Saturday, March 29, 2014

Solving the Primary Riddle of Magnetic Reconnection in Solar Flares
















A letter in Physics Today (January. p. 8, 'The Search for Magnetic Reconnection in Solar Flares' ) summarized the problem of establishing the theory of  magnetic reconnection associated with solar flares.  Peter Foukal noted that we need a direct observational method, as opposed to mere tantalizing clues. He used as an analogy the nature of sunspots and how a century ago the vortex -like structures (e.g. penumbral whorls)  suggested magnetic fields. However, the actual magnetic field existence wasn't really established until George Ellery Hale used the Zeeman splitting of a spectral line to actually detect spots' magnetic fields. E.g.

Where the left image shows the line-centered sunspot for which the Zeeman effect (right image) is detected and measured. The greater the spectral line splitting the greater the magnitude of the associated magnetic field.

In a similar way, studies of coronal morphology and motions have left solar physicists in a similar position today. There are tantalizing clues for reconnection, but no direct evidence. Foukal cites an earlier article (Physics Today, Sept., 2013) by Johanna Miller that mentions a key signature of reconnection appears to be an intense motional electric field. This would be defined:

E = vB

where v is the plasma velocity, B the magnetic induction, and ℓ  a length element. Foukal notes that "some evidence for such fields has been observed using a relatively simple polarimeter to measure the Stark effect", and that comparison of such observations with the recently developed three dimensional models that Miller describes "might finally enable us to decipher the role of reconnection in solar flares." (The graphic attached shows one such 3-D model for a solar coronal loop with an assumed potential to spawn solar flares via magnetic reconnection).

Key to this is settling, establishing "whether the potential drops expected with reconnection occur across solar structures that produce detectable emission in Stark - affected hydrogen lines."

Make no mistake this would be an enormous advance given that so many current flare parameters, including for energy and power, are more in the way of indirect estimates.

For example, estimation of flare energy from the soft x-ray record is fairly straightforward and entails multiplying the SXR flux (left axis) of the “half-power” points by the time duration (horizontal axis) then by the recorded flare area in square meters.   A segment of such a record is shown below:
No automatic alt text available.
Consider the flare occurring at 04h 30m UT on Nov. 6,  1980 with an estimated half-power point flux of F = 10 -5 W m –2  and a duration t » 3h » 10800s. If the associated Solar Geophysical Data records show it has a flare area of 10 23  m 2    then:

Flare energy » (10 -5 W m –2) (10800s)( 10 23  m 2 )
 »  1.1  x 10 23  J


 The power of the flare is then estimated, by dividing the energy by the time of duration, so:


Power = Energy / time = (1.1  x 10 23  J)/ 10800s


 Flare power » 10 19 W


 Other quantitative estimates are possible but they require that specific models be applied (say for ‘double layers’) or that other ancillary measurements be known (say the magnetic flux, j =  BA, where A is the area of the spot, say, and B the magnetic induction).


  If the electrical resistance R, associated with a pre-flare system is known, then the current I can be estimated and the region assessed for a flare. Thus, if R is known and we know (from basic physics) that:


P =  Io 2 R 


Then the pre-flare current :   Io = [P/ R]1/2


If Io   is then known it is possible to obtain the voltage drop (V(t)) in a double layer (assuming that model applies) since:
 P =  I V(t)

If both V(t) and I are  known, it is feasible to obtain the change in the system’s inductance (dL/dt). Conversely, if we can estimate dL/dt (say using the Spicer (1980) method), and can also estimate I, then we can also estimate the magnitude of the potential drop:
V(t) =  I dL/dt  
For example, say the pre-flare current is estimated to be:  Io »   1.1 x 10 10  A . If  we can also estimate the change in self-inductance, say  dL/dt   »  0.1  H/s then the potential drop would be estimated as:

V(t)  »   1.1 x 10 10  A (0.1  H/s)  »     1.1 x 10 9  V

 Which is a reasonable value though one would like to know its time evolution up the instant of flare eruption.
Clearly, as Foukal indicates, it would be far more satisfactory to be able to obtain a direct measurement of V(t) - say using the Stark effect*.  Fortunately, we may not have too much longer before we can rise above mere estimates of potential drops. Foukal references (ibid.), a "state of the art electrograph installed, for example, on the Advanced Technology Solar Telescope" which could "open the door to a more sensitive study of motional electric fields."  Provided the NASA budget isn't further  cut, this would be a huge boon.
If we can more accurately identify the actual measured (Stark-effect) related locations in coronal loops where flare -associated potential drops occur, we can more confidently predict them - including large, geo-effective flares. Also the type that can cause CMEs or coronal mass ejections. This would have enormous import for our telecommunications, as well as aircraft navigation - which can be disrupted, adversely affected, by large solar flares and particularly those with CMEs.
*See, e.g.

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