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Astron. Astrophys. 357, 1093-1104 (2000)

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Appendix A: a relationshipNabetweenexcess and magnetic field

A quantitative relationship between the CaII K line core intensity and the absolute value of the magnetic flux density has been clearly established by several studies (Skumanich et al. 1975; Schrijver et al. 1989; Nindos & Zirin 1998). The best agreement with the data is given by a power law relation with an exponent of 0.6 (Schrijver et al. 1989). Given the excellent spatial coincidence of the sodium network points and the magnetic structures present in our data (see Sect. 3.3, we searched for such a quantitative relationship also for this case.

Fig. A1 shows a scatterplot of the sodium "excess" for the 11 NBPs, vs. the corresponding absolute values of magnetic flux density. As done by Schrijver et al. (1989, 1996) for the CaII K emission, we subtracted to the NaD2 intensities a threshold equal to the average intensity in the quiet areas ([FORMULA] in arbitrary units). The graph was obtained plotting the temporal average of both the sodium intensity and magnetic flux. It does not display, hence, any temporal variation of either quantity, but only a general trend among the persistent structures. Five-minutes oscillations do not play a role in this relationship, nor do they contribute to the scatter of the points. Saturation, as reported by Schrijver et al. (1989) is not apparent in our data, but it must be remarked that the maximum value of the magnetic flux density for the average quantities is below 400 G, the "critical" value indicated by those authors.

[FIGURE] Fig. A1. Scatter diagram of the NaD2 intensity, after subtraction of a threshold of about 104 (see text), vs. the absolute longitudinal magnetic flux density. All the 11 analyzed NBPs are plotted. Solid line is the power law fitting described in the text

The sodium excess is best fitted by a power law of the type [FORMULA]I [FORMULA], with [FORMULA]=0.58 [FORMULA]0.1. The exponent is very close to [FORMULA]=0.6[FORMULA]0.1 found by Schrijver et al. (1989, 1996) for the CaII K excess. These results indicate that the emission in the center of the NaD2 line is also a good proxy for the magnetic flux density and, at least for values of magnetic flux density smaller than a few hundred G, its use is equivalent to that of the CaII K emission.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000