Astron. Astrophys. 363, 1145-1154 (2000)

3. Results

3.1. Comparison of line parameters

Fig. 6 shows the relative difference of the averaged intensity at the meridian to that at the other positions along the limb. It was calculated using the expression (Imeridian - Iother locations) /(Imeridian + Iother locations). As described in Sect. 2.4, the data at small µ and at large µ were treated individually and are represented by different symbols in Fig. 6. The stars represent the relative difference for the data in the spatial range near the limb (small µ sector). The diamonds represent this difference for the data in the spatial range closer to disk center (large µ sector). The stars are thus representative of the difference between coronal hole and quiet-Sun regions. For the hottest lines, the relative intensity is smaller for data sampled in a coronal hole than for the quiet Sun, in agreement with expectations. The large µ sector, which is outside the hole for every location, also shows a smaller emission for the meridian data. The effect is nevertheless smaller than for the actual coronal hole. The reason for this behaviour is unknown. A possible explanation is the fact that we observed the Sun at activity minimum, when it has well defined streamer belts at low latitudes. Thus line-of-sight effects could lead to excess brightness in low latitude coronal lines compared to the quiet-Sun at high latitudes. It does suggest, however, that to some extent the plasma at the meridian, but outside the coronal hole boundary (as deduced from EIT images), exhibits the main property of a coronal hole, namely less intense emission from hot ions. We cannot rule out, however, that the behaviour of the large µ data points is dictated simply by the intrinsic solar variation. For example, the scatter shown by the large µ data points suggests that there is still some residual solar variation, even after averaging over all the available data.

Fig. 6. Relative intensity difference between the meridian and the other locations along the limb vs. formation temperature. Diamonds : large µ sector (only quiet Sun); Stars : small µ sector (including coronal hole). The solid line shows a second order polynomial fit to the stars. Due to the larger uncertainty of the parameters of the Fe XII line, its value is not used for the regression. A representative error bar is also plotted (see text for details).

In Fig. 6 (as well as in Fig. 7 and Fig. 8) the average uncertainty has been calculated using the standard deviation for each parameter of the Gaussian fit obtained at each spatial pixel, and averaged over all the data available for a given spectral line. The plotted uncertainty is thus a measure of the scatter of the parameter values of a given spectral line. The statistical uncertainty of the plotted (averaged) parameters are considerably smaller than the plotted one. The uncertainty obtained for three typical spectral lines have been averaged to get a representative value.

Fig. 7. Width difference vs. formation temperature. The "width difference" represents the difference between the line width observed on the meridian and that at other locations. Diamonds : large µ sector; Stars : small µ sector (i.e. widths of hole profiles relative to non-hole profiles). The solid line shows a second order polynomial fit to the small µ sector points, while the dot-dashed line shows a fit to the large µ sector points.

Fig. 8. Wavelength difference in velocity units vs. formation temperature. The "wavelength difference" represents the difference between the wavelength observed on the meridian and the one observed at other locations at the same µ. Since the wavelength scale is not absolute, we equalized the wavelengths at the meridian and the equator outside the hole. Diamonds : large µ sector (identically zero due to equalization); Stars : small µ sector (i.e., shift of hole profile relative to non-hole profiles). The solid curve shows a second order polynomial fit to the small µ sector points. Negative shifts signify blueshifts.

Fig. 7 shows the difference between the line widths observed on the meridian (data with coronal hole at small µ and quiet Sun at large µ) and those observed at other locations (only quiet Sun) at the same µ (Wmeridian - Wother locations).

Almost all spectral lines are broader inside the coronal hole, which confirms similar results found by Lemaire et al. (1999). This increase in line width indicates higher non-thermal velocities inside coronal holes. The Fe XII line exhibits an anomalous behaviour in the sense that it does not follow the trend exhibited by the other lines. Blends from cooler ions in its wings may contribute to this. The widths of the lines in the large µ sector at the meridian again display the same behaviour as the small µ data, although less clearly. This strengthens the case for the interpretation, made on the basis of the diamonds in Fig. 6, that the large µ sector at the meridian behaves like a weak coronal hole.

If we assume that the Doppler width resulting from temperature is the same at the meridian as at the other locations then we can calculate the difference in turbulent velocity. This difference is given by

For our data (averaged over all spatial pixels and spectral lines) we obtain:

Fig. 8 displays the difference between the wavelengths observed on the meridian (data with coronal hole) and the ones observed at other locations (purely quiet Sun) at the same µ. Since the wavelength scale does not have an absolute calibration, we equalized the shifts between meridian data and other data for the sector outside the hole (large µ) by adding to the , where and are averaged over all data sets at large µ. The same offset, , was then also added to the shifts of the meridian data in the small µ sector. In this manner the line shifts in the coronal hole can be determined relative to the shifts in the quiet Sun at equal µ, i.e., close to the limb. Fig. 8 shows a distinct blueshift relative to the quiet Sun at high temperatures in the coronal hole and a small redshift at low temperatures. Hence there is a steadily increasing relative blueshift with temperature. This may represent evidence of solar wind outflow at low altitudes in coronal holes, as has been previously concluded by Hassler et al. (1999) and Wilhelm et al. (2000). The small µ sector points in Fig. 8 may actually underestimate the trend, if the large µ sector at the meridian also weakly exhibits coronal hole properties, as suggested by Fig. 6 and Fig. 7. In that case, lines formed there are also expected to be shifted relative to the quiet Sun.

To express our results in terms of absolute speeds, we can use line shifts found by other authors in the quiet Sun (Doschek et al. 1976; Brekke et al. 1997; Teriaca et al. 1999). Fig. 9 shows the results for coronal-hole and quiet-Sun regions with respect to the shift values obtained by Teriaca et al. (1999). As expected, the curve laid through the quiet-Sun symbols follows exactly Teriaca's curve.

Fig. 9. Absolute wavelength shift in velocity units vs. formation temperature. The absolute shifts are determined using the data of Teriaca et al. (1999). Diamonds : large µ sector; Stars : small µ sector. The solid curve shows a third order polynomial fit to the small µ sector points while the dot-dashed curve shows a similar fit to the large µ sector points. Negative shifts signify blueshifts.

The Ne VIII 770.43 Å line has also been analysed in detail by Dammasch et al. (1999). He found line shifts of -6.2 in coronal holes and -0.8 for the quiet Sun. This is in very good agreement with our values (-6.1 and -1.9 ).

Fig. 9 reveals how small the differences between quiet-Sun and coronal-hole regions are with respect to the temperature dependence of the wavelength shift. In particular, only the coronal lines show a true blueshift (both inside and outside the coronal hole), which is not significantly larger than the redshift exhibited by the transition region lines (even in the coronal hole). In view of this result one may need to be more cautious about assigning the small extra blueshift within coronal holes to the initial phase of the fast solar wind, since it may have to do with (small) changes in the mechanism giving rise to the red- and blueshifts observed in the quiet Sun. It would be useful to have observations of additional coronal lines to put this conclusion on a more sound basis.

3.2. Distribution of intensities

Next we try to characterize better the intensity differences between coronal hole and quiet-Sun regions in view of the unexpected brightening displayed by chromospheric and some transition region lines in coronal holes (Fig. 6). To this end, we plot the intensity histograms for four representative lines belonging to N I, Ni II, O IV and Ne VIII in Figs. 10-13. Here we have put the intensities from all spatial pixels into 35 bins. We plotted the histogram for the small µ sector at the meridian (i.e., the coronal hole data), for the small µ sector at other locations and finally for the large µ sector at other locations (the large µ sector data at the meridian have not been included to avoid cluttering the figures). The chromospheric lines (N I and Ni II ) show a higher average intensity inside the coronal hole area (Fig. 10 and Fig. 11). It appears that in the coronal hole more bright network locations exist than in the quiet Sun. The Ni II line exhibits a higher contrast, i.e., a wider distribution in the coronal hole. In the case of N I, however, the whole distribution appears to be shifted to higher intensities. These histograms show that the higher intensities shown by these lines in the coronal hole are of solar origin and are not due to some calibration problem (which would have led to the histograms in coronal hole and quiet Sun being the same within a multiplicative factor). To what extent the larger network contribution in the coronal hole is due simply to insufficient statistics (too few sampled points) is as yet unknown. Alternatively, it may be a result of the fact that the magnetic filling factor (i.e. fractional area covered by magnetic field) in regions with significant excess of one polarity typically underlying coronal holes is a factor of approximately two larger than in the normal (mixed polarity) quiet Sun (Zhang et al. 1997). Since chromospheric and transition-region spectral lines are as a rule brighter in regions with higher magnetic filling factor, this might explain the somewhat larger brightness of such spectral lines in the coronal hole.

Fig. 10. Intensity histogram of the N I line at 1319.0 Å. Solid line : meridian data in the small µ sector, i.e., in the coronal hole. Dashed line : quiet Sun data in small µ sector. Dotted line : quiet Sun data in large µ sector, at locations away from the meridian.

Fig. 11. Same as Fig. 10 for Ni II at 1317.22 Å.

Fig. 12. Same as Fig. 10 for O IV at 1401.16 Å.

Fig. 13. Same as Fig. 10 for Ne VIII at 770.43 Å.

The typical transition-region line O IV at 1401.16 Å exhibits no significant difference in the intensity distribution of the network (Fig. 12). Finally, in the coronal line (Ne VIII at 770.43 Å) the distribution in the coronal hole is much narrower than in the quiet Sun (Fig. 13). This is in agreement with the results obtained by Gallagher et al. (1998) with data from the Coronal Diagnostic Spectrometer (CDS) onboard SOHO (Harrison et al. 1995). In all cases the difference between the dashed and dotted curves indicates the center-to-limb variation in the quiet Sun.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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