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Astron. Astrophys. 364, 829-834 (2000)

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3. Results

In this paper we present the results obtained from our best data set at [FORMULA]. We have carried out the same analysis for various position angles of the same spot (i.e. different observing days) and find consistent results (see also SS2000).

A systematic difference between the velocity field of the bright and dark component is apparent in Fig. 2. In order to elaborate on this impression quantitatively, we investigate the relation between the intensity of the penumbral filaments and the velocity pattern. A simple correlation analysis between the intensities and velocities comprising the whole penumbra would not provide useful information, since the measured flow depends both on radius and on azimuth. Thus we correlated the fluctuations of the velocity and intensity: In order to filter out the sinusoidal variation of the velocity signal, the velocity fluctuations are defined as the deviations from a local mean, which is obtained by a boxcar average with a width of [FORMULA] in azimuth. The intensity fluctuations are determined relative to the azimuthal mean for each radial position: [FORMULA]. The intensity values were taken from the best continuum image recorded together with the co-spatial spectra, i.e. the intensity and velocity values are simultaneous, but independent, measurements. In Fig. 4 we show the correlation between the velocity fluctuation and the intensity variation for the inner penumbra of the center-side of the spot. The azimuth angle, [FORMULA], ranges from [FORMULA] to [FORMULA]. The inner penumbra comprises pixels with a spot radius, r, between 6.5 Mm and 11.1 Mm (corresponding to the range of the dotted line in Fig. 5). Positive velocity is clearly correlated with brightness, i.e. the strongest upflows occur in the brightest parts. This has already been reported by Schlichenmaier & Schmidt (1999). In the outer parts of the penumbra the correlation disappears, as can been seen in Fig. 5. This is not surprising, since the flow is mostly horizontal and occurs both in dark and bright filaments.

[FIGURE] Fig. 4. Scatter plot of velocity versus brightness fluctuations in the center side ([FORMULA]) of the inner penumbra ([FORMULA], corresponding to the range of the dotted line in Fig. 5) for [FORMULA]. The velocity fluctuations are defined as the deviations from a boxcar-smoothed local mean in km s-1, and the intensity fluctuations are given relative to the azimuthal mean of a specific slice.

[FIGURE] Fig. 5. Correlation coefficient of azimuthal slice between velocity and brightness fluctuations as a function of spot radius. As in the previous figure, only a central sector of [FORMULA] is considered. The penumbra spans from the left end of the abscissa to the vertical line.

As a next step, we divided the observed line-of-sight velocity maps in a "bright" and a "dark" component, using the local intensity criterion described above. Using Eqs. (4) - (6), we derived the inclination angle, the azimuthal mean velocity, and the magnitude of the flow for each of the ensembles (all, bright, and dark) separately.

The azimuthal mean, the inclination angle and the absolute flow velocity for the data set with [FORMULA] are shown in Figs. 6 to 8. Fig. 9 displays the inclination angle for our data set at [FORMULA]. The azimuthal mean [FORMULA], i.e. the vertical velocity component, of the bright component is larger than [FORMULA] in the dark component everywhere in the penumbra. Both components decrease with radial distance. We find that the flow angle (Fig. 7) of the bright component is always less inclined with respect to the surface normal than the dark component. In the inner penumbra, the flow in the bright component is more vertically oriented (due to a larger vertical velocity) than the flow in the dark one. Since the seeing conditions were somewhat worse for our data set at [FORMULA], the absolute difference between the bright and dark component is smaller. The flow in the dark component bends downwards ([FORMULA]) already at a about two thirds of the penumbral width ([FORMULA] Mm) to reach a downflow angle of [FORMULA] ([FORMULA]) at the outer penumbral edge (due to a negative vertical velocity), whereas the bright component never shows a significant downflow. The maximum inclination difference between dark and bright is about [FORMULA].

[FIGURE] Fig. 6. Azimuthal mean, [FORMULA], of the penumbral velocity as a function of spot radius for [FORMULA]. Dotted line: bright points; dashed line: dark points; full line: all data. The shaded areas are the [FORMULA] error bars.

[FIGURE] Fig. 7. Inclination angle, [FORMULA], of the penumbral flow. As Fig. 6.

[FIGURE] Fig. 8. Penumbral flow speed, [FORMULA], for [FORMULA]. As Fig. 6, except that only the bright and dark component is plotted. To distinguish between the overlapping error bars, each of the two areas is surrounded by gray lines (dotted for bright points and dashed for dark points).

[FIGURE] Fig. 9. As Fig. 7, but for [FORMULA].

The shaded areas surrounding each plotted line mark the [FORMULA] error bars, as obtained from the analysis of Sect. 2.3. These error bars demonstrate that the results concerning the azimuthal mean and the inclination angle (Fig. 6 and Fig. 7) are significant everywhere in the penumbra. The errors are significantly larger for the absolute flow velocity (Fig. 8): the flow speed of the bright component lies within the [FORMULA] error bars of the dark component, and vice versa. Since the flow is predominantly horizontal, the main source of this error is the uncertainty of the position angle, [FORMULA]. Near disk center, i.e. for small [FORMULA], only a small fraction of the horizontal velocity component is measured. From Eq. (8) we see that any error in [FORMULA] is amplified by [FORMULA], where [FORMULA] is the position angle in radian. Indeed, for larger [FORMULA], the [FORMULA] error becomes smaller, as is seen in Fig. 10 and Fig. 11, which display the dependence of the flow velocity for [FORMULA] and [FORMULA], respectively. In these figures, the dark component shows a significantly larger velocity in the outer penumbra than the bright component. This indicates that the flow field of the outer penumbra is dominated by the dark component.

[FIGURE] Fig. 10. Same as Fig. 8, but for [FORMULA]. The [FORMULA] error bars of the bright and dark component do not overlap in the outer penumbra.

[FIGURE] Fig. 11. Same as Fig. 8 and Fig. 10, but for [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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