7. Discussion and conclusions
In this paper we have described an analytical method to model the coronal magnetic field arising from wide, infinitely long photospheric sources. The model is stationary, but can be used to investigate the slow evolution of a system taken as a series of equilibrium states. The present approach represents an improvement over previous works in that photospheric magnetic elements have a finite width in comparison with the infinitely thin line sources used before.
We have prescribed a particular spatial distribution of magnetic flux in the photospheric fragments. It has first been shown that, as the width of the elements tends to zero the coronal configurations produced by line sources are recovered, both for a single source and for more complicated combination of photospheric magnetic sources and sinks.
The model of cancelling magnetic features proposed by Priest et al. (1994) has been re-examined using extense magnetic sources. It has been found that the width of photospheric elements must be taken into account as it has a strong influence on the formation of a coronal null point and on the subsequent magnetic reconnection during the slow evolution of the system. Thus, wide and/or weak sources are not sufficiently strong as to overpower the background field at low heights and so the energy release resulting in the formation of the coronal X-ray bright point is not produced. During the flux cancellation of strong and/or narrow sources the null point forms in the corona, although its maximum height is always smaller than that for line sources of the same strength. Moreover, the interaction phase (during which the coronal X-point is present) is longest for thin sources and tends to shorten, or even disappear, for wider magnetic fragments.
Concerning the quadrupolar configuration used to model prominence formation, two main conclusions can be extracted: Firstly, as the inner sources approach one another, the neutral point first rises and later returns to the photosphere, with the maximum height attained depending on L as well as on the ratio . Again, the X-point returns to for , contrary to what happens for point or line sources. Secondly, the first field line that reconnects, assumed to be responsible for dragging photospheric material up to prominence heights, does not remain above the photosphere if the two inner sources are assumed to cancel. Even for total flux cancellation produces the fall of this field line because of the imposed condition . This means that the raised mass cannot be supported high in the corona and that the prominence disappears when the cancellation occurs () or before it is finished (). For this model to be operative, prominences, lasting long within the solar corona, need to be fed by a constant supply of mass and flux provided by a continuous emergence and cancellation of magnetic flux.
Finally, it may also be possible to consider different forms of the photospheric flux distribution, , rather than the one used here (Eq. ). This would allow to determine the influence of the flux distribution within the source, although it should not be too important as long as the flux is more or less concentrated towards the source centre.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999