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.

Papers: Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

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• Nelson, Nicholas J., Brown, Benjamin P., Brun, Allan Sacha, Miesch, Mark S., & Toomre, Juri, 2013, "Buoyant magnetic loops generated by global convective dynamo action", Solar Physics, 289, 441

This paper looks in greater detail at a large sample of buoyant loops from case S3 - a solar-like convective dynamo simulation. Below are three different views on a single buoyant loop - (a) looks south along the rotation axis, (b) looks radially inward, and (c) looks west along the axis of the loop.

Previous work has focused on small numbers of loops which were identified by visually inspecting 3D renderings of magnetic field line. Using an automated pattern recognition algorithm, I was able to locate 150+ buoyant loops in a systematic search of this simulation. The process is extremely data-intensive so I was only able to to a complete search for one magnetic activity cycle, however this provides enough loops to provide a statistical look at the properties of these loops. Here's a time-latitude map of the longitudinally-averaged magnetic field strength (red shows positive polarity, blue shows negative polarity) with wreaths of opposite polarity in each hemisphere. The southern wreath is clearly much stronger than the northern one. Over-laid are the times and latitudinal locations of each of the 138 buoyant magnetic loops located in this activity cycle, with red squares showing positive polarity loops and green diamonds showing negative polarity loops.

With a large sample of loops, we can compare properties of our simulated loops with observed properties of solar active regions.  For example, we find that our loops show similar latitudinal tilts to those proscribed by Joy's Law. We can also compare the twist of the loops with previous simulations and observations. Previous simulations have indicated that loops must have a certain amount of negative (left-handed) twist or they will break apart and dissipate as they rise. Observations show a wide variety of levels of twist at the solar surface, but a preference for left-handed twists. Our simulations show a slight preference for negative twists, but a wide variety of levels of twist are seen.

Papers: Magnetic Wreaths and Cycles in Convective Dynamos

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• Nelson, Nicholas J., Brown, Benjamin P., Brun, Allan Sacha, Miesch, Mark S., & Toomre, Juri. 2013. "Magnetic Wreaths and Cycles in Convective Dynamos", The Astrophysical Journal, 762, 73

This paper discussed a series of 3D dynamo simulations with ASH of sun-like stars. These dynamos achieved magnetic wreaths - bands of primarily longitudinal magnetic field in each hemisphere. Ben Brown's work had previously shown that persistent wreaths could become cyclic with increased rotation rate.  Here Ben and I used a series of simulations to show that cycles can also occur when simulations are made more turbulent at a fixed rotation rate.

Three ASH simulations which were the focus of this paper: D3 (left), D3a (center), and D3b (right). The simulations are identical except in their diffusion. D3a is about twice as turbulent as D3, and D3b is about twice again as turbulent. From top to bottom, the panels show radial velocities near the top of each simulation, longitudinal magnetic fields at mid-convection zone, and 3D volume renderings of magnetic field lines near the equator colored by longitudinal magnetic field.

In addition to the onset of cycles, we also showed that as these simulations become more turbulent a number of fundamental balances change. The transport of angular momentum which supports differential rotation in D3 is a balance between Reynold's stresses and viscous diffusion, but in D3b diffusion has been replaced by magnetic stresses.  The wreaths in D3 are dissipated primarily by resistive diffusion, but in D3b resolved turbulence has assumed the primary role.  Finally, we showed that the cycles themselves are caused by a breakdown in the balance between turbulent correlations and diffusion in maintaining the poloidal magnetic field.

Cartoon diagram of how cycles operate in case D3b. Magnetic wreaths (a) lead to an electromotive force (b) via an alpha-like effect, which generates poloidal magnetic field (c) through induction, which generates wreaths of the opposite polarity (d) through the Omega effect.

Finally, we showed that the so-called "alpha" effect which closes the loop on our cycles has the same timescale as convection.

Papers: Buoyant Magnetic Loops in a Global Dynamo Simulation of a Young Sun

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• Nelson, Nicholas J., Brown, Benjamin P., Brun, Allan Sacha, Miesch, Mark S., & Toomre, Juri. 2011. "Buoyant Magnetic Loops in a Global Dynamo Simulation of a Young Sun", The Astrophysical Journal Letters, Volume 739, Issue 2, L38

Longitudinal magnetic field as a function of radius and latitude at successive times. Two buoyant magnetic structures are captured here,

 This letter introduced a dynamo simulation of a sun-like star which produced buoyant magnetic loops.  The simulation, which we call case S3, uses an improved treatment of diffusion which allowing the simulation to be much more turbulent than was previously possible.

Papers: Global magnetic cycles in rapidly rotating younger suns

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• Nelson, Nicholas J., Brown, Benjamin P., Browning, Matthew K., Brun, Allan Sacha, Miesch, Mark S., & Toomre, Juri. 2011, "Global magnetic cycles in rapidly rotating younger suns", The Physics of Sun and Star Spots, Proceedings of the International Astronomical Union, IAU Symposium, Volume 273, p. 272-275

This paper was based on a conference talk given at the IAU Symposium #273: The Physics of Sun and Star Spots in Ventura, California in August 2010. I ran and analysed all but one of the simulations here.  Ben Brown was instrumental in developing many of the analysis techniques used. Mark, Sacha, and Juri played key roles in the formulation and analysis of the simulations. This was the first presentation of buoyant magnetic loops in ASH simulations.

Papers: Strong Dynamo Action in Rapidly Rotating Suns

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• Brown, Benjamin P., Browning, Matthew K., Brun, Allan Sacha, Miesch, Mark S., Nelson, Nicholas J., & Toomre, Juri, 2007, "Strong Dynamo Action in Rapidly Rotating Suns", in UNSOLVED PROBLEMS IN STELLAR PHYSICS: A Conference in Honor of Douglas Gough. AIP Conference Proceedings, Volume 948, pp. 271-27

My contribution was in running and analysing one of the three simulations presented here.