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Astron. Astrophys. 362, 737-745 (2000)

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4. Temperature dependence of the distribution function

To study the dependence of the parameters of the distributions we included more data in the chromospheric and transition region temperature ranges. The additional data sets in the range between [FORMULA] K and [FORMULA] K were SUMER raster scans covering 60"[FORMULA]120" made in Jun. 1996 in the lines CI 1311 Å and CII 1334 Å, and a time series in the OI line at 1152 Å made in Mar. 1996. In the range between [FORMULA] K and [FORMULA] K SUMER raster scans covering 90"[FORMULA]100" were available, made in Sept. 1996 in the lines SiIV 1402 Å, OIII 703 Å, OIV 1401 Å, and OV 629 Å. A lognormal fit was made to all distributions. We normalized the shape of the fitted distributions with respect to the number of pixels and additionally rescaled the radiance to a common range by dividing by the mean value.

Fig. 6a shows the fitted lognormal distribution functions of all available data in the temperature range between [FORMULA] K and [FORMULA] K. The transition region lines show significantly different distribution shapes. These lines have their most common value in a lower radiance regime but their tails extend further out than for the chromospheric and coronal lines indicating that there is a greater probability for relatively high radiance values. This could be due to the large number of short-time scale enhancements seen at these temperatures. The chromospheric lines have a sharper peak at higher radiances, and their tails drop off more steeply. Finally, the coronal lines exhibit an intermediate behaviour. Fig. 6b depicts one of the corresponding fit parameters, namely the strength ([FORMULA] from Eq. (4)), which measures the height and position of the most probable radiance value. The larger this parameter, the higher the peak and the more "outward" shifted and symmetric is the shape of the lognormal function. This figure qualifies the results already visible in Fig. 6a.

[FIGURE] Fig. 6a and b. Lognormal fits to the normalized histograms of SUMER data at different temperatures. Plot a shows the fitted functions, plot b shows the corresponding strength parameter [FORMULA] of the lognormal fit, which is a measure of the height and position of the peak. The squares represent the results from the larger data sets, the diamonds those of the additional data.

Figs. 7a and b show the corresponding position (µ) and width ([FORMULA]) parameters of the fitted lognormal functions. As pointed out by J. G. Doyle (priv. communication) the shape of the curve in Fig. 7b looks similar to that of the Doppler shifts versus temperature profile found by a number of authors (e.g. Teriaca et al. 1999 and references therein). The chromospheric lines showing little or no Doppler shift have the most symmetric and "peaked" radiance distributions, the transition region lines with pronounced redshifts exhibit large tails in their radiance distributions. It is, however, unclear to what extent or how these two results are related.

[FIGURE] Fig. 7a and b. The other two fit parameters corresponding to Fig. 6. (Note that due to the normalization the three parameters are not independent.) Plot a shows the position parameter µ, plot b shows the width parameter [FORMULA] of the lognormal fit.

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© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000