Astron. Astrophys. 332, 367-373 (1998)

1. Introduction

The connection between the lower solar corona and the chromospheric network from which the solar wind is believed to emanate [Axford & McKenzie (1993)] is complicated both by the complex magnetic field topology and the different physics operating in different regions. Elsewhere [McKenzie et al. (1997)] we have analyzed how the solar wind plasma flow in magnetic funnels located at the boundaries of the network, are connected to thin (O(10 km)) ionizing layers situated at the bottom of these funnels. In this case the dominant ionizing agent is electron impact driven by a downward electron heat flux from the lower corona. However in the lower regions of the layer, where the temperature is low (O (few 10⁴ K)) the impact ionization length can exceed the photoionization length scale (O(40 km)) and therefore it is relevant to consider the structure of a pure photoionization layer.

As a model we take a one dimensional, steady configuration in which a downward flux of EUV photons ionizes neutral hydrogen flowing upward. The structure equations show that there is a unique critical solution which links the physical variables at the bottom of the layer to those at the top. Both hydrogen atoms and protons are accelerated within the layer so that the protons exit the layer with a number density relative to that of the incoming hydrogen equal to the ratio of the entering hydrogen speed to the exiting proton speed. The structure is completely analogous to a classical weak, constant pressure, deflagration [Courant & Friedrichs (1963)], or a very weak D-type ionization front [Axford (1961)]. For the case in which there are sufficiently frequent hydrogen - proton collisions in a characteristic photoionization length scale to maintain approximately equal speeds for hydrogen atoms and protons we have obtained a simple analytic solution which neatly highlights the properties of the layer. In particular the ratio of the densities of the exiting protons to the entering hydrogen atoms is simply , where is the temperature of each component.

It is of interest to generalize this model to include the photoionization of minor singly ionized elements in the presence of the hydrogen-proton background. In subsonic flow the momentum equations for the neutrals and their ionized counterparts reduce simply to the balance between the partial pressure gradients and collisional friction with the hydrogen-proton background flow. It is evident that the neutrals enter the layer at the hydrogen speed and their ionized counterparts exit at the proton speed. Therefore no fractionation, i.e. an enhancement or depletion of any species relative to another, can occur and hence such one dimensional, steady flows cannot give rise to a FIP effect as, indeed, appears to be confirmed by observations [Geiss et al. (1995)].

Our calculation should be regarded as merely illustrative because it is artificial in that it requires that we have just the right amount ionizing of photon flux for each species. In reality there exists an excess of such photon fluxes in the form of , in which case the ionizing layer for each species would not be stationary and in fact would move down, so that the elements would come in ionized from deep down. We should then regard the metals as coming into the hydrogen-proton layer fully ionized and with the same speed as hydrogen. Since all ions exit the layer at the proton speed again no fractionation can take place. In order to obtain such an effect, namely an excess of metals, one must have a procedure for removing hydrogen in some way, or by implanting metals.

On the basis of the assumptions made in these calculations, elements with photoionization cross-sections greater than that of hydrogen (e.g. ) are ionized deeper in the layer than hydrogen, whereas those with smaller cross-sections (e.g. ) are ionized higher up, with the notable exception of helium. This is rather misleading however: we have not allowed for the fact that the low FIP species are fully ionized long before entering the layer since there is a great excess of ionizing photons. The ionizing time determined by convolving the cross-sections with the corresponding ionizing flux is probably a more useful means of distinguishing the behaviour of different species (e.g. Geiss & Bochsler (1986)). In any case the scope of the analysis must be altered somewhat since photo-ionization is not a significant cause of photon loss in these circumstances and it is therefore necessary to describe the distribution of photons in particular in a different way.

© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998
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