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We present a statistical analysis of the X-ray flux distribution of Sgr A*from the Chandra X-ray Observatory's 3 Ms Sgr A* X-ray Visionary Project (XVP)in 2012. Our analysis indicates that the observed X-ray flux distribution canbe decomposed into a steady quiescent component, represented by a Poissonprocess with rate $Q=(5.24\pm0.08)\times10^{-3}$ cts s$^{-1},$ and a variablecomponent, represented by a power law process ($dN/dF\propto F^{-\xi},$$\xi=1.92_{-0.02}^{+0.03}$). This slope matches our recently-reporteddistribution of flare luminosities. The variability may also be described by alog-normal process with a median unabsorbed 2-8 keV flux of$1.8^{+0.9}_{-0.6}\times10^{-14}$ erg s$^{-1}$ cm$^{-2}$ and a shape parameter$\sigma=2.4\pm0.2,$ but the power law provides a superior description of thedata. In this decomposition of the flux distribution, all of the intrinsicX-ray variability of Sgr A* (spanning at least three orders of magnitude influx) can be attributed to flaring activity, likely in the inner accretionflow. We confirm that at the faint end, the variable component contributes ~10%of the apparent quiescent flux, as previously indicated by our statisticalanalysis of X-ray flares in these Chandra observations. Our flux distributionprovides a new and important observational constraint on theoretical models ofSgr A*, and we use simple radiation models to explore the extent to which astatistical comparison of the X-ray and infrared can provide insights into thephysics of the X-ray emission mechanism.

The X-ray Flux Distribution of Sagittarius A* as Seen by Chandra