2 Observations and data reduction

The observations were carried out on October 23rd, 1999, with the "Göttingen'' Fabry-Perot Interferometer (FPI) in the 70 cm Vacuum Tower Telescope (VTT) at the Observatorio del Teide, Tenerife. The telescope was pointed to a quiet granular region at disk center. A 45 min time series of spectral scans across the non-magnetic Fe I line at $\lambda =5576$ Å together with simultaneously exposed bursts of broad band images (100 Å FWHM) centered at the same wavelength have been obtained. The exposure time for both types of images was 20 ms. The time between the starts of two subsequent spectral scans was 70 s. The pixel size is $0\hbox{$.\!\!^{\prime\prime}$ }1$ and the field of view of the raw data is $384~\mbox{pixel}\times 286$ pixel in size. The iron line has been scanned at 11 spectral positions separated by $\Delta\lambda = 35.25$ mÅ and the actual FWHM of the FPI was approximately 52 mÅ.

The data have been carefully corrected for dark offset, flat fields and global image motions. In addition, the narrow band images have been corrected for the transmission curve of the pre-filters and for the wavelength shift across the field of view which appears due to the mounting of the FPIs in the collimated, parallel beam of the setup.

The broad band data have been reconstructed for the optical transfer functions of the telescope and the Earth's atmosphere applying speckle interferometric techniques as described in de Boer (1993). Since the narrow band images have been simultaneously exposed with the broad band ones, a quasi-speckle reconstruction as described in Krieg et al. (1999) could be applied to them. For a more detailed description of the observation procedures and the data reconstruction techniques see Hirzberger et al. (2001).

Line profiles at each pixel of the field of view can be retrieved from the narrow band images. Since the resolution of the data is not expected to be better than $0\hbox{$.\!\!^{\prime\prime}$ }3$ and for improving the signal-to-noise ratio, the line profiles have been averaged by a $3~\mbox{pixel}\times 3$ pixel boxcar smoothing over the field of view. From each of the resulting profiles the line bisector has been computed providing intensities and line-of-sight velocities at different heights, $i=(I-I_{\rm lc})/(I_{\rm c}-I_{\rm lc})\cdot 100$ [%], in the line profiles. (The quantity $I_{\rm lc}$ denotes the line center intensity, $I_{\rm c}$ is the intensity of the local continuum, and I is the measured intensity in the line profile.) An absolute velocity reference cannot be determined from the data because only relative wavelengths have been obtained. The zero points of the velocity maps have, therefore, been defined as the average values in the field of view. The precision of the velocity measurements, derived from noise, is in the range $\Delta v_{\rm rms}\approx\pm 50~\mbox{m~s}^{-1}$. The intensity maps have been normalized to their mean values.

Since the Airy functions - which describe the transmission curves of the FPIs - have extended wings, the response functions corresponding to the intensity maps are relatively broad and so the separation of the photospheric heights where the light is emitted from is rather low. This problem has been overcome by calculating linear combinations of images from different line depths. For the present study intensity maps, I₅₀, from i=50% (barycenter of the response function at $h_{\rm bc}=53$ km above the continuum level) and intensity maps $I_{0}=I(i=0\%) - 0.2\cdot I(i=25\%)-0.15\cdot I(i=75\%)$ with $h_{\rm bc}=320$ km have been computed. The width of the velocity response functions is much smaller than that of the corresponding intensity response functions. Therefore, a linear combination of several velocity maps is not necessary. For the present study velocity maps, v₀, from $i=0\%$ ( $h_{\rm bc}=250$ km) and v₅₀, from i=50% ( $h_{\rm bc}=130$ km) have been used. (A detailed description of the computation of intensity and velocity maps and plots of the corresponding response functions are given in Hirzberger et al. 2001.)

The last step of the data reduction was to co-align all the maps from the time series and to apply a subsonic filter (with a cut-off phase velocity of 5 km s^-1) which removes the influence of solar p-modes and of residual image distortions with apparent phase velocities larger than 5 km s^-1. The subsonic filter was applied to the time series of broad band images, $I_{\rm BB}$, and to the narrow band intensity and velocity maps. Finally, the data consist of 5 cubes, $I_{\rm BB}(x,y,t)$, I₀(x,y,t), I₅₀(x,y,t), v₀(x,y,t), and v₅₀(x,y,t) depending on two spatial dimensions, x and y and the time, t. After removing the apodized edges each cube contains 36 images with $260~\mbox{pixel}\times 190$ pixel in size.