Astron. Astrophys. 318, 947-956 (1997)

6. Discussion

A schematic representation of an open flux tube is given in Fig. 5, which shows the location and direction of the radial and vertical currents and the motions of the fluids of neutrals and ions. Excluding here the heating that currents can produce (Hirayama, 1992), three main effects of the electromagnetic forces generated by DC currents flowing in this flux tube can be distinguished, i.e. coronal abundance anomalies, formation of chromospheres, spicule acceleration.

Fig. 5. Cut of the current shells near the external boundary of an open flux tube. Thick arrows: DC current; thin arrows: velocity of neutrals (high FIP elements); double thin line arrows: velocities of ions (low FIP elements). Spicules rise between the two current shells and ion-neutral separation takes place at the external border of the internal current shell contributing to the formation of a chromosphere. Notice the change with height of the sign of the azimuthal component of the magnetic field.

6.1. Coronal abundance anomalies

Composition observations in the photosphere, upper transition region and corona, imply a change of composition of the solar atmosphere somewhere above the photosphere. The most prominent feature is an enrichment of elements with a low First Ionization Potential (FIP) relative to elements of high FIP. The process leading to such separation is estimated to operate at temperatures 7000 K (Meyer 1989).

The several possible mechanisms that could lead to neutrals-ions separation are reviewed in Meyer (1988, 1993a, 1993b), Von Steiger and Geiss (1989) and in Feldman (1992). Most models are based on the ion-atom separation occuring across magnetic field lines. For example, the gas could be driven across the field either by gravity (Vauclair and Meyer, 1985) or by a density gradient (Von Steiger and Geiss, 1989). The last authors considered a slab, parallel to an uniform magnetic field, filled with an initially neutral gas mixture. They looked at the evolution of the gas composition under the effect of diffusion across magnetic field lines and of photoionizing UV radiation. Their conclusion was that the leakage, out of narrow magnetic field structures, of atoms not yet ionized leads to ion-atom separation and to an overabundance of elements with low FIP in the ionized gas that is fed into the corona.

As pointed out in Hénoux and Somov (1992), forced diffusion across magnetic field lines and lift of the plasma to the corona are the necessary ingredients for any model of FIP fractionation. The most quantitative work on coronal abundance anomaly was published by Von Steiger and Geiss (1989) and it was based on ion-neutral separation in a gas injected as a pressure pulse in a magnetic field. Such conditions occur naturally in the current carrying flux tubes considered in our model and the ion neutral separation takes place at the right place, i.e. in the chromosphere: due to the pinch effect in the photosphere produced by the internal current shell, the partially ionized photospheric plasma rises into the flux tube and is depleted at chromospheric level in neutral high FIP elements. Consequently the gas inside the inside the internal current shell is enriched in low FIP elements in the chromosphere and above.

The possibility to detect the resulting change in abundances are presumably limited to the coronal level since at chromospheric level the internal current shell depleted in high FIP will be surrounded by the high FIP elements ejected between the two current shell. There must be a lower limit of the height at which the enrichment is high enough for the effect to be detectable and not compensated by the effects of the surrounding. Indeed such model is still qualitative, and a quantitative study must be done that would include a precise study of the ionization equilibrium taking into account ionization, recombination and radiative transfer processes.

6.2. Formation of chromospheres

Decoupling between ions and neutrals takes place at chromospheric heights and starts around the temperature minimum level. This suggests that the chromosphere - defined as a rise of the ionization degree with height - could result from the ion-neutral separation in concentrated magnetic flux tubes.

It can be shown that the degree of ionization rises with height. Considering a flux-tube slab of thickness , the increase of the ion density number per unit of time, inside this slab, due to an upflow at velocity of ions and neutrals is

Where is the degree of ionization. Assuming that the net flux of neutrals inside the slab is null, and

where . Indeed an accurate computation of the degree of ionization inside the flux-tube has to include the effect of recombination and photoionization. This is outside the scope of our paper. However, Eq. (24) shows that, even if the final temperature and density distribution is not accurately determined, electromagnetic separation between ions and neutrals enhances the ion population and that this effect increases with height. Consequently, the degree of ionization is expected also to increase with height, and a rise of the degree of ionization and of the temperature with height is a typical characteristic of chromospheres.

According to our model, energy can be brought into the chromosphere as ionization energy carried by ionized low FIP elements. The energy flux into the chromosphere in the internal current shell is then , where is the mean value of the product of , the ionization potential, by , the number density of low FIP elements. Taking  cm^-3 the energy flux required to heat the chromosphere is obtained for upflow velocities 300 m s^-1 at photospheric level. Such velocity is low compared to the so called macro-turbulence used to explain photospheric line profiles and can be generated by pinch effect as discussed in Sect. 4.1. It was shown in this section that velocities of the order of 3.5 km s^-1 can be generated. Since the pressure increase due to pinch is limited to the periphery of the internal current, i.e. in about one tenth of the flux tube cross section area, the mean velocity is well in the 300 m s^-1 velocity range. This despite the slow downward motions of a few m s^-1 that take place in the low gas pressure part of the flux tube near it axis of symetry, as a result of slow motions transverse to the magnetic field (see Paper I).

Consequently, as suggested by observations (e.g. Ayres, 1989; Kozlova and Somov, 1995), the upper part of the atmosphere becomes structured in cool non-magnetic regions and magnetic hot "bright points". The last can be enriched in elements of low FIP. To the contrary, in the lower part of the photosphere, magnetic points are cooler than the surroundings.

In fact, Ayres and Testerman (1981), Ayres et al. (1986), Ayres and Wiedeman (1989) assumed the existence of a highly thermically structured atmosphere in order to explain the low brightness temperature of the strongest CO lines (Noyes and Hall, 1972; Ayres and Testerman, 1981). The upper atmosphere would contain substantial amount of cool material in addition to hot gas (  K). Less than 10% of the atmosphere in quiet regions and about 50% in magnetic active regions would contain chromospheric hot gas. The chromospheric temperature inversion would take place only in hot regions.

The need for a thermal structured atmosphere also comes from the impossibility to get energy balance at the temperature minimum and in the low chromosphere with an horizontally homogeneous model of the quiet sun. With such model, H , that dominates the total net rate of radiative cooling, is a net radiative heating agent (Vernazza et al. 1981; Avrett 1985), and the CO cooling is not a sufficient cooling agent to compensate for the energy deposite (Mauas et al. 1989).

Therefore, the thermally structured model of the atmosphere was observationally well justified, but its origin was never clearly understood. The coexistence of cold and hot components in the high atmosphere was attributed by Ayres and Testerman (1981) to a thermal instability driven by an assumed very powerfull cooling in the CO bands. The creation by cooling of CO molecules would enhance the cooling in low-temperature regions untill all the carbon is in CO molecules. A different conclusion was, however, reached by Mauas et al. (1989). They found that in the temperature range 3700-4700 K the CO cooling rate is insufficient to cancel the negative H heating rate. These authors also ruled out the possibility of CO cooling to be responsible for the existence of the cool gas.

Our computations show that due to the difference in the velocities of neutrals and ions across the magnetic field lines:

1. Neutrals are injected into non-magnetic regions, but ions fill magnetic "bright points", creating a structure separated into regions of high and low degree of ionization.

2. Hot regions are associated with thin magnetic flux tubes and cool gas with non-magnetic regions, as was presumed but not explained in the empirical model by Ayres.

3. The electric current required to maintain a pressure excess in the upper part of the flux tube can be generated in the photosphere.

Therefore, we propose that the thermal structure of the chromosphere and the chromospheric temperature inversion take place inside thin magnetic flux tubes.

6.3. Spicules

In open magnetic flux tubes, in the low pressure region between the two current shells, the force can accelerate the plasma to high velocities in the chromosphere. Since the plasma motion is not slow down by pinch effects in the chromosphere, these velocities are high enough for the plasma to reach the altitude of about 7000 km reached by spicules, Hirayama (1992) suggested a possible rôle of Joule heating on spicule formation. We think that the electromagnetic force is the best candidate to explain spicule formation. The amplitudes of the upward force and of the upward velocity depend on the flux tube radius and on the azimuthal velocity at the periphery of the tube. Since the values used in this study are moderate, higher values can be used, and there is no doubt that the inflow of angular momentum into flux tubes can generate the required high upwards velocities for spicule formation. However, since spicules are transitory phenomena, the force must have a transitory character. This may come naturally from the transitory character of the azimuthal velocities.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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