominant player in the formation phase. Instead the green line, which represents amplification of local, small-scale magnetic fields by turbulent flows, is the most important. Further it turns out that over 70% of the magnetic energy in our loops is generated in the ~15 days prior to their rise. This supports what we call the turbulence-enhanced flux emergence paradigm.