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Astron. Astrophys. 321, 643-651 (1997)

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5. Results and discussion

5.1. Weakening of the magnetic field in UDs

The variation of magnetic field strength inside the umbra shows the well known inverse correlation with the variation of intensity. Fig. 4 shows the temporal variation of the maximum magnetic field strength in each sequence obtained with the Stokes synthesis code. The variation of the umbral field strength with time is subject to fluctuations, with no significant variation over the whole observing run. The influence of the titanium blend on the position of the [FORMULA] -component seen in the [FORMULA]  846.85 nm line may lead to a misjudgement of the magnetic field strength but this is a second order effect, which affects the determination of the magnetic field ratios by a small amount.

[FIGURE] Fig. 4. The maximum value of magnetic field strength [FORMULA] of the CUD1 sequence as a function of time. The magnetic field strength is derived from a comparison with synthetic line profiles.

Fig. 5 displays the ratios of [FORMULA] versus time for the selected sequences. The derived values for [FORMULA] from the synthetic line profiles are slightly lower than 1.0 and the average field reduction amounts to [FORMULA]  3 % for the CUD1 sequence and 1-2 % for the PUD1/PUD2 sequence. The weakening of magnetic field strength is higher in the CUD2 sequence and amounts to [FORMULA]  7 %. In Fig. 5 are also plotted the field strength ratios of UD to adjacent umbra [FORMULA] and [FORMULA], where [FORMULA] and [FORMULA] denote the field strengths as seen to each side of the UD, either in direction to the penumbra (outer footpoint) or to the deep umbra (inner footpoint). These ratios show a significant deviation from unity. This can be explained by the overall variation of the umbral magnetic field strength and the fact, that [FORMULA] and [FORMULA] are measured at a position considerably beside the UD, whereas [FORMULA] approximates the umbral field strength that would be present at the UD position, if there would not be an UD.

[FIGURE] Fig. 5. Magnetic field reduction in UDs. The magnetic field ratios [FORMULA] ([FORMULA]), [FORMULA] ([FORMULA]) and [FORMULA] ([FORMULA]) versus time are shown for the selected sequences of the [FORMULA]  846.85 nm line and the [FORMULA]  630.25 nm line. bg - umbral background, in - UD footpoint towards umbra, out - UD footpoint towards penumbra.

Further systematic errors are introduced due to the different temperature of UDs compared to the surrounding umbra. Thus the iso- [FORMULA] -levels belong to different heights in- and outside UDs. Therefore we compare field strengths in UDs with those of the adjacent umbra, although these measurements correspond to different geometrical heights inside the umbral atmosphere. As mentioned before, our results concerning the height levels of the observed lines in and outside UDs cannot be used for a direct comparison of geometric height scales, since they originate from different model atmospheres and we do not know the difference in height between the [FORMULA] levels of the umbral models M4 and IAC-H. In order to overcome this lack of information we use the theoretical model of Degenhardt & Lites (1993). They find that the continuum level of the UD is shifted towards higher layers compared to the surrounding umbra (see Fig. 2a, page 387). The difference in height between the [FORMULA] level in- and ouside the UD amounts roughly to 100 km for a typical model. Adding this value to the results in Table 3 shows that the observed spectral lines originate higher in the UDs than in the surrounding umbra. If we further adopt an umbral field gradient of 2 G/km, the shift of 100 km results in a decrease of the background magnetic field strength [FORMULA]. Hence we underestimate the ratio [FORMULA] by a few percent. For equal geometrical heights the reduction of magnetic field strength in UDs becomes negligible even for the [FORMULA]  630.25 nm line.

5.2. Temperatures and intensity contrasts of UDs

We investigated the brightness temperature and intensity contrast of the observed UDs. Fig. 6 (left panel) displays the temporal variation of the calculated temperature ratios [FORMULA] and [FORMULA]. The right panel shows the variation of the UD-to-background intensity ratio [FORMULA] as a function of time for the continuum and the line core. The intensity contrasts indicate that the PUD1 vanishes after 33 min, while the PUD2 and the CUD1 slowly fade away during the observation interval. No such trend is visible in the CUD2 sequence. Seeing shows fluctuations but does not become bad towards the end of the sequences, so that the observed fading of the UDs is real.

[FIGURE] Fig. 6. Brightness temperature and intensity contrast of UDs. Shown are the UD brightness temperatures relative to the quiet sun [FORMULA] ([FORMULA]) and the umbral background [FORMULA] ([FORMULA]) versus time (left panel) and the UD contrasts measured in the continuum ([FORMULA]) and the line core ([FORMULA]) (right panel).

Table 5 includes all results of the analysis as time averages for the selected sequences. Since the measured intensities are subject to fluctuations caused by different effects, some care must be taken by calculating averages. All measurements indicating either bad seeing, an imperfect positioning of the slit, or the possible disappearence of the UD due to the intrinsic development, have been excluded.


Table 5. Results of the UD analysis at [FORMULA]  846.85 nm and [FORMULA]  630.25 nm.
[FORMULA] - Temperature difference UD-quiet sun. [FORMULA] - Temperature difference UD-background. [FORMULA] - magnetic field strength ratio UD-to-background derived from the synthetic line profiles. The indices 0 and c refer to continuum and line core respectively.

The average values of the temperature reduction [FORMULA], the temperature difference Quiet Sun - UD, [FORMULA], and the continuum intensity contrast [FORMULA] show a dependence of the radial position of the UD inside the umbra (see Table 4). This effect can partially be due to an insufficient stray light correction (see Sect.3) concerning the PUD1/2 sequence.

The simplified stray light procedure neglects the spatial variation of the stray light across the spot and leads to a certain undercorrection near the umbra-penumbra boundary and hence to an overestimation of intensities [FORMULA] and temperatures [FORMULA] for the peripheral UDs. This is in turn partially compensated by using photospheric brightness instead of penumbral intensity. On the other hand, a stronger correction for stray light would lead to higher continuum contrasts [FORMULA], together with a decrease of the temperature reduction [FORMULA] and an increase of the temperature difference [FORMULA]. Thus the PUDs would become much brighter but also much more inconspicuous than the CUDs concerning their temperature signatures. Thus the observed difference between CUDs and PUDs cannot be explained by an insufficient stray light correction. We therefore conclude that the radial dependence is real and there exists a physical difference between CUDs and PUDs.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998