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Astron. Astrophys. 335, 691-702 (1998)

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3. Basic fractionation mechanisms

The rates for (electron) collisional ionization at temperatures of [FORMULA] K, as found in the fractionation layer, are small compared to the photoionization rates; e.g. for hydrogen the respective rates are [FORMULA] (Lotz 1967) and [FORMULA] (von Steiger & Geiss 1989). Thus only the photoionization can be expected to have a significant impact on the fractionation. Following the Marsch et al. (1995) model the ionizing UV radiation is coming from the above layers of the upper chromosphere and transition region. As the chromosphere is more or less optically thin in the EUV (except for some lines like e.g. Ly[FORMULA]) the ionization rates are approximately constant with depth for the minor species.

In Fig. 2 (left) the basic fractionation mechanisms are illustrated:

[FIGURE] Fig. 2. Basic fractionation mechanisms and the "bathing tub analogy" following an idea of R. Bodmer.

The ionization of the material is the main process that causes the fractionation. The low-FIPs have short ionization times and are coupled quickly to the solar wind flow of the main gas, ionized hydrogen. The high-FIPs with their longer ionization times are harder to ionize: for this, they remain longer in the neutral phase and are coupled later to the solar wind than the low-FIPs. Thus the low-FIPs are preferably transported out of the chromosphere into the interplanetary space. This simple picture renders the enrichment of the low-FIPs understandable.

As well the diffusion in the neutral phase plays an important role. At the top of the ionization layer, where the material is ionized, the very effective Coulomb-coupling causes equal velocities of the different species. But at the bottom of the layer, in the neutral phase, the collisions are less effective: neutral-neutral as well as neutral-ion collisions are about a factor of 1000 less effective than the ion-ion interaction (see Table 2). For this a diffusion at the bottom of the layer is possible (see also Sect. 6.2for a more quantitative discussion). This diffusion regulates the fractionation simply by regulating the velocity differences of the trace gases. It should be kept in mind that even if the diffusive velocities are small, the influence on the fractionation could be non-negligible: following (7), the quotient of the diffusion velocities is of importance, which can be large, even if the absolute values of the diffusion velocities are small.

At last the combination of ionization and diffusion leads to the two-plateau structure of the fractionation as shown in Fig. 1. Quantitatively speaking the combination of atomic parameters, namely the cross sections for photoionization and elastic collisions, forms the two plateaus, see (7). Thus the presented model is independent of the assumptions concerning e.g. the structure of the magnetic field topology: the results of the model can be used for the explanation of the fractionation in a wide variety of solar structures, like coronal funnels, loops or polar plumes.

But there is yet a third mechanism, leading to a velocity-dependence of the fractionation. If the transit time through the ionization layer is shorter, the fractionation will be weaker than for a longer transit time, because the above described processes have less time to act. As shorter transit times mean higher velocities, this implies that the fractionation is weaker for higher velocities. This mechanism, first pointed out by Peter (1996), is reflected in (5) below. But this discussion also clarifies that the fractionation depends only on the absolute value of the velocity (which corresponds to the transit time), but not to the direction of the flow!

It is helpful to look at the analogy between the fractionation processes in the solar chromosphere and the evaporation of different kinds of perfumes which are dissolved in a bathing tub (see right of Fig. 2, following an idea of R. Bodmer). If the water is heated, buoyancy will drive a flow of steam; this is the analogy to the solar wind. The heating lamp, which causes the evaporation of the perfumes, compares to the ionizing UV radiation. The volatile kinds of perfume have a shorter "evaporation time" (corresponding to the ionization time); for this they will be enriched in the steam above the tub. But as in the solar chromosphere the diffusion also regulates the fractionation: the enrichment of the volatile elements is regulated by their ability to diffuse through the background of water.

In this bathing tub analogy it is immediately perceptive that the abundances in the water (the photosphere) do not have to be the same as in the steam above the tub (the corona) and thus a fractionation is present. The ionization-diffusion layer in the solar chromosphere as described in the present paper compares to the (thin) layer under the water surface.

The thickness of the ionization-diffusion layer on the Sun can be estimated by using the typical flow speed of 500 m/s and the ionization time, which is roughly speaking of the order of 10 s (see Table 1), leading to some km. This means that the "natural" length scale for the fractionation processes as proposed in the present paper is very small and the ion-neutral separation takes place in a very thin layer.


Table 1. Atomic data.

This is finally the reason, why the recombination is not of great importance. Because of the long recombination times of typically 200 s (see Table. 1, [FORMULA]), the length scale of recombination is of the order of some 100 km. Even though this is much smaller than the length scale of the objects in mind (coronal funnels or loops, see Sect. 2.5), it is much larger than the thickness of the ionization layer where the fractionation takes place. In fact it turns out that the numerical models including recombination as discussed in Sect. 5.3, give results comparable to the analytic studies in Sect. 5.1, where recombination is neglected.

Also an other mechanism can be present, especially if a coronal loop is considered: fractionation due to diffusion perpendicular to the magnetic field as described by von Steiger & Geiss (1989). In their (time-dependent) calculations they need up to 100 s to reach the fractionation as observed in the slow wind (see their Figs. 2 and 3). As the thickness of the ionization-diffusion layer, where the present model operates, is only of the order of some km (see above), the transit time is shorter than the fractionation time of von Steiger & Geiss (1989). For this no strong additional effect can be expected by the diffusion perpendicular to the magnetic field - nevertheless it should be included in future models.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998