Sgr A* exhibits flares in radio, millimeter and submm wavelengths with durations of $\sim 1$ hour. Using structure function, power spectrum and autocorrelation function analysis, we investigate the variability of Sgr A* on time scales ranging from a few seconds to several hours and find evidence for sub-minute time scale variability at radio wavelengths. These measurements suggest a strong case for continuous variability from sub-minute to hourly time scales. This short time scale variability constrains the size of the emitting region to be less than 0.1\,AU. Assuming that the minute time scale fluctuations of the emission at 7\,mm arise through the expansion of regions of optically thick synchrotron-emitting plasma, this suggests the presence of explosive, energetic expansion events at speeds close to $c$. The required rate of mass processing and energy loss of this component are estimated to be $\ga 6\times 10^{-10} \msol$ yr$^{-1}$ and 400\,$L_\odot$ respectively. The inferred scale length corresponding to one-minute light travel time is comparable to the time averaged spatially resolved 0.1AU scale observed at 1.3mm emission of Sgr A*. This steady component from Sgr A* is interpreted mainly as an ensemble average of numerous weak and overlapping flares that are detected on short time scales. The nature of such short time scale variable emission or quiescent variability is not understood but could result from fluctuations in the accretion flow of Sgr A* that feed the base of an outflow or jet.
Comment: 26 pages, 10 figures, ApJ (in press) Additional number of figures