Statistics of X-ray flares of Sagittarius A*: evidence for solar-like self-organized criticality phenomenon

X-ray flares have routinely been observed from the supermassive black hole, Sagittarius A${}^{\star }$ (Sgr A${}^{\star }$), at our Galactic center. The nature of these flares remains largely unclear, despite of many theoretical models. In this paper, we study the statistical properties of the Sgr A${}^{\star }$ X-ray flares, by fitting the count rate (CR) distribution and the structure function (SF) of the light curve with a Markov Chain Monte Carlo (MCMC) method. With the 3 million second $\mathit{\text{Chandra}}$ observations accumulated in the Sgr A${}^{\star }$ X-ray Visionary Project, we construct the theoretical light curves through Monte Carlo simulations. We find that the $2-8$ keV X-ray light curve can be decomposed into a quiescent component with a constant count rate of $\sim 6\times {10}^{-3}$count s${}^{-1}$ and a flare component with a power-law fluence distribution $dN\mathrm{/}dE\propto E^{-{\alpha }_{\mathrm{E}}}$ with $\alpha_{\rm E}=1.65\pm0.17$. The duration-fluence correlation can also be modelled as a power-law $T\propto E^{{\alpha }_{\mathrm{E}\mathrm{T}}}$ with ${\alpha }_{\mathrm{E}\mathrm{T}}<0.55$ ($95\mathrm{\%}$ confidence). These statistical properties are consistent with the theoretical prediction of the self-organized criticality (SOC) system with the spatial dimension $S=3$. We suggest that the X-ray flares represent plasmoid ejections driven by magnetic reconnection (similar to solar flares) in the accretion flow onto the black hole.