Astron. Astrophys. 326, 842-850 (1997)

3. Analysis and results

The first step of the analysis is the separation of the "active" region (hereafter "A region") from the "quiet" region (hereafter "Q region"). The active region is defined using the average image in the MgIb₁ line wing over the whole 109mn time sequence. This image is smoothed using a boxcar window 30 pixels wide (equivalent to approximately 10"), and then, pixels having an intensity higher than the average are defined to be the region A. The Q region is made of the pixels outside these contours, having intensities lower than the average (see Figs. 1 and 2). However this definition is not sufficient due to the small scale magnetic structure of an active region. A more sophisticated definition is necessary for the A region. Correlograms of intensities in the continuum and in the MgI line are then calculated for the A and Q regions, separately for each pair of images of the temporal sequence (Fig. 3). There, one can see three components in the correlograms for the A region: one is very similar to the distribution of points in the correlogram of the Q region, whereas a second group of points corresponds clearly to the bright points in the MgI image and a third to the pores. The results of the correlogram of the Q region (Fig. 3a) is used to analyse the correlogram of the A region. We divide it in sub-regions: -firstly, pixels having an intensity in the continuum lower than are considered as pores. This limit is illustrated by the vertical line in Fig. 3. -secondly, another separation is needed to discriminate the pixels corresponding to abnormally bright points in the MgI line wing. This limit is defined as the line , where is the linear regression coefficient.

Fig. 1. Image averaged over the 109 mn sequence obtained in the wing of the MgIb1 line. The A region is defined as the interior of the black contours, while the Q region is the region outside the contours (see text)

Fig. 2. Sample image of the granulation obtained in the true continuum. The closed contours separate A and Q region, as in Fig. 1

Fig. 3. Correlogram between continuum and MgIb1 intensities, for a sample pair of images, for the Q region (a) and the A region (b). Dividing lines are the same in a and b

Pixels from A region but not from the pores sub-region and below this second limit will correspond to a region called "active quiet" (hereafter "AQ region") since they are in the A region but their intensity distribution is similar to that of the pixels of the Q region. Pixels above this level (and not from pores sub-region) will correspond to an "active active region" (hereafter "AA region") since their abnormally high intensities in the MgI line wing indicate high non-spot magnetic field values. Points with abnormally low intensity in the continuum (pores), will not be taken into account in this analysis. The approximate number of pixels of the Q, AQ and AA regions are respectively: 300000, 20000 and 4000.

3.1. Spatial behaviour of intensity fluctuations

Once the regions are defined, it is possible to calculate some of their statistical characteristics as their mean intensity and their spatial standard deviation, also called or RMS. These parameters were computed for each image of the time sequence, yielding an averaged value and its dispersion from which we derived errors intervals as the range. The mean intensity of each region (Q, AQ and AA) was calculated for the continuum images, and then normalised to the mean intensity in the Q region. The results over the 110 images show (see Table 2) that the AA region is slightly but significantly darker than the Q region at the continuum level, whereas the AQ region is slightly brighter. The spatial standard deviation of intensities were computed as well for these regions, outlining an abnormal granulation in both the AA and AQ region. The same parameters were computed for the images taken in the wing of the MgIb₁ line. It appears that the intensity in the AA region is in average about 12% higher than in the Q region. In order to investigate the influence of acoustic waves on these results, we have employed a so-called "acoustic" filter (see e.g. Title et al. 1989 for a thorough description) which allows the separation of the component due to acoustic modes from the rest of the signal. All of the previous parameters have been computed using "subsonically" filtered (p -modes removed) data. Despite changes in absolute value, no relative differences arise from the comparison of the two datasets (see Table 2).

Table 2. Averaged intensities and spatial standard deviation for the Q, AQ and AA regions, computed with no filtered data and subsonically filtered data. For both continuum and MgI line, intensities are normalised by the averaged intensity in the Q region ( =100 and =100

3.2. Intensity correlations

Another important result yielded by this analysis is the spatial correlations in the Q region when the intensities in the MgIb₁ line wing are plotted as a function of the intensities in the continuum. The correlation coefficient C between continuum and MgIb₁ intensities in the Q region for the 110 raw images has an averaged value of , and is always included in the interval . In order to investigate the origin of this correlation we made a more detailed study using the three data sets yielded by the acoustic filter: the raw, the subsonically filtered (p -modes signal suppressed) and the supersonically filtered (every but the p -modes eliminated) data sets. The correlation coefficient between continuum and MgIb₁ intensities as a function of time difference has been computed. Figure 4 shows the three curves (raw, subsonically and supersonically filtered data), which have been averaged for a number of cases. In the three cases, the correlation remains positive. The maximum of the correlation function of the raw images is slightly shifted towards negative values. The correlation function of the supersonic images is symmetric and maximum for a time difference , which is expected since acoustic modes are standing waves, and thus, are well in phase in the whole photosphere. More surprisingly, the correlation of the subsonic filtered images peaks at a negative time difference  mn. This implies that, for the "subsonic" part of the signal, the variations of intensities at the MgIb₁ level precede those at the continuum level. We next carried out a careful analysis of the images, in order to determine the pattern responsible for this correlation. We established that the observed correlation is related to dark structures of spatial scale larger than that of granulation, but we did not draw further conclusion.

Fig. 4. Mean correlation curves between continuum and MgIb1 images, as a function of time difference, for original (solid), subsonically filtered (dot-dashed) and supersonically filtered (dashed) images

It is also worthwhile to compare the RMS of the intensity of single images (SI) with the RMS of the mean image (MI) after averaging over the whole 109 mn time sequence. The RMS value of the averaged image is 1.2%, whereas the RMS of instantaneous images (SI) is on average %, illustrated by the fact that a clear pattern subsists in the average image (Fig. 5). The observed decreasing of the RMS from 2.8% to 1.2% should be attributed to the averaging of a succession of independent "realisations" of the granulation pattern. Obviously, the lifetime of the granulation must be accounted for, but this number seems small compared to the duration of the time sequence. Moreover, the spatial correlation of each instantaneous image with the mean image was computed taking into account only the Q region, yielding a mean value of , which suggests that there is a persistent, long-lived granulation giving rise to the observed pattern. In order to determine the spatial scale responsible of this correlation, we computed the same correlation using spatially filtered images. The instantaneous images and the averaged one were filtered with different spatial bandpass. The variations of the correlation coefficient versus wavenumber show a maximum between and (Fig. 6), indicating that the spatial scale responsible of the correlation is between 1500 km and 3000 km, which is about the size of the granulation pattern.

Fig. 5. Blow-up of a quiet region taken in the continuum, after an averaging over the whole time sequence (109mn). The residual RMS of the intensity fluctuations is 1.2%. This should be compared to the average RMS of instantaneous images: 2.8% (see text)

Fig. 6. Correlation between instantaneous continuum images and the time averaged continuum image, as a function of the wavenumber

3.3. Horizontal motions

In order to investigate the behaviour of the horizontal velocities versus height in the solar atmosphere, we applied the so-called "local correlation tracking" technique (November 1986 , Molowny-Horas & Yi 1994 ) to both time sequences (continuum and MgIb₁ line). Time separation between correlated images was 1 mn. The resulting averaged correlation function from the 108 image pairs was convolved by a gaussian window with a full width at half maximum of 4.1:00, and then the offset was calculated by a parabolic interpolation. The corresponding "flow" maps are shown in Figs. 8 and 9. The flows at the continuum level outline clearly the supergranulation cells (visible in simultaneous intensity observations in H wings, see Fig. 10), whereas these cells are not visible at the level of the MgIb₁ line, where structures of smaller spatial scale are identified.

Fig. 7. Histogram (normalised to the total number of counts in each region) of the horizontal velocities calculated in Section 3.3, at the continuum level (a ) and at the MgIb1 level (b ) for the quiet (solid) and the active (dot dashed) regions, showing strikingly different behaviours

Fig. 8. Map of the horizontal velocity field at the continuum level plotted over a sample continuum image

Fig. 9. Map of the horizontal velocity field at the MgIb1 level, plotted over a sample MgIb1 image

Fig. 10. Blow-up of the horizontal velocity field at the continuum level plotted over the H (sum of the two wings) intensity map

We calculated the average horizontal velocities both in A and Q regions, at the two levels of the atmosphere. In the A region, the average velocities are very similar:  m/s and  m/s, whereas in the quiet region, they increase drastically when going higher up in the atmosphere:  m/s and  m/s. This behaviour is illustrated by the histograms of the velocities calculated (Fig. 7). We also computed the correlation between the modulus of the velocity at the two levels. We obtained a correlation coefficient of for the A region and for the Q region. We also made these computations using the X and Y components of the velocity vector and we found a correlation about 0.45 for the Q region and about 0.60 for the A region, which confirms a similar behaviour of the flows when magnetic field is present.

Using the horizontal velocities, we have also studied the motions of the bright points seen in the MgIb₁ images. Some of them exhibit steady proper motions during the 109 mn observing interval. Figure 11 shows three subimages of one bright point during the time sequence. It has moved by 1450 km after 109 mn, leading to a transversal velocity of 220 m/s. This agrees well with the radial velocity component of intranetwork fields (Wang et al. 1989 ), as well as with the proper motion of filigrees (Zhang & Engvold 1993 ). To investigate whether this motion is partly or totally mirroring the horizontal velocity field of the photosphere underneath, a test particle whose initial position coincides with that of the bright point has been allowed to drift during 109mn with the photospheric flow field. The resulting trajectory (Fig. 11) follows very closely that of the bright point. However, one must note that other bright points in the same figure do not display any detectable motion. A close inspection of the whole field of view reveals that out of the fraction of migrating points, all but one move in accordance with photospheric flow field underneath.

Fig. 11. Transverse displacement of a bright point during 109 min. Numbers on the upper right corner indicate minutes lasted since the beginning of the observations. Initial position of the bright point corresponds to the crossing point of the two thin dotted lines. The solid black cross represents the position of a test particle which is drifting with the photospheric flow field underneath. The scale of the figure in arcseconds is given by the solid bar on the lower left corner. The average velocity of this bright point is 220 m/s

© European Southern Observatory (ESO) 1997

Online publication: October 15, 1997
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