Statistical Properties of Photospheric Magnetic Elements Observed by SDO/HMI

Magnetic elements of the solar surface are studied in magnetograms recorded with the high-resolution Solar Dynamics Observatory / Helioseismic and Magnetic Imager . To extract some statistical and physical properties of these elements (e.g., filling factors, magnetic flux, size, lifetimes), the Yet Another Feature Tracking Algorithm (YAFTA), a region-based method, is employed. An area with 400$^{\prime\prime}\times$400$^{\prime\prime}$ was selected to investigate the magnetic characteristics during the year 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 arcsec$^2$ were found to be -2.24 and -4.04, respectively. The exponents of power$-$law distributions for fluxes smaller and greater than 2.63$\times$10$^{19}$ 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 in the form of $S\propto F~^{0.69}$. The lifetime and its relationship with the flux and size of quiet-Sun (QS) elements are studied during three days. The code detected patches with lifetimes of about 15 hours, which we call long-duration events. It is found that more than 95\% of the magnetic elements have lifetimes of less than 100 minutes. About 0.05\% of the elements were found with lifetimes of more than 6 hours. The relationships between the size (S), lifetime (T), and the flux (F) for patches in the QS, indicate the 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 find a Hurst exponent of 0.82, which implies long-range temporal correlation in the system.