Burst Fluence Distributions of Soft Gamma Repeaters 1806-20 and 1900+14 in the Rossi X-Ray Timing Explorer PCA Era

We study the fluence distributions of over 3040 bursts from SGR 1806-20 and over 1963 bursts from SGR 1900+14 using the complete set of observations available from the Rossi X-Ray Timing Explorer/Proportional Counter Array through 2011 March. Cumulative event distributions are presented for both sources and are fitted with single and broken power laws as well as an exponential cutoff. The distributions are best fitted by a broken power law with exponential cutoff; however the statistical significance of the cutoff is not high and the upper portion of the broken power law can be explained as the expected number of false bursts due to random noise fluctuations. Event distributions are also examined in high and low burst rate regimes and power-law indices are found to be consistent, independent of the burst rate. The contribution function of the event fluence is calculated. This distribution shows that the energy released in the soft gamma repeater (SGR) bursts is dominated by the most powerful events for both sources. The power-law nature of these distributions combined with the dominant energy dissipation of the system occurring in the large, less frequent bursts is indicative of a self-organized critical system, as suggested by Goǧus et al. in 1999.