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Astron. Astrophys. 343, 983-989 (1999)

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5. Results and discussion

We are now close to the point where we can relate the restored images to heights in the solar atmosphere. The RFs give intensity variations relative to the continuum intensity. Therefore we multiply the fluctuations in the images, which are relative to the mean intensity at each wavelength position, with the factor [FORMULA] taken from the convolved D2 profile (dot-dot-dot-dashed profile in Fig. 1) at the appertaining wavelength [FORMULA]. Likewise, the speckle-reconstructed image fluctuations were multiplied with the above factor 0.87 resulting from the averaging over 8 Å about the Na D2 line. Furthermore, for a linear combination of images, these have to be of the same image quality, i.e. they must possess the same spatial resolution. Thus, the speckle reconstructions were treated locally (in each sub-image) with the same filter H as the D2 wing images with which they are to be combined. And finally, the linear combinations of images according to the prescriptions in the previous section were built: We calculated, pixel by pixel, new intensities with the same linear combinations as for the response functions in Fig. 4c. For instance, we calculate a new image [FORMULA].

Fig. 6, now, shows in two rows a 20"[FORMULA]20" section of Fig. 2 treated in the above manner at 450 mÅ and 250 mÅ off line centre, respectively. The left images give the granular pattern as it is seen from the deep photosphere. In Fig. 4c, the RFs 1a (solid) and 1b (long-dashed) correspond to the upper and lower left images of Fig. 6, respectively. Comparing these with the speckle reconstruction of Fig. 2 one certainly notices the decrease of spatial resolution due to the filtering necessary for the linear combinations. But most of the features are still present. The middle images in Fig. 6 are the direct reconstructions of the wing observations at the above wavelengths. Here, the granulation is still shining through, more at 450 mÅ off line centre than at 250 mÅ. The right images are the linear combinations according to the recipe of the previous section. The granular pattern has essentially disappeared. Only with the knowledge of the left images one can recognize few low-contrast, granular structures, less clearly at 250 mÅ off line centre (lower image) than at 450 mÅ (upper image). In other words, in view of the curves 1a, 1b, 2, and 3 of Fig. 4c, granular intensity fluctuations are a matter of the deep photosphere alone. This agree with the result by Espagnet et al. (1995).

[FIGURE] Fig. 6. 20"[FORMULA]20" images from the deep photosphere (leftmost ) and higher up (rightmost ) constructed from the same spectral scans as the images of Fig. 2, according to the above prescription of linear combinations for 450 mÅ off line centre (upper image ) and 250 mÅ (lower image ). The middle two images are the restored images from the wings. Distance of tickmarks: 1".

Fig. 7 shows the result from the other spectral scan, the same as in Fig. 3, and for 500 mÅ and 300 mÅ off line centre. It is again clearly seen that the granular intensity fluctuations disappear rapidly with height in the atmosphere.

[FIGURE] Fig. 7. 20"[FORMULA]20" images from the same spectral scan as Fig. 3; linear combinations as in Fig. 6 but calculated for 500 mÅ off line centre (upper row ) and for 300 mÅ (lower row ). Distance of tickmarks: 1".

At some places very dark features occur in the images from the high atmosphere. In most cases, they are related to intergranular spaces. Referring to Fig. 5b we conjecture that these are formed higher than average. These dark features may thus extend over heights of 200-300 km in the photosphere. The bright borders of granules (de Boer et al. 1992) may also be seen in high layers. But generally this is not the case. Considering the overlap of the RFs in Fig. 5a (for [FORMULA]T/T = +0.25), we cannot decide from this analysis whether the corresponding temperature enhancements are bound to the deep photosphere or whether they penetrate to layers of 100 km or more. Still better separated RFs are needed (or combinations of them) together with low noise data amenable to more refined linear combinations. In any case, there is no indication of an anti-correlation of intensities formed in the deep photosphere and in higher layers. The anti-correlation was expected in early models of the granular overshoot into stably stratified atmospheric layers (see e.g. Holweger & Kneer 1989 and references there).

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999