Tuesday, August 10, 2010

Comparing Sub-storms and Solar Flares (II)

We continue looking at the major differences which apply to typical solar flares of the optical type 1N category (See Fig. 1) and auroral sub-storms. (Fig. 2)

3) Unobserved Structures and quantities derived from them

In their dynamo flare model, Kan et al (1983, op. cit.) make use of so called “V-potentials” and “S-potentials” (op. cit., their Figure 6). V-shaped potential structures or inverted V events, actually refer to discrete auroral arcs in the ionosphere, at energies of several keV or more, obtained by space-based observations. They are auroral precipitation structures or events, because the energy –time plots (of particle fluxes associated with auroras made by space borne detectors) roughly mimic the shape of an inverted V.

The problem is that there is absolutely no observational analog of these structures on the Sun, and certainly not in solar flare regions. Thus, the role of these sub storm artifacts is entirely vague in the context of the solar situation and moreover unobserved. Up to now no solar team or researcher has unambiguously identified a specific solar structure or process that might be tied to these. In other words, their use represents an artificiality or contrivance. This also applies to the “S-potentials”.

4) Dynamo Flare Regions?

In their Figure 3 (Kan et al, 1983) a “dynamo flare region” is depicted that forms the basis of the authors’ “dynamo flare process”. A close inspection of the structure discloses it is basically a generic “slab model” of the type used in auroral-magnetospheric mechanisms. (See, e.g. Cravens, 1997)[1]

In more familiar terms, the model resembles a large horseshoe magnet with a width of ‘2W’ – and a length (L) that can be thought of as the thickness. The total arch height (undefined in the diagram) evidently reaches to some unspecified altitude in the corona. What they call their “dynamo region” (the lower block of width 2W by length L by height h) is in fact equivalent to the “bottom plasma slab” in the slab –MHD generator model.[2] Meanwhile, their “conjugate region” is equivalent to the top plasma slab in the generic slab model. (Cravens, ibid.)

The conflict between models in auroral (space physics) and for actual solar flares can be highlighted by comparing the authors’ Fig. 1 and Fig. 3 (Kan et al, 1983). While Fig. 1 certainly embodies the topology of a coronal loop, it loses validity by superimposing the auroral slab model at the base. Thus, we do not observe “neutral winds” with velocities (± V_n) at loop footpoints, but rather we observe the footpoints executing distinct independent displacements that enhance the magnetic helicity (Demoulin et al, Solar Physics, 2006).

In addition to this, it isn’t clear at all that a “loss cone effect" for coronal arches or arcades is significant enough to drive the currents needed to trigger flares. In the auroral context, of course, the loss cone concept has validity in connection with field –aligned potential drops and enhancing parallel current densities (e.g. Birkeland currents). To be specific, in the magnetospheric context only electrons of small pitch angles contribute to J . Any parallel electric field increases the flux of electrons inside the loss cone and increases J such that (Cravens, p. 430):

J / J(max) = R[ 1 – (1 – 1/R) exp (e V / k_B T_e 1/ (R – 1)]

where R = B( ionos)/ B (top) refers to the mirror ratio (ratio of respective magnetic inductions) in the ionosphere to the top of the potential structure. J(max) is the maximum current density and V is the potential drop. Also, k_B is the Boltzmann constant and T_e the electron temperature, respectively. We know also:
Jmax = (N_e e)[ k_B T_e / 2pi m_e ]^1/2

where N_e is the electron number density, e the electron charge, and with the substitution of V_th = [ k_B T_e / m_e ]^1/2 and multiplying both sides of the J / Jmax equation by Jmax one obtains equation (11) in Kan et al (1983). Given typical conditions in the ionosphere, one obtains a value of about J = 0.1 mA/ m^2 or nearly an order of magnitude less than the value arrived at from shearing of the field.

The upshot of seriously comparing the energetics and dynamics in the solar flare (Fig. 1) to magnetic sub-storm (Fig. 2) is that they are now realized to be covered respectively under two distinct energy paradigms, the B-v (driven) and E-J ("unloading"). The latter has received most prominence in the Space Physics domain, with Magnetosphere-Ionosphere (M-I) coupling models explored by Akasofu (1979)[3], Kan et al (1983, op.cit.) that invoke such auroral substorm mechanisms as V-, S-potentials, double layers and field-aligned potential drops. The general emphasis is on currents and current systems, namely the “field aligned” current density and how it can configure an energy balance in solar flare descriptions. This has also been labeled the “E-J paradigm” (see, e.g. Parker, 1996 (op.cit.) after the electric field (E) and current density (J) that is emphasized.

So long as this paradigm was limited to magnetospheric substorms, little controversy developed. However, this altered once the substorm E-J models began to be extrapolated to solar conditions, and especially solar flares. Perhaps the first such effort was carried out by Akasofu (1980)[4] who attributed all flares as arising from a “photospheric dynamo process”. According to this paradigm, the solar flare is a result of a progression that begins with increasing currents channeled through the photosphere via the solar wind. This leads to increased ionization and conductivity, which in turn leads to joule heating and a flare.

Fortunately, a lot of confusion and controversy may have been eliminated in Afkasofu's most recent article ('Auroral Substorms: Paradigm Shifts in Research', Eos Transactions, Vol. 91, No. 31, August 3, 2010, p. 269) wherein the author points out:

"The transfer mechanism of solar wind energy to the magnetosphere...is now known to be a dynamo process that converts the kinetic energy of the solar wind to electrical energy on the magnetopause - because most auroral and geomagnetic phenomena are various manifestations of energy dissipation processes."

This clarification is just as well, since as I noted in my presentation at the AAS Solar Physics Division last year, any current densities as large as 5 x 10 ^3 A /m^2 (as proposed in the paper of Kan et al, 1983), would've yielded an associated (unobserved) magnetic induction, B, of nearly 25 million Gauss in the current carrying loop designated "BC" in the active region AR2776! This, as opposed to the observed value of ~ 1800 G.

Thus, we can perhaps allow for the phenomenon of substorm "dynamos", but in small, localized regions peculiar to the scale of the auroral oval - as opposed to the scale of solar flares! However, it isn't plausible that such dynamos can be extrapolated beyond the magnetospheric-ionospheric domain to powerful flares on the Sun.

[1] T. Cravens., Physics of Solar System Plasmas, Cambridge Univ. Press, 1997, pp.373 and 379

[2] It is important to note that in standard solar physics parlance the “dynamo region” actually refers to the deep convective zone region responsible for the alpha- omega dynamo that gives rise to the solar cycles. In any case, a dynamo region of the type Kan et al propose would likely have to occur much deeper than what they posit to deliver the magnitude of current, field etc.

[3] S.-I. Akasofu: 1979, Solar Phys., 64, 333.

[1] S.-I. Akasofu: 1980, Nature, 284, p. 248

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