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

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2. Observational constraints

The fractionation compares the relative abundance of an element j in relation to another element k in the solar wind (SW) or the corona with the respective value in the photosphere. It is defined as


Especially for the in-situ measurements in the solar wind the fractionation is mostly taken in relation to the typical high-FIP element oxygen. This is because O is the third abundant element (after H and He) in the solar atmosphere and wind.

The abundances in the solar photosphere can be found e.g. in the work of Anders & Grevesse (1989). These values are quite well known. But it is harder to determine the abundances in the corona: there the densities have to be deduced by more or less problematic UV-diagnostic techniques, e.g. line ratio or emission-measure analysis. Much more reliable are the in-situ measurements in the solar wind. But in both cases it is hard to determine the absolute abundances, i.e. the values in relation to hydrogen. In the corona absolute abundances have to be determined by the complicated line to continuum ratio techniques because of the absence of hydrogen lines. In the solar wind the enormous difference in the densities of hydrogen and the trace gases, and thus of the respective count rates, causes huge technical problems; e.g. in the time one oxygen particle is measured about 1200 protons will be found.

The most relevant observational constraints are collected in Fig. 1, showing the fractionation from the photosphere to the solar wind as given by different references: The in-situ measurements in the slow and fast wind are represented by the bars and rectangles respectively (from the collection of von Steiger et al. 1995). The high- and low-FIP plateaus are indicated by the dotted lines (see Sect. 2.1). The open diamonds show the relative abundances as obtained from lunar regolith for the heavy noble gases (Wieler & Baur 1995; see Sect. 2.3).

A more detailed discussion of the measurements of the fractionation in a great variety of coronal and solar wind structures, e.g. of hot and cool loops, can be found in the review article of Meyer (1996).

2.1. Two-plateau-structure and velocity-dependence

First of all there are two clearly distinguishable plateaus, one for the low-FIPs and one for the high-FIPs, in the slow as well as in the high speed solar wind.

This two-plateau-structure becomes even clearer in measurements of solar energetic particles (e.g. Anders & Grevesse 1989, their Fig. 3), where more elements are observable. The dotted lines in Fig. 1 should only indicate the location of the two plateaus (they are not a fit to the measurements). The step-height between the two plateaus is a factor of four in the slow, a factor of two in the fast wind. Just recently Raymond et al. (1997) presented spectroscopic measurements of UVCS on SOHO also showing this structure in streamers (see below).

Another important feature, which is not shown in Fig. 1, is the result of e.g. Widing & Feldman (1992) or recently Sheeley (1996). They found a very strong fractionation of Mg to Ne of the order of 10 (!) in polar plumes. And they conclude that these plumes have to be quasi-static; because of their strong abundance anomalies they cannot contribute to the solar wind.

This leads to a velocity-dependence of the fractionation: in the quasi-static plumes the fractionation is stronger than in the slow wind, while the separation is weakest in the fast wind. Additionally Bochsler et al. (1996) reported that in some high-velocity streams no fractionation was found.

2.2. Absolute fractionation

As hydrogen is the most abundant element it is of importance to know the fractionation in relation to hydrogen, i.e. the absolute fractionation. This is the key to find out which elements are absolutely enriched and which are depleted.

Following von Steiger et al. (1995) the fractionation of hydrogen to oxygen is of the order of 2 in the slow and a factor of 1.2 in the fast wind. Thus the high-FIPs are absolutely depleted in the slow wind, while their absolute abundance remains nearly unchanged in the fast wind. As pointed out in the review of Meyer (1996) there are many other results for coronal measurements, derived from spectroscopic diagnostics. E.g. recently Raymond et al. (1997) found a fractionation of H to O corresponding to the slow wind measurements of von Steiger et al. (1995) in active region streamers and the legs of quiescent helmet streamers. This paper will concentrate on the more reliable values of the in-situ measurements of von Steiger et al (1995), see above.

2.3. Heavy noble gases

Plotting the fractionation versus the FIP, the noble gases form their "own line" (see Fig. 1) Because of their very low abundance the noble gases Xe and Kr cannot be measured in the corona or in-situ in the solar wind. But as the solar wind hits the moon directly, some of the solar wind particles can be implanted into the lunar material. The non-volatile elements, i.e. the noble gases, can remain in the material without a significant change of their abundances over a long period. Wieler & Baur (1995) took advantage of this effect and determined the abundances of Xe, Kr and Ar from samples of lunar regolith. As the moon is (more or less) in the ecliptic plane, their results should reflect the conditions in the slow wind. It should be noted that Wieler & Bauer have found that the fractionation in the older samples (1-[FORMULA] years) is about 30% stronger than in the younger ones ([FORMULA] years).

2.4. Helium

Helium shows a somewhat strange behaviour: in the "quiet" solar wind it is depleted compared to the other high-FIPs by a factor of up to two (see Fig. 1), but it can also be strongly enriched, e.g. in the driver gas of flare-induced interplanetary shocks (e.g. Hirschberg et al. 1970). As shown by Peter & Marsch (1998) these effects cannot be understood by the same processes leading to the fractionation of the minor species, as presented in this paper. This negative result is not surprising as helium is not a minor element.

But the changes in the abundance of helium can be understood in a coronal/solar wind model, where also effects like the thermal force in the transition region are taken into account (see Hansteen et al. 1997).

2.5. Location of the relevant processes and geometry

The fact that an ion-neutral separation is used to describe the fractionation restricts the possible locations of the fractionation processes to regions where neutrals and ions are present, i.e. where the first ionization takes place. Applied to the solar atmosphere this is the region well above the temperature minimum and below [FORMULA] K. Because of the short ionization-diffusion times, this fractionation layer is thin (see e.g. Marsch et al. 1995). For typical velocities of the solar wind in its source region of 500 m/s (see below) and ionization times of 1 to 100 s, the ionization layer has a thickness of up to only 50 km. In the paper of Peter & Marsch (1998), describing the background models for the here presented fractionation models, a detailed description of this region can be found.

Concerning the source region of the fast wind the material is assumed to flow out of the coronal funnels. Mapping back the measured particle flux at 1 AU to the base region of a funnel the resulting velocity is of the order of 500 m/s (see Peter & Marsch 1998 for a more detailed description). The fractionation processes are located at chromospheric low temperature regions at the base of the funnels. Above the fractionation layer, where the material is ionized, the trace gases are trapped by the proton background and are transported into the solar wind. Through the transition region and the corona the abundances remain unchanged, because the very efficient Coulomb-coupling renders equal velocities for all species, which prevents any further fractionation (compare Sect. 6.2). Thus the fractionation in the chromosphere as described by the presented model is comparable to the measurements in the solar wind.

In the case of the slow wind the situation is a bit different. A possible scenario, supported by recent SOHO observations (see Sheeley et al. 1997), is as follows. The loops are fed by a flow at their footpoints, which are located in the chromosphere. In a thin layer at below [FORMULA] K (see above) at the footpoints of the loops the material gets fractionated; thus fractionated material is accumulated in the loops. After some time the loops open and the fractionated material escapes forming the slow wind. In this scenario, the fractionated material is accumulated in the loops leading to a higher pressure, which is trying to stop the flow. But the aim of this paper is not to establish a loop model - this scenario should be taken just as an idea.

Another possibility for the loop situation is a kind of "siphon flow" through the loop (e.g. Cargill & Priest 1980). Klimchuk & Mariska (1988), who modeled heating related flows in loops, found velocities at the foot point regions of a loop of the order of 0.3 km/s (see their Fig. 2) - an up-flow in the one, a down-flow in the other footpoint. This velocity is a bit lower than the the velocities at the base of the funnels as mentioned above.

As it can be seen from (5), the sign of the velocity does not play a role for the fractionation, which means that only the transit time through the ionization-diffusion layer is of importance and not the direction of the flow (see Sect. 3). For this in an up-flowing as well as in a down-flowing region (i.e. in two foot points of a loop with a siphon flow) the material in the ionized region becomes fractionated. This means that a siphon flow through a loop may well cause an enrichment of the low-FIPs in the loop.

Concerning the geometry, the footpoint region of a loop is comparable to the base of a coronal funnel: in both cases the magnetic field is more or less vertical and a one-dimensional model (along the field lines) can be applied. Thus a one-dimensional multi-fluid model for a chromospheric region at below [FORMULA] K will be considered to describe the fractionation of the elements.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998