## 2. Observations and data reductionThe observations have been carried out at the German Vacuum Tower
Telescope in the Observatorio del Teide, Tenerife, from 8 to 11
November 1998. We used the filter spectrometer TESOS (Kentischer et
al. 1998) to take two-dimensional spectra of a sunspot and its
immediate surroundings. The Doppler velocity has been derived from the
Fe II line at 542.5 nm, which is formed in the deep photosphere, at an
optical depth . For the velocity
measurements we used a Fourier phase method: The phase of the first
Fourier component of the line profile provides the wavelength position
(c.f., SS2000). At a spatial resolution of some 500 km, we have
observed an isolated round sunspot (NOAA 8578). In the present
analysis we concentrate on the data set, taken at a position angle of
11 ## 2.1. Selection of bright and dark componentThe intensity distribution in the penumbra is rather broad (e.g., Grossmann-Doerth & Schmidt 1981) and the mean intensity also depends on the spot radius. Therefore, a local definition of "bright" and "dark" has to be made. To this end, we converted the intensity data to polar coordinates relative to the spot center, and applied an azimuthal boxcar smoothing (box size Mm) to the continuum intensity values. For each radius, values above the mean were defined as "bright", and vice versa. With this definition, about half of the pixels are bright, and the other half are dark (50.5%, 49.5%). An example of that procedure is shown in Fig. 1. The graph contains part of an azimuthal slice of the continuum intensity at a spot radius of 10.3 Mm (inner penumbra). A boxcar average (not shown in the figure) has been applied to distinguish locally between bright and dark features. The plusses denote the bright component and the triangles correspond to the dark one. At the smallest spatial scale there are some very weak local darkenings that are not recognized as "dark" filaments, but the vast majority of (locally) dark and bright structures is correctly identified. White light images and filtergrams (being recorded simultaneously by TESOS) were co-aligned to find the co-spatial information within the velocity maps. The velocities corresponding to bright and dark pixels are plotted in Fig. 2 for the same spot radius as in Fig. 1. Here, the entire azimuthal slice is displayed, to demonstrate the sinusoidal modulation of the LOS-velocity in azimuth. Note that in most cases, the velocities corresponding to the bright (dark) features are above (below) the local mean.
## 2.2. Flow angle and flow velocityWe take advantage of the azimuthal variation of the line-of-sight velocity in order to determine the mean flow vector. In this paper we perform the analysis not only for the mean flow (as in SS2000), but also for the flow of the bright and dark component, separately. Neglecting an azimuthal component of the penumbral flow field, the line-of-sight measurement, , is related to the material flow on the Sun through where is the flow velocity, is the heliocentric angle of the sunspot, denotes the inclination angle of the flow with respect to the surface normal and is the azimuth angle of the sunspot, with pointing to disk center. Since the deviation of the penumbral flow field from axisymmetry is small, we describe the flow vector by azimuthal means. From the measurements, , we extract the vertical and horizontal components of the line-of-sight velocity. The vertical contribution to the line-of-sight velocity is given by its azimuthal mean, , and the horizontal contribution is described by A(r) is the amplitude of the azimuthal sinusoidal variation. The
mean, using the Marquardt algorithm (e.g., Bevington & Robinson 1992). The inclination angle, , is computed from Eqs. (2) and (3) as The absolute flow velocity, , is given as ## 2.3. Error analysis
Several sources of error have to be considered for the determination
of Fig. 3 shows the radial dependence of
for all pixels (solid line), for the
bright (dotted line) and for the dark component (dashed line). In
comparison with Fig. 2, it is seen that the rms values within the
penumbra are small compared to the amplitude of the azimuthal
variation of the velocity. Note that for all radii, the rms of the
velocity fluctuation is smaller in the individual components (bright
and dark) than for all data points. This indicates that the fit
parameters
The standard deviations of the fit parameters, and , correspond to the diagonal of the error matrix, which is calculated by the Marquardt algorithm (cf. Eq. (4)). The uncertainties for the flow angle, , and for the flow velocity, , result from analyzing the error propagation. In addition to and , one has to consider the error in the position angle, , which is taken from synoptic maps. We estimate this error to be rad and ignore the slight variation of across the spot. Using Eqs. (5) and (6), we obtain: © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |