Astron. Astrophys. 318, 963-969 (1997)

1. Introduction

Solar coronal plumes were first observed in white light eclipse photographs as long, faint rays of enhanced density (3 - 5 times denser than the background) located inside coronal holes (e.g. Van de Hulst, 1950; Saito, 1965; Koutchmy, 1977). In extreme ultraviolet (EUV) spectroheliograms they appear as shorter spikes near the polar limb (Bohlin et al., 1975; Ahmad & Withbroe, 1977; Widing & Feldman, 1992; Walker et al., 1993) and they show lifetimes of several hours or even days. Recently, diffuse Mg IX plume-like structures have been observed inside low-latitude coronal holes undergoing limb passage (Wang & Sheeley, 1995a), thus suggesting that coronal plumes are common features of all coronal hole regions and not only in the polar caps (therefore the term coronal plume should be preferred to polar plume, although the latter is more commonly used). Plumes have been also identified in soft X-ray images (Ahmad & Webb, 1978) and possibly even as weak radio sources (Gopalswamy et al., 1992). More recently, white light observations by the Spartan spacecraft coronograph, up to a height of 5 solar radii, have been analysed by Fisher & Guhathakurta (1995).

Characteristic values of coronal plumes, as seen at the solar limb, are widths of , number densities in the range and temperatures around (Mg IX lines, where plumes intensities peak, form around ). The outflow velocity is unknown, but it should not be larger than, say, at the base of the plume (plumes are observed to be roughly in hydrostatic equilibrium), thus suggesting that the bulk of the solar wind acceleration occurs at larger heights. Finally, no measures of the magnetic field are available, although usual coronal values for the plasma beta () are commonly assumed.

Together with macrospicules, short-lived ( minutes) jets of cooler chromospheric material, coronal plumes are believed to trace the open field lines structure and to provide a major source of the solar wind. Possible remnants of the signature of these coronal hole fine structures have been discovered (Thieme et al., 1990) by analysing high-speed streams data taken by the Helios probes in the range 0.3 - 1 AU. Their results show that plumes expand while retaining an overall pressure balance with the background, thus suggesting that the magnetic field open lines play an important role in confining the plume plasma even in the outer corona. This behaviour has been investigated by Velli et al. (1994), who proposed an interesting thin flux-tube model in which the magnetic flux is conserved separately both in the plume and in the surrounding coronal hole and total pressure is balanced across the field lines.

Another fundamental observational result, confirming the intrinsic magnetic nature of coronal plumes, is the connection between plumes and magnetic surface features related with flux concentrations. Before the Skylab era plumes were believed to be rooted in unipolar flux concentrations in relation with photospheric or chromospheric faculae, located at the vertices between supergranular cells (Newkirk & Harvey, 1968). This picture was supported by the coincidence of the mean plume separation () and the size of a typical supergranular cell. After the discovery of the presence of compact EUV enhancements at the base of the most bright plumes (Bohlin et al., 1975), which in turn correspond to X-ray bright points, the attention has shifted towards magnetic bipolar regions (Golub et al., 1974; Habbal, 1992; Dowdy, 1993). These observations have suggested a possible explanation for plumes formation: one or more bipoles are pushed by photospheric motions towards an open flux region located at a supergranular junction; eventually reconnection occurs, field lines open up and the required energy for plume formation is released. This mechanism has been analysed in more detail by Wang & Sheeley (1995b), whereas a systematic analysis of the effect of heating of the inner corona at the plume base may be found in Wang (1994), who also investigated the solar wind implications by solving the full energy equation along the radial direction (although pressure balance across the field lines is not taken into account).

However, so far there is little direct evidence for the relationship between plumes and network activity (magnetograms cannot be taken at the limb, where the plumes are more easily observable), though anyway it seems reasonable to assume that plumes are rooted in open flux concentration regions. In support of this idea come the observations of a super-radial expansion of plumes near their base, say in the range (Saito, 1965; Ahmad & Withbroe, 1977; Ahmad & Webb, 1978). What is observed is obviously a density behaviour, but if the plume is to be in equilibrium, then it must be threaded by diverging field lines with increasing height (Ahmad & Withbroe, 1977). Potential field models trying to explain this behaviour were proposed by Newkirk & Harvey (1968) and by Suess (1982), but none of them include the plasma parameters in their analysis. Suess's model consists of an analytical, two dimensional field in Cartesian geometry with a given vertical field at the plume base. A comparison with the results by Ahmad & Withbroe is also made, but unfortunately the whole analysis is affected by a trivial mistake (a factor missing in the decaying exponential function of height).

The main goal of the present paper is to present a self-consistent MHD model which correctly reproduces the observed super-radial expansion near the plume base, assuming that magnetic effects are dominant in the inner corona but taking into account the pressure, inertial and gravity forces as well. This will be achieved by solving the steady, ideal, 2-D MHD equations linearised with respect to the magnetic field under the assumption of a low-beta coronal plasma. The method of solution and the general equations are presented in Sect. 2, whereas the actual plume model is discussed in Sect. 3, first in the simple radial case and then assuming a flux concentration at the base of the plume.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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