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

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Find in Plasma Physics and Controlled Fusion

• 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.

Conferences: The 29th New Mexico Symposium

On January 17th I presented a talk entitled "Generating Buoyant Magnetic Loops in Convective Dynamos" at the 29th New Mexico Symposium at the National Radio Astronomy Observatory facility on the campus of New Mexico Tech in Socorro, New Mexico. This was the first time I had been to Socorro and to be honest I wasn't expecting much from the town. I was very pleasantly surprised by the town and the campus. New Mexico Tech is a very nice place to spend a day talking about astrophysics.

It was great to learn about things like the Jansky Very-Large Array, the CHILES survey, and variable stars studied by the Kepler Asteroseismic Consortium, but my personal favorite was hearing about the Magdelena Ridge Observatory. MRO is currently under construction on South Baldy mountain west of Socorro and when completed it will be 10 1.4 meter telescopes spaced over as much as 340 meters, which will be used together as an optical interferometer. By doing so it will be able to achieve an angular resolution equivalent to a single telescope with a diameter of 340 meters - or about 30 times bigger than the world's current largest optical telescope.  When it comes online, MRO will be able to create resolved images of stars like our Sun - something that gets people like me very, very excited.

I focused on what we can do with the ASH code to simulate dynamo action and buoyant magnetic loops in sun-like stars. Below are a PDF copy of of the slides from my talk.

Doctoral Thesis: Magnetic Wreaths, Cycles, and Buoyant Loops in Convective Dynamos

I successfully defended my doctoral thesis on August 5th, 2013. You can download a PDF copy here or get the "official" copy from the JILA web database.

My thesis included the results from my previously published papers as well as chapters on the validation of the dynamic Smagorinsky subgrid-scale model and a new upper boundary condition which applies small-scale plumes on the top of the simulation in order to mimc the effects of near-surface convection.

Sample snapshot of the upper boundary condition for case P in Mollweide projection. (a) Radial velocity field applied at the outer boundary. (b) Pressure field implicitly applied by a boundary condition on the plume opening angles. The pressure is generally negative in the cold downflows. (c) Entropy field for the same plumes with low entropy in the downflows and high entropy in the upflows. 

Conferences: Flux Emergence Worshop 2013

From April 15th through the 18th I attended the 5th edition of the Flux Emergence Workshop in Nice, France. I also attended the 4th edition of FEW at the Space Sciences Lab in Berkeley, California in 2011. FEW is a fairly unique conference compared to others I have attended in that it is topically very focused and registration is capped at about 40 people. This allows every attendee to give a 35 minute presentation. Presentations are generally much more interactive than in other conferences. The audience members regularly interrupt talks with questions which often result in some extended discussion involving the speaker and several other people. Because the meeting is so small these tend to be very productive and focused discussions.

I presented a talk entitled "Modeling the Origin of Tilt, Twist, Active Longitudes, and More: Buoyant Loops in Global Convective Dynamos", which was focused on the statistical properties of the ensemble of buoyant magnetic loops from my convective dynamo simulation (see papers here and here). One of the very interesting topics discussed at length concerns twist in sunspots. Previous simulations have indicated that buoyant magnetic loops need to be twisted in order to coherently rise through the solar convection zone. Measuring the twist in real sunspots is difficult and requires vector magnetograms which are only now becoming widely available, but observations seem to indicate that sunspots have an order of magnitude less twist on average than the minimum required by previous simulations. My simulated buoyant loops show a wide variety of amounts of twist and, on average, even slightly less than what is observed at the solar surface.

The histogram above shows the distribution of twists in my convective dynamo simulation (case S3) with a best-fit Gaussian distribution over-plotted in the black dashed curve. The vertical red dashed line shows the average twist observed in sunspots. Previous simulations have required a minimum twist rate on the order of +/-3 in these units. If the question is "Is twist required for the coherent rise of buoyant magnetic structures, or is it merely acquired from the dynamo generation mechanism?", the answer appears to be the latter.

It was a great conference and at a particularly beautiful location. The venue was Masion du Seminaires in Nice. As you can see from the pictures below, it was a spectacular venue.

View of Masion du Seminaires in Nice, France from the Mediterranean See.

View of Nice and the Mediterranean See from a room like mine at the conference hotel.

The next FEW will be in Boulder in 2015 and I am already excited to attend.

Movie: Rising Buoyant Loops

This of a 3D rendering of magnetic field lines in buoyant magnetic loops (see my papers on these loops here and here). I have taken care not to render other field lines to visual clarity. The coloring gives the magnitude of the magnetic field. The black surfaces represent the inner and outer boundaries at 0.72 and 0.96 R_sun, respectively. The view is looking south along the rotation axis at a region roughly from the equator to 30 degree north latitude and about 30 degree in longitudinal extent. The movie covers 18 simulated days. You can download a copy of this movie by going to the Vimeo hosting site. If you use it please remember to acknowledge its source.

My CV

Click here to download the PDF.

Papers: Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

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Find in the arXiv

• 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.