Statistics of Photospheric Supergranular Cells Observed by SDO/HMI

Aims: The statistics of the photospheric granulation pattern are investigated using continuum images observed by Solar Dynamic Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) taken at 6713~\AA. Methods: The supergranular boundaries can be extracted by tracking photospheric velocity plasma flows. The local ball-tracking method is employed to apply on the HMI data gathered over the years 2011-2015 to estimate the boundaries of the cells. The edge sharpening techniques are exerted on the output of ball-tracking to precisely identify the cells borders. To study the fractal dimensionality (FD) of supergranulation, the box counting method is used. Results: We found that both the size and eccentricity follow the log-normal distributions with peak values about 330 Mm$^2$ and 0.85, respectively. The five-year mean value of the cells number appeared in half-hour sequences is obtained to be about 60 $\pm$ 6 within an area of $350^{\prime\prime}\times350^{\prime\prime}$. The cells orientation distribution presents the power-law behavior. Conclusions: The orientation of supergranular cells ($O$) and their size ($S$) follows a power-law function as $|O| \propto S^{9.5}$. We found that the non-roundish cells with smaller and larger sizes than 600 Mm$^2$ are aligned and perpendicular with the solar rotational velocity on the photosphere, respectively. The FD analysis shows that the supergranular cells form the self-similar patterns.