3 Data processing

Data reduction and analysis were performed using the data processing software package and language ANA (Shine 1990).

   
3.1 Spectra and filtergrams

The reduction of the spectrograms was performed using standard procedures, including flatfielding, wavelength calibration and noise reduction using Fourier filtering techniques (more details in Paper I).

The slit-jaw images were first flatfielded and then rescaled to match the spatial size of spectrogram pixel. The alignment to the spectrograms was done by cross-correlation of two spatial intensity profiles of the area covered by the slit. The slit is etched on a Cr-coated glass plate, so that besides being transmitted into the spectrograph, part of the light falling on the slit is being reflected by the glass into the slit-jaw camera beam. The spatial intensity profile under the slit could therefore be recovered from the slit-jaw images and be correlated for alignment with the corresponding spatial intensity profile from the spectrograms, derived from the convolution of the spectrograms with the transmission profile of the slit-jaw filter.

Finally, a movie was produced in order to study the time evolution of the solar scene around the slit. The movie frames were stabilized using cross-correlation to a reference image, correcting for image jitter induced by seeing and the scanning mode. No destretching was applied to the slit-jaw images since that would introduce a deformation of the straight slit in the image domain.

From the alignment of the slit-jaw images, the exact offsets of the spectrograph slit could be determined. From each 3-step scan cycle, one spectrogram/slit-jaw image pair was selected so that in the resulting series, the spectrograph slit had minimum relative offsets. The selected series has a maximum jitter in the slit position of less than 2 slit-widths and a cadence of 55.5 s.

The reduction of the DOT images include flatfielding, rigid alignment, destretching and correction for the instrumental and atmospheric MTF (more details in Balthasar et al. 2001).

The SVST G-band images were manually aligned to the slit-jaw images after flatfielding and rescaling the pixel dimensions. These images were used to facilitate a solid alignment of the DOT G-band images to the SVST observations. A pixel-to-pixel alignment of the DOT images to the slit-jaw images was not attempted to be achieved but the alignment is accurate enough to determine the slit location at the photospheric level.

   
3.2 Doppler- and intensitygrams

Figure 2:  Pairs of line-core intensity (bottom) and velocity (top) space/time diagrams for the four spectral lines. The Doppler diagrams are gray-scaled according to the scaling box at the top left, the intensity diagrams are scaled individually for each spectral line. The spatial coordinates have the same origin as in Fig. 1. Small white rectangles mark the different filaments discussed in the text, dark filaments have letter designation A-I (bottom left diagram) and bright filaments K-M (bottom right). Below the space/time diagrams a Ca II K slit-jaw and a G-band image (the approximate location of the slit indicated by the dashed line) with the same filament markings. The arrow points towards disk centre.

From the set of spectral lines present as blends in the Ca II K wings, a subset was selected to study the Evershed effect at different heights in the penumbral atmosphere. These spectral lines are well isolated and relatively strong, Table 1 presents the line core wavelengths determined from a spatially-averaged disk-centre intensity solar atlas (Neckel 1999). The line core mean height of formation is determined from LTE line formation modelling in the quiet Sun atmosphere model of Holweger & Müller (1974, HolMul hereafter). More details, including a summary of atomic data, are presented in Paper I.

The weak slope of the Ca II K wings on which the line blends are superposed, affects the shape of the spectral line profiles as compared to spectral lines with a clean continuum. Van der Waals broadening is the dominant broadening agent and the slope of the Ca II K wings depends on the temperature stratification of the atmosphere under the slit. Since the Doppler shifts of the line blends are determined over a small portion of the line profile, variations in the slope of the Ca II K wings could in principle affect these measurements. To estimate the strength of this effect, some numerical tests were performed of Doppler measurements on synthetic lines from hot and cool penumbral atmospheres (from Paper I) with realistic velocities present. It was found that the measurement differences between the lines was on the order of less than a few m s^-1 - much smaller than other uncertainties involved (see below).

The Doppler shift of the line core was determined from the analytical minimum of a second order polynomial fitted to 5 pixels (0.044 Å) centered at line minimum. From a numerical experiment, the uncertainty due to noise was determined to be on the order of 120 m s^-1. This uncertainty is reduced by binning the spectrograms in the spatial dimension over 3 pixels (0 $.\!\!^{\prime\prime}$25). Random errors introduced by seeing variations can be estimated from the difference in velocity between consecutive spectrograms. For these lines, the rms of the differences in the penumbra ranges between 150-200 m s^-1. Note that this is an overestimate since these differences are partly real and partly introduced by alignment errors and slit displacements.

The line-core shifts were calibrated to a reference constructed from the line core positions of the spectra well outside the penumbra. The centroid of a Gaussian fitted to the line-core shifts from a 34 $^{\prime\prime}$ long part of all 207 spectrograms served as reference line core position. This procedure is too biased to serve as an absolute velocity calibration: there is relatively small spatial smearing because of the rather stable slit pointing and the abnormal granulation surrounding a sunspot introduces an unknown offset with respect to standard quiet sun granulation. However, this calibration is precise enough for this study which focuses on the relative change of the Doppler signal in the penumbra.

After determining the Doppler shifts in each spectrogram, intensity and velocity space/time diagrams were constructed for each line by subsequently putting an intensity or velocity profile from each spectrogram on top of another. In such a diagram, the spatial dimension is along the horizontal axis and time runs along the vertical. The initial diagrams had a continuous spatial drift introduced by image rotation and an additional jitter from seeing variations and the scanning mode. These were largely removed by shifting each subsequent profile by an amount determined from a rigid alignment of an intensity space/time diagram in the far Ca II K wing where the intensity profile has largest contrast. The shifts determined from a cross-correlation procedure on this diagram were applied to all diagrams and the results are shown in Fig. 2.

 

 

Table 1: Summary of spectral lines. Line core wavelength is determined from a disk-centre intensity solar atlas. Height is line-core mean height of formation above the continuum in the HolMul atmosphere model (from Paper I).

Ion	Wavelength	Height
	[Å]	[km]
Mn I	3926.475	148
Fe I	3940.039	177
Fe I	3925.207	283
Ti I	3929.874	323

   
3.3 Tracking filaments

The solar image under the spectrograph slit was in constant motion, by translation and distortion due to seeing effects, by image rotation from the telescope and by deliberate translation from the scanning procedure. After determination of the magnitude of the shifts and a careful inspection of the slit-jaw movie, it was concluded that a number of penumbral filaments were covered during the whole sequence. In order to study the velocity signal in each of these filaments in close detail, tracks were selected in the space/time diagrams. The algorithms to set up the different tracks were based on either following local minimum intensity (for dark filaments), maximum intensity (for bright filaments) or maximum velocity signal. Maximum velocity signal and minimum intensity turned out to give very similar results - reflecting the often reported observation of the strongest Evershed effect being found in dark filaments (see e.g. Beckers 1968; Title et al. 1993; Shine et al. 1994; Rimmele 1995). Each track was displayed in the slit-jaw movie to assure that the same filament was followed during the whole sequence. In all the velocity/intensity diagram pairs plus the G-band and slit-jaw images in Fig. 2, the tracks are marked with small white rectangles, with their letter designation given in the lower diagrams. Track A and B, corresponding to the two left-most dark filaments were covered only part of the sequence, image rotation moved the spectrograph slit away from these filaments after about 40 min.