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Astron. Astrophys. 357, 767-776 (2000)

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5. Discussion

The best fit to the observed ratios for each model yielded optimal parameters for each model and for each of the two ions. The two most effective models in each case were models 3 and 4 for which the most significant parameter is the density scale height. Optimisation of this parameter yields scale heights of 1.2 and 2.5 arc sec for both models 3 and 4 for C II and C III respectively. Fig. 7b shows that within the pointing accuracy of the SUMER instrument (around 10 arc sec - see Paper I), model 4 is slightly more effective than model 3 in describing the C III ratio variation across the limb. However, the relative magnitude of model 1 to model 3 in the composite case was treated as an adjustable parameter and whilst a large value ([FORMULA] 100) is optimal in the C III case, a low value, namely zero, is the optimal value for C II . As a consequence it is felt that model 4 is, in this study, largely redundant. The scale heights in both cases are similar to the [FORMULA] 1.5 arc sec findings of Mariska, Feldman & Doschek and to those found in Paper I - noting that the C III scale height is likely to be an over estimate as the slope of the ratios in the region from 964 [FORMULA] 970 arc sec is not matched. They also agree with both in terms of the decrease with decreasing temperature of line formation.

[FIGURE] Fig. 8. Intensity ratio of C III (2-2)/(1-2) vs optical depth for the unblended (dashed) and blended (solid) cases.

[FIGURE] Fig. 9. Observed and model flux ratios of the (2-2)/(1-2) lines of the C III  2s2p 3P - 2p2 3P multiplet for model 3 in the blended and unblended case.

In order for the scattered light to dominate at the appropriate points, a departure from the exponential fall off of density is required. A cut-off was introduced in the model for this purpose, the position of which was optimised for agreement with the observed ratios. For C II the optimal position was found to be [FORMULA] 974 arc sec. For C III this cut-off was found to be at [FORMULA] 969 arc sec. This latter value is influenced by the fact that the scale height is optimised as described above and is thus overestimated. Consequently in the absence of a cut-off the predicted onset of scattered light occurs later than observed.

A possible interpretation for this departure from an exponential fall off, or at least a change or even discontinuity in scale height, follows from the model considered by Mariska, Feldman & Doschek who, as stated above, envisaged cylindrical spicules. The exponential fall off of density in this picture reflects the change in filling factor as the number of spicules intersected by the line of sight decreases with distance beyond the limb. Ultimately, however, the density variation will reflect the genuine density variation at the top of a spicule.

In Paper I the extension of the line of sight with raster position was treated as a single effect on the layer as a whole for each density model. However, in the variable density case, lines of sight at and near the limb see a greater geometric extension of the line of sight for the inner most sublayers compared to those toward the outer extreme of the emitting layer. Since these inner sublayers correspond to regions of higher density, a proper treatment of the geometric extension leads to a greater variation of optical depth between the disk and the limb (and hence a stronger dip in the C III ratios at the limb) in comparison with a model that only considers the geometric extension of the emitting layer as a whole. With this in mind it is interesting to note the comparative success of the simpler escape probability approach of Paper I and of Doyle & McWhirter (1981) in regard to the ratio behaviour of C III in the vicinity of the limb. In both these works the line of sight extension was modelled as [FORMULA] where [FORMULA] is 0 at disc centre and [FORMULA] at the limb. This is infinite at the layer edge (hence the discontinuity in the models in Figs. 13, 14 and 15 of Paper I at this point) and consequently the extension of the line of sight is overestimated as are the optical depths in this region. This error serves to improve the fit to the data.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000