Distribution of the magnetic flux in elements of the magnetic field in active regions

The unsigned magnetic flux content in the flux concentrations of two active regions is calculated by using a set of 248 high-resolution Solar and Heliospheric Observatory Michelson Doppler Imager magnetograms for each active region. Data for flaring active region NOAA 9077 (2000 July 14) and nonflaring active region NOAA 0061 (2002 August 9) were analyzed. We present an algorithm to automatically select and quantify magnetic flux concentrations above a threshold p. Each active region is analyzed using four different values of the threshold p (p = 25, 50, 75, and 100 G). Probability distribution functions and cumulative distribution functions of the magnetic flux were calculated and approximated by the lognormal, exponential, and power-law functions in the range of flux Phi > 10(19) Mx. The Kolmogorov-Smirnov test, applied to each of the approximations, showed that the observed distributions are consistent with the lognormal approximation only. Neither exponential nor power-law functions can satisfactorily approximate the observed distributions. The parameters of the lognormal distribution do not depend on the threshold value; however, they are different for the two active regions. For flaring active region 9077, the expectation value of the magnetic flux content is mu = 28.1 x 10(18) Mx, and the standard deviation of the lognormal distribution is sigma = 79.0 x 10(18) Mx. For nonflaring active region NOAA 0061, these values are mu = 23.8 x 10(18) and sigma = 29.6 x 10(18) Mx. The lognormal character of the observed distribution functions suggests that the process of fragmentation dominates over the process of concentration in the formation of the magnetic structure in an active region.