Mathematics – Probability
Scientific paper
May 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aas...204.2004a&link_type=abstract
American Astronomical Society Meeting 204, #20.04; Bulletin of the American Astronomical Society, Vol. 36, p.686
Mathematics
Probability
1
Scientific paper
Probability distribution functions (PDFs) of the unsigned magnetic flux content in flux concentrations in a mature active region NOAA 9077 were calculated by using a set of 248 high resolution SOHO/MDI magnetograms. Two independent routines to outline magnetic flux concentrations were elaborated. The analysis was performed with 4 different values of the threshold, p, of the magnetic flux density (p=25, 50, 75, 100 G). We have found that: i) the best analytical approximation of the observed PDFs in the range of low flux (1 x 1018 Mx < F < 150 x 1018 Mx ) is a lognormal distribution, LN(m ,s2), with the expected value m=(0.7-5) x 1018 Mx and the standard deviation s = (10-45) x 1018 Mx. The peak of the lognormal distribution tends to shift toward the lower flux as the threshold p decreases. This tendency suggests that the real expected value may be even smaller than 0.7 x 1018 Mx; ii) for the flux F > 150 x 1018 Mx the observed PDFs fall off slower than the lognormal approximation predicts. In this flux range, the power law is found to be the best analytical approximation with the power law index approximately equal to 2. The transition region between the lognormality and the power law shifts toward the lower flux as the threshold p is lowered. This implies that the functional form of the distribution changes continuously with the scale. The above findings are consistent with the concept of highly intermittent (or multifractal) nature of photospheric magnetic fields and offer a new tool to study their multifractality.
SOHO is a project of international cooperation between ESA and NASA. This work was supported by NSF-ATM 0076602, 9903515 and NASA NAG5-12782 grants.
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