Astron. Astrophys. 353, 1094-1100 (2000)

3. Data reduction

We aim at detecting weak magnetic signals from the IN elements at the limit of noise. Thus the data reduction has to be done with much care. This holds also for semi-automatic treatments which are needed for the large amount of data, especially from time sequences. For each position of the scanner a separate gain table as well as the correlation of the separate spectrograms for best overlap and their destretching have to be calculated and applied. For the correlation the two telluric O₂ lines contained in the spectrograms and the scan with the pattern in front of the slit are very useful. The accuracy of the physical quantities to be derived from the spectral lines is essentially limited by the accuracy of the gain tables resulting from non-exact alignments of the spectrogram pairs, i.e. from residual spectral line features in the gain tables, and from limited knowledge of the pixel sensitivities. This hampers mostly quantities taken from the Stokes-V profiles. The data reduction, then, follows the common way: Subtraction of the dark level, application of the gain tables which removes also the effects of dust and vignetting, and subtraction of a constant level of spectrographic scattered light which was estimated by comparing the line depressions of our average spectrograms with those of the FTS-Atlas (Neckel 1987).

A noise filtering of the spectra by the "wavelet-shrinkage and thresholding" method (Donoho 1993) was applied to each line profile of each spectrum in each scan. This way of noise filtering proved to be better than a common low-pass filter.

To analyse the polarimetric signal, we decided to use the centre-of-gravity (COG) method developed by Semel (1967). It uses the wavelength distance of the and profiles to obtain the magnetic flux. Rees & Semel (1979) demonstrated that the COG method is independent of the pattern of the line splitting and not sensitive to the amplitude saturation of the Stokes-V signal. The accuracy is better than 10% for low line weakening (line gap effect). Del Toro Iniesta et al. (1990) mentioned that instrumental polarization and crosstalk are effects of second order on the COG method. The detection limit achieved here for the magnetic flux is 2 10⁸ Wb on an area of 0, which corresponds to an average flux density of 0.8 mT.

The COG method is insensitive to the amplitude of the Stokes-V profile. Thus, comparing Stokes-V amplitudes to determine the intrinsic magnetic flux density of the IN elements proper (Stenflo 1973) is not applicable. However, Semel (1981) has shown by means of a two-component model how to use simultaneous observations of several magnetically sensitive lines to derive flux densities and area filling factors of magnetic elements. Semel's (1981) procedure was extensively applied in combination with the COG method, e.g. by del Toro Iniesta et al. (1990).

Moreover, the asymmetries of the Stokes-V amplitudes and areas are obviously not obtained with the COG method. We suggest, instead, to define the asymmetry of the intensity of the COG (relative to the local continuum intensity) and of the equivalent width W by

and

respectively. and have similar meanings as the V amplitude- and area asymmetry, respectively. Yet, as for the amplitude- and area asymmetries, very low noise data are needed to calculate and . This requirement in combination with high spatial resolution has to await larger telescopes with excellent image quality. We will thus not expand further on asymmetries.

From the profiles of , treated in the above manner at each pixel in the field of view, we can compose images of quantities such as: continuum intensity, line center intensity (Stokes I), equivalent width W relative to its average, velocity derived from the average of the COG positions, velocity from the minimum of , and the magnetic flux. Contrary to velocities derived from the zero-crossing of the V profiles, which need sufficient V signal above noise, may also be measured at positions without measurable magnetic flux. The velocities ==0 are defined by the mean COG position and mean line position, respectively, in the field of view. We shall present upflow (downflow) as negative (positive) velocities.

© European Southern Observatory (ESO) 2000

Online publication: January 18, 2000
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