Expert: Philip A. Stahl - 9/22/2010

Question
Hello. I'm interested in what you think of dynamo flare models which try to use aurora substorm processes to model solar flares (One of these was actually called 'A Dynamo Flare Model' and appeared around 1983, I believe). Can it work or are such models all defective and if so how?

Answer
The paper to which you’re referring is:

“A Dynamo Theory of Solar Flares” by J.R. Kan,  S.I. Akasofu, and L.C. Lee. in  Solar Physics, Vol. 84, p.153, 1983.

While Kan et al’s "Dynamo" model commendably incorporates both energy generation and dissipation, it exhibits a number of defects which translate into a hidden cost for using unobserved structures, processes. In general, their model overtaxes the similarity between substorms and solar flares, while ignoring key facts concerning the magnetic aspect of flares – such as the well-established relationship between magnetic complexity and important flares (e.g. Tanaka and Nakagawa.: Solar Physics, Vol. 33, p. 187, 1973)

Some major issues:

1) "Neutral wind":

In the Dynamo model of Kan et al (1983), the “neutral wind” acts perpendicularly to the field –aligned ( J ‖ ) and cross-field (J ⊥ ) current (see Fig. 1 of Kan et al, 1983). The wind is described in their paper as a “shear flow” (p. 154) . The problem is that there is no evidence of such “neutral gas” in the region of the solar chromosphere or photosphere, nor of any consistent “flow” of the order of 1 km/s. Thus, it is an entirely fabricated construct bearing no similarity to real solar conditions.

More accurately, in the regions wherein real magnetic loops reside, the physical features of sunspots and their concentrated flux dominate. Thus, instead of some vague “neutral wind’ one will expect for example, a convective downdraft which helps to contain the individual flux tubes of a sunspot in one place (e.g. Parker, Astrophysical. J., 230, p. 905, No. 3, 1979.) The problem is that the downdraft velocity is not well-established and can vary from 0.3 to 1.5 km/s.(Parker, op. cit.)

In the proper space physics (magnetopheric) context, the “neutral wind” arises from a force associated with the neutral air of the Earth’s atmosphere (e.g. Hargreaves, The Solar-Terrestrial Environment, Cambridge Univ. Press, 1992, p. 24). This force can be expressed (ibid.):

F = mU f

where f is the collision frequency. It is also noted that this wind blows perpendicular to the geomagnetic field (ibid.)

If one solves for f above, and uses the magnitude of magnetic force (F = qvB) where B is the magnetic induction, and v the velocity one arrives at two horizontal flows for electrons and ions moving in opposite directions. mU f = qvB = (-e) vB = (e) vB

Thus,

v1 = mU f / (-e) B and v2 = mU f / (e) B

These ions and electrons thus move in opposite directions, at right angles to the neutral wind direction. Such “neutral wind” velocities are depicted in Kan et al’s Fig. 1 (into and out of the paper on the right side of their arch configuration) as ±V_n. In the magnetospheric system the current is always extremely small since the frequency is large. (Hargreaves, ibid). The region where the wind is most effective in producing a current in this way is known as “the dynamo region”.

Again, there is no similar quasi-neutrality in the solar case, since the ions and electrons move as one governed by the magnetic field in the frozen-in condition. This shows that the whole neutral wind concept has no validity in the solar magnetic environment.

2) Plasma motions – Lorentz force (J ⊥ X B)

In Kan et al’s (1983) dynamo flare model, predicated on space physics concepts, it is required that the dynamo action send currents to specific regions to provide a Lorentz force: (J ⊥ X B). This implies a current system which is non-force free in contradiction to numerous existing observations, and the fact that at the level of the photosphere –chromosphere, the plasma beta = rho v^2 u/ B^2 << 1.

For example, contrary to their claim that the currents in the chromosphere are not parallel to the magnetic field, we have actual vector magnetographs which show otherwise. For example, gyro-resonance emission depends on the absolute value of the magnetic field in the region above sunspots, and contour maps of such regions at discrete radio wavelengths disclose the controlling influence of magnetic fields. Penumbral filaments of sunspots themselves lie in vertical planes defined by the horizontal component of the magnetic field .

Again, both coronal and chromospheric gas pressures are insignificant relative to magnetic pressures, so fields in these regions must be at least very nearly force-free. [1]
In the case of filaments or prominences in the low corona or chromosphere, the plasma as we saw before, would again have a very high magnetic Reynolds number, Re(m). The conductivity of the plasma would therefore be ‘infinite’ so that even a minuscule induced voltage arising from, E = -v X B (e.g. due to very small relative motion v) would produce an infinite current j = o E (o = conductivity). The only way one avoids this unrealistic situation is to require the plasma motion in the filament to follow magnetic field lines rather than cut across them.

Clearly, the error being made in this case and others is the overextension of space physics structures and concepts (e.g. as applicable to the aurora) to the solar physics – and specifically the solar flare, context. To be more precise, one can visualize (in the case of the aurora) bundles of open field lines that map to the region inside the auroral oval. Many of these field lines can be traced back to the solar wind. The configuration is such that one is tempted to conceive of a mechanism that links certain mechanical or dynamic features to the production of cross currents, including Birkeland currents.

In detailed auroral models it can be shown that the "dynamo currents" in such a process flow earthward on the morning side of the magnetic pole and spaceward on the evening side. The circuit can be visualized completed by connecting the two flows across the polar ionosphere, from the morning side, to the evening side. This is exactly what Kan et al have done in arriving at their “dynamo solar flare” model. That is, taken a mechanism that might be justified in the case of the aurora – and transferred it to the solar flare situation.

The problem inheres in the fact that circuits on the Sun – given unidirectional current flows – need not be driven by any “dynamo action” – or be part of any dynamo. Further, one doesn’t require a dynamo to have a conservative energy system to account for solar flares. It is possible to use the conservation of magnetic helicity in a more general context to explain energy balance – especially for large, two-ribbon flares.

Given the fact that we can actually observe magnetic helicity buildup in terms of the angles made by solar arcade footpoints, it stands to reason that this is a superior proxy for assessing energy accumulation in the pre-flare stage. Indeed, a heuristic “fast dynamo” has been developed predicated on a “stetch-twist-fold” cycle that generates helicity. In this case, the field is maintained by the motion of the MHD fluid, rather than currents at infinity.

Lastly, the final result obtained by Kan et al on the basis of the Poynting theorem (Eq. 34) is not uniquely tied to a dynamo model of the type they present, but to any MHD generator model! [2] Thus, the rate of change of electromagnetic energy density is equal to the energy source (-E •J) minus the divergence of the Poynting vector S = E X H = (E X B)/ uo, where u is the magnetic permeability and o is the conductivity.

While this is a most satisfying aesthetic result, it is of little or no use in the solar situation which must take into account a more authentic and detailed alteration of the local topology, especially in the vicinity of large, complex sunspot groups.