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Astron. Astrophys. 360, 1157-1162 (2000)

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2. Observations and data analysis

The observations for this work stem from one of the data sets described in Paper I. They were taken on June 21, 1997, with our FPI at the VTT on Tenerife from quiet Sun disc centre. The FPI was scanned through the Na D2 line with a bandwidth of 200 mÅ at steps of 100 mÅ. At each wavelength position 5 short exposure (6 ms) narrow-band images were taken. Strictly simultaneously with these, integrated light (broad-band) images through a 10 Å interference filter centered at Na D2 were taken. The image scale on the CCDs (Thompson TH 7863 FT, 384[FORMULA]286 pixels) is [FORMULA]/pixel leading to an original field of view of [FORMULA].

A scan over the relevant part of the Na D2 line takes approximately 18 s. This is not critical for slow convective motions of few km s-1. But changes of dynamics occurring on shorter time scales will be smeared out, at least. Modifications of the apparatus, e.g. by using substantially faster CCDs, to speed up the scanning process are under way.

The observed Na D2 profile is very similar to the fully drawn profile in Fig. 1 of Paper I. As is demonstrated there, the observed profile differs much from one taken with a high resolution spectrograph due to the broad transmission curve of the FPI of 200 mÅ (Airy's formula) and to the transmission curve of the pre-filter needed for order sorting. The line center intensity is increased from 0.04 (relative to the continuum intensity) to 0.31 and the wing intensities are much depressed, while the width of the profile remains approximately unchanged (full width at half minimum = 550 mÅ). We do not treat here the line center region of the profile, and the smearing effect (convolution with Airy's FPI function) is taken into account for the velocity response function (see below). The depression of the wing intensities could be removed from measuring the transmission curve of the pre-filter with a continuous light source (haline lamp). The slopes of the observed profiles are still steep enough to determine shifts for velocity measurements. The results on the velocity analysis are described below.

The data analysis proceeded in the usual way (see also Paper I). We applied dark frame and flat field corrections and shifted the images to correct for image motion. This latter processing reduces the field of view to [FORMULA]. Next we reconstructed the broad-band images with speckle techniques, i.e. with the spectral ratio method (von der Lühe 1984) and with speckle masking (Weigelt 1977). The narrow-band reconstructions were also obtained as in Paper I, by means of the instantaneous optical transfer functions derived from a combination of the simultaneous broad-band images and the broad-band speckle reconstruction.

Here, for the determination of the granular velocities in the low photosphere, we combined the images at -500 mÅ and -600 mÅ off line center, and at +500 mÅ and +600 mÅ giving 10 images for reconstruction in the blue and red wing of Na D2, respectively. The Doppler shifts are measured from the differences of the intensity fluctuations in the blue and red wing via

[EQUATION]

The [FORMULA] values are taken from the average D2 profile observed with the FPI. To build the difference of the intensity fluctuations in the above equation identical optimum noise filters (Brault & White 1971) were applied to the blue and red wing intensity fluctuations. This is done by using the product of the noise filters obtained from the data of both wings (and the flat fields). From the wavenumber cutoffs of the noise filters we estimate a spatial resolution of our velocity measurements of [FORMULA]-[FORMULA]. The speckle reconstruction of the granular intensities has a better spatial resolution, approximately [FORMULA].

The height of formation of the velocity signal is best seen from response functions (Mein 1971, Kneer & Nolte 1994, cf. also Paper I). Following the prescription by Mein (1971) and according to Eq. (1), it is obtained from the intensity changes due to a velocity pulse at a limited height range [[FORMULA]]. We show in Fig. 1 the (normalized) velocity response function [FORMULA] calculated in LTE for the [FORMULA] = 500-600 mÅ off D2 line center velocity measurements. Here, the limited spectral resolution is accounted for. The center of gravity of [FORMULA] in Fig. 1 is at [FORMULA] = 140 km (above [FORMULA] = 1).

[FIGURE] Fig. 1. Velocity response function for the measurements in the band 500-600 mÅ off the center of Na D2. The instrumental profile of the FPI spectrometer is taken into account. The calculation was performed in LTE with the model of Vernazza et al. (1981).

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000
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