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Astron. Astrophys. 317, 925-928 (1997)

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4. Relation to the solar magnetic field

As demonstrated above, the DIFOS irradiance data are in anticorrelation with the solar activity parameters over the 27 days time scale. Now, it is useful to compare the DIFOS records with solar magnetic field data directly. However, before that, we should make some remarks.

It is widely known that a local and a global (or large-scale) magnetic field system exist on the Sun (Obridko 1983, Ivanov 1993, Grigoriev and Ermakova 1986). These fields, though closely connected, as a rule display different cyclic variation and different organization in space and in time. This difference is especially important when we deal with long term variations. In the case of the short range of DIFOS observations the difference between the two field systems should not strongly influence the analysis. Nevertheless, we would like to stress that we use magnetic field observations of very low resolution. Moreover, the mathematical method, applied to data processing, makes the resolution even lower and sometimes we shall use the fields of global scale.

4.1. Processing method

All components of the magnetic field at any point of a spherical layer, which extends from the photosphere to the so-called source surface, can be calculated in the potential approximation by using longitudinal magnetic field observations in the photosphere. We used the magnetic synoptic charts from the John Wilcox Observatory of Stanford University. The source surface is, by definition, a sphere where all field lines are radial. It is assumed to exist at a distance [FORMULA] from the centre of the Sun.

The equations used to calculate the magnetic field components are written as follows:

[EQUATION]

[EQUATION]

[EQUATION]

Here, [FORMULA] (conventionally [FORMULA]), [FORMULA], [FORMULA] are the Legendre polynomials, [FORMULA] and [FORMULA] are the coefficients of the spherical harmonic analysis based on the original observational data. For the period under consideration, the coefficients were calculated directly from the synoptic maps.

According to Eqs. (1)-(3), the magnetic field can be calculated at every point between the photosphere and the source surface determined by three coordinates: the radial (R), azimuthal ([FORMULA]), and meridional ones ([FORMULA]).

4.2. Sector structure of the solar field

It is reasonable to begin the comparison with a global field of very large scale. Most convenient to our investigation is the field on the source surface. Here, the highest small-scale harmonics are automatically filtered out and only harmonics of the first and the second order are important.

Fig. 4 shows the synoptic maps of the source surface magnetic field during the two solar rotations when the DIFOS records were obtained. It is easy to see that the DIFOS records coincide in time with the very pronounced and extremely stable 2-sector structure of the global magnetic field. This, again, is in good agreement with the stable structure of the sunspot forming zone (see above). It accounts for the pronounced 27-day variation of all solar parameters and, as a result, of solar irradiance.

[FIGURE] Fig. 4. Synoptic maps of the source surface magnetic field for the interval of the DIFOS records. Isolines correspond to 0, 1, 2, 5, 10, and 20 µTesla. Magnetic field data from the John Wilcox Observatory.

Now, let us compare the indices of large-scale magnetic fields. First, we compute the magnetic field [FORMULA] at the intersection of the "Earth-Sun center" line with the source surface for every day. At the time of the DIFOS experiment this point was [FORMULA] southwards from the centre of the solar disk. Then, we compute the radial field component - the only present on the source surface. We compare the [FORMULA] data with the everyday data on the Sun as the star [FORMULA] measured at Stanford and published in Solar-Geophysical Data. The results are represented in Fig. 5. We find that the two indices, [FORMULA] and [FORMULA], which are usually not alike, are very similar during the 53 days under consideration. The correlation coefficient is 0.956. It is again the effect of the very simple and stable structure of the large-scale magnetic field.

[FIGURE] Fig. 5. Comparison with large-scale magnetic field indices. The source surface field, [FORMULA], is plotted in µTesla with a dash-dot line, and the mean solar magnetic field (Stanford) [FORMULA] is divided by 10 and plotted with a solid line. Data from the DIFOS channel 400-1000nm are plotted with asterisks.

Coming back to the DIFOS data, we can see that the irradiance data are in anticorrelation with the magnetic data. The correlation coefficient is -0.467. At first sight, this result seems a bit strange. In fact, the solar irradiance variation should not be related to the sign of the solar magnetic field. This is only the result of our definition and depends on the observer's site. But the comparison, made in the following paragraph, makes the problem more clear.

4.3. Comparison of the photospheric and the source surface magnetic fields

Let us calculate the absolute value of the vector magnetic field at intersection of the "Earth-Sun's centre" line with the photosphere, [FORMULA]. The difference between this and the point discussed above is that the [FORMULA] field was calculated at the height of 2.5 solar radii and is strictly radial. As stated above, it is a very large-scale field, really global. The [FORMULA] field is calculated at the same line, but in the photosphere. There are some shortcomings in these calculations that concern the influence of active regions (potential field approximation, low spatial resolution of 3' and use of the 9th order Legendre polynomials, which are not good enough to describe the real field structure in active regions). Consequently these calculations yield a mixed field intensity, which partially includes the large-scale and partially the local field. Therefore, we do not claim any actual physical meaning of our everyday calculation. However, we use as an index of field intensity in the photosphere the absolute value of the vector magnetic field.

Now, let us compare the [FORMULA] and [FORMULA] fields in Fig. 6. We see that during the period under investigation the days with large photospheric magnetic fields are in the positive, and those with weak fields in the negative sector. But the intervals with large photospheric magnetic fields [FORMULA] correspond to the minima of solar irradiance near March 28 and April 18.

[FIGURE] Fig. 6. Magnetic fields in the intersection of the "Earth-Sun centre" at the photosphere [FORMULA] (dash-dotted line) and at a height of 2.5 solar radii [FORMULA] (solid line). Ordinate in µTesla, for [FORMULA] divided by 50.

4.4. Relationship between 2800 MHz solar flux, DIFOS "irradiance" data, and the magnetic field

Finally we compare the 2800 MHz solar flux variation with the magnetic field B [FORMULA] (Sun as star). Both curves in the upper part of Fig. 7 are very similar to each other, but the radio flux curve is shifted by 3-4 days westwards from the magnetic curve. When matching the two curves we obtain an excellent correlation coefficient as large as 0.835.

[FIGURE] Fig. 7. Comparison between radio flux and magnetic field: solid line mean solar magnetic field B [FORMULA] in µTesla, dashed line Penticton 2800 MHz solar flux after subtracting the 3rd-order trend. Flux variation between 70 and 90 sfu. dash-dot line below - Magnetic field at the photosphere [FORMULA], scale in µTesla at the right.

The origin of the shift is not clear yet. Some hints at an explanation can be obtained by comparing the radio flux with the photospheric field, [FORMULA] (dash-dot line in the lower part of Fig. 7). It is seen that the region of large magnetic fields has a fine two-maximum structure. The positive part of the radio flux (the days when it is larger than on the average) corresponds to the western maximum in the region of large fields (i.e. to the western part of the positive sector of the large-scale field - see Fig. 6). In Fig. 7 upwards arrows mark these points. On the contrary, the negative part of the radio flux (that means the deficit of the flux compared with the mean value) corresponds to the interval from weak fields up to the eastern maximum. Obridko et al. published a detailed version of the comparison between DIFOS irradiance data and magnetic fields in 1996.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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