The Chaotic Nature of Magnetic Reconnection and Coronal Dynamics

TRACE image of a hot coronal loop. Image credit: NASA

The solar corona is a strange place. For the last few decades solar physicists have been trying to understand why it is so hot. Yes, it’s the Sun, and yes, it’s hot, but the corona is too hot. There are many possible solutions to the “coronal heating phenomenon”, but physicists are generally in agreement that this extreme heating is down to waves propagating along magnetic fields, interacting with coronal plasma, or by reconnection events (small explosions). In a study published earlier this year, scientists suggest that to account for the temperatures and densities observed in the corona, chaotic forces may be at work, regulating the scales of reconnection in the coronal plasma.

To put this problem into perspective, the Suns atmospheric gases can be hotter than a million Kelvin (or degrees Celsius). The solar “surface” (or photosphere) is about 6000 K. How can the atmosphere of a solar body be hotter than the Sun itself? It is like finding that the temperature of the air surrounding a light bulb is actually hotter than the bulbs glass surface, it’s an impossible situation, breaking all sorts of physical laws, principally the second law of thermodynamics:

Heat cannot spontaneously flow from a material at lower temperature to a material at higher temperature.” – Rudolf Clausius (1822-1888)

So, since the mid-1900s solar physicists have been searching for an answer to this puzzling phenomenon. The two main contenders to the mechanism which supports coronal heating are:

  • Magnetohydrodynamic (MHD) wave heating
  • Small-scale reconnection events (i.e. nanoflares)

Both mechanisms have their advantages and disadvantages, but ultimately neither theory can explain why the corona is the temperature it is or the density it is. Generally, it is agreed that observational instrumentation currently may be of insufficient resolution to detect small-scale waves or flares, but this is cold comfort to solar physicists who continue to observe and model the solar corona.

In a recent paper, a group from the Bartol Research Institute (University of Delaware, USA) believe the corona may be governed by self-organized critical dynamics, put simply: chaos. By studying other stars, and assuming the coronal dynamics is similar in all Sun-like stars, a picture can be formed of how stellar coronae are driven.

The Bartol research group calculates the dynamical processes that convert stored magnetic energy into kinetic energy. Basically, they assume the vast amount of energy stored in the stars magnetic field is somehow liberated to go on and heat coronal gas particles. But how can this energy be released? This is where extreme plasma physics steps in, when magnetic field lines get too close.
Diagram of a reconnection region. Field lines are forced together and particles flow across a diffusion region. Source: http://en.wikipedia.org/wiki/Image:Reconnection_Illustrations.png
Should two field lines be forced together (a common occurrence in the solar corona), they may “reconnect” (i.e. snap apart and reconnect). Magnetic energy may then be liberated, heating the surrounding solar plasma. But, there are two different types of reconnection event: collisional (slow) and collisionless (fast). Both are critical to ensuring energy can be explosively released.

In its “energy storage state” the magnetic field lines coexist with coronal plasma. Field line and plasma are “frozen in”, where the plasma flows, the magnetic field line follows. Should magnetic flux cross and reconnection begin, collisional reconnection may occur (it is collisional as the plasma particles are close enough to “feel” each other – they are colliding). Now, collisional reconnection, also known as Sweet-Parker reconnection, is very slow and insufficient at generating a rapid release of energy. It is however useful at making the reconnection region more and more collisionless, speeding up the reaction.

A logistic map of a bifurcation pattern, as the system progresses, finer and finer scales are possible. Source: http://en.wikipedia.org/wiki/Image:LogisticMap_BifurcationDiagram.png
Now this is where it gets exciting. As the coronal reconnection region slowly reconnects in the Sweet-Parker regime, coronal plasma slowly diffuses across the crossed magnetic field lines and is ejected, but this is too slow for an explosive event. More and more field lines are dragged into the diffusion region as the reaction progresses, feeding the reconnection. The diffusion region becomes thinner and thinner as more and more magnetic field lines are dragged in, forcing plasma out of the region. When the diffusion region becomes thin enough, non-linear processes are sparked causing a catastrophic collapse. Reconnection goes from slow (Sweet-Parker regime) to fast (Hall regime), causing the region to erupt.

This transition is made possible through the non-linear process known as bifurcation, where any small change to the coronal conditions can kick-start a massive explosive event. As these events are driven by a chaotic process, they become hard to predict, but exhibit a pattern nonetheless. What’s more, due to the self-sustaining build-up of stored energy in the incoming magnetic field, this process can be repeated over and over until the magnetic energy has dissipated. So long as magnetic field energy is forced into the reconnection region, and the diffusion region is forced so thin non-linear processes are allowed to be kick-started, Hall reconnection will occur, rapidly releasing energy in the form of a flare, heating the stars corona. As magnetic energy is lost through reconnection, the corona will relax into a cooler state as less reconnection events become possible. Magnetic energy therefore becomes the regulator of coronal temperature.

Reconnection can directly heat coronal plasma, but it may also generate waves that propagate through the solar atmosphere and heat the corona. Also, there may be the possibility that these waves may destabilize magnetic fields so much that secondary reconnection events may occur.

Although the implication of non-linear dynamics and coronal heating is not new, this recent paper compares its theoretical findings with analysis of power spectra of our Sun and other stars and finds that the reconnection model outlined here agrees well with observation.

So, the jury is still out on deciding what mechanism heats the solar corona. But these results, combining so called self-organized criticality (SOC) models of the solar corona with known reconnection models to trigger flare events, will be encouraging to solar physicists still tracking down the causes of the coronal heating problem.

Reference: From Solar and Stellar Flares to Coronal Heating: Theory and Observations of How Magnetic Reconnection Regulates Coronal Conditions” – P. A. Cassak, D. J. Mullan and M. A. Shay, arXiv:0710.3399

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15 thoughts on “The Chaotic Nature of Magnetic Reconnection and Coronal Dynamics”

  1. Except that “magnetic reconnection” has been strongly argued against by Nobel prize winning plasma physicist Hannes Alfvén and electrical engineer Don Scott.

    (Double layers and circuits in astrophysics; Alfven, 1986)
    http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19870013880_1987013880.pdf

    (Real Properties of Electromagnetic Fields and Plasma in the Cosmos; Scott, 2007)
    http://members.cox.net/dascott3/IEEE-TransPlasmaSci-Scott-Aug2007.pdf

    Likewise Alfvén recanted on “frozen-in” field lines (which he had suggested many years earlier), stating that underlying electrical currents MUST be taken into account in light plasmas (probably wouldn’t hurt in dense plasmas as well).

    Cheers,
    ~Michael Gmirkin

  2. Sorry, one more comment I forgot to include… Don Scott’s explanations of the solar corona issue and an alternative viewpoint of stars, from an EE point of view. For what it’s worth. As well as a short tit-for-tat debate between Tim Thompson & Don Scott.

    Keep in mind this is well outside the mainstream school of thought, but interesting nonetheless. Appears to incorporate an apparently consistent explanation for the solar corona, et al. Albeit from a radically different vantage point(some seem to think it’s “dangerous” and must be quashed).

    (The Electric Sun Hypothesis)
    http://www.electric-cosmos.org/sun.htm

    (Tim Thompson’s rebuttal)
    http://www.tim-thompson.com/electric-sun.html

    (Don Scott’s Rejoinder)
    http://www.electric-cosmos.org/Rejoinder.htm

    (Electric Cosmology; Stellar Evolution in an Electric Model)
    http://www.electric-cosmos.org/hrdiagr.htm

    (Solar Surface Transistor Action)
    members.cox.net/dascott3/SDLIEEE.pdf

    Off we go, into the wild blue yonder! ;o]

    Cheers,
    ~Michael Gmirkin

  3. I’ve written a review of Don Scott’s book “The Electric Sky”, available on my web site. No comments from the Electric Cosmos community about the errors they’ve made as yet.

    1. Maybe no one gives a tinkers dam about your math assignment, Mr. Bridgman. Why don’t you take your know it all arrogant ass elsewhere?

  4. I see that Michael Gmirkin from the Thunder[bollocks].info group has been spreading his “Electric Sun/Universe” bullshit here, as he has done recently on Universe Today.The question that these “Electric Sun” proponents can never plausibly explain is: if the Sun is some kind of giant gas discharge lamp — which is what “Electric Sun hypothesis” implies — then WTF is the source of that electrical power that 'powers' the Sun?Also, who the bloody hell pays for that electricity bill? God? Aliens? Maybe the Solar System is just some kind of giant experiment being run by an alien intelligence — like in Isaac Asimov's science fiction short story, “Breeds There a Man…?” — and while they vary the energy output of the Sun at will, the poor astrophysicists try in vain to work out the bloody physics of it! Furthermore, the Thunder[bollocks].info group actually believe in aliens influencing the whole bloody Solar System; check out this latest video of a series of five:

    Note that, in the second half of the video, the term “bull” is often mentioned in reference to some mythical creature. Well, the term “bull” is half right, but it's missing the obvious second syllable!Those nutters are not interested in real science; they are a religious cult — like Scientology — masquerading as 'science'!

    1. Wow. Why are you so full of swears? Hardly a rational scientific perspective.EU does not claim to understand the SOURCE of electricity in space, it simply observes that it is there. What is the SOURCE of anything in the universe, really?

      1. There's a big difference between ionized atoms of gas (plasma) in the Universe, and an electric current (electron flow) in a copper wire conductor on Earth — the former is the result of high-energy electromagnetic waves (e.g., gamma rays, X-rays, and ultra-violet light) displacing electrons from their parent atoms; the latter is the result of charge separation by some means, e.g., dynamos (electromagnetic induction), batteries (electrochemical), solar cells (photoelectric), thermocouples (thermoelectric), and also by mechanical strain of electrically anisotropic molecules or crystals (piezoelectric).

  5. Dear Ian O'Neill,with reference to your comment on the solar corona problem: “Both mechanisms have their advantages and disadvantages, but ultimately neither theory can explain why the corona is the temperature it is or the density it is.”Could you please explain more the last point about the density? Is the density used to explain the coronal brightness smaller or bigger, and by how much? Thanks for your clarification in advance, and if you give some reference we can go a little deeper.Konstantin Zioutas, spokesperson of the CAST experiment at CERN

  6. Dear Ian O'Neill,with reference to your comment on the solar corona problem: “Both mechanisms have their advantages and disadvantages, but ultimately neither theory can explain why the corona is the temperature it is or the density it is.”Could you please explain more the last point about the density? Is the density used to explain the coronal brightness smaller or bigger, and by how much? Thanks for your clarification in advance, and if you give some reference we can go a little deeper.Konstantin Zioutas, spokesperson of the CAST experiment at CERN

  7. The electric or plasma universe hypothesis has been around for a long time. Immanuel Velikovsky, a Russian Jewish immigrant, in his book, “World’s in Collision”, printed in 1950 and a NY Times Best Seller, popularized the concept. I found a used, 1950 edition for $30 at Amazon. I don’t regret it a bit. New editions are around $300. His other books are fascinating too. I also like the guy’s attitude. In the forward of his second book, “Earth in Upheaval”, paraphrasing said, in my first book I T’ed off the astronomers. In this book I will T off the geologists. True to his nature, in his third book, “Ages in Chaos”, he T’ed off historians. Albert Einstein corresponded with him on his work.
    John T. Banewicz 

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