Statistical Properties of Photospheric Magnetic Elements Observed by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory

Abstract

Magnetic elements of the solar surface are studied (using the 6173 A Fe i line) in magnetograms recorded with the high-resolution Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI). To extract some statistical and physical properties of these elements (e.g. filling factors, magnetic flux, size, and lifetimes), we employed the region-based method called Yet Another Feature Tracking Algorithm (YAFTA). An area of $400^{\prime\prime}\times400^{\prime\prime}$ was selected to investigate the magnetic characteristics in 2011. The correlation coefficient between filling factors of negative and positive polarities is 0.51. A broken power-law fit was applied to the frequency distribution of size and flux. Exponents of the power-law distributions for sizes smaller and greater than $16~\mbox{arcsec}^{2}$ were found to be −2.24 and −4.04, respectively. The exponents of power-law distributions for fluxes lower and greater than $2.63\times 10^{19}~\mbox{Mx}$ were found to be −2.11 and −2.51, respectively. The relationship between the size [ $S$ ] and flux [ $F$ ] of elements can be expressed by a power-law behavior of the form of $S\propto F^{0.69}$ . The lifetime and its relationship with the flux and size of quiet-Sun (QS) elements during three days were studied. The code detected patches with lifetimes of about 15 hours, which we call long-duration events. We found that more than 95% of the magnetic elements have lifetimes shorter than 100 minutes. About 0.05% of the elements had lifetimes of more than six hours. The relationships between size [ $S$ ], lifetime [ $T$ ], and flux [ $F$ ] for patches in the QS yield power-law relationships $S\propto T^{0.25}$ and $F\propto T^{0.38}$ , respectively. Executing a detrended-fluctuation analysis of the time series of new emerged magnetic elements, we found a Hurst exponent of 0.82, which implies a long-range temporal correlation in the system.