BURST FLUENCE DISTRIBUTIONS OF SOFT GAMMA REPEATERS 1806−20 AND 1900+14 IN THE ROSSI X-RAY TIMING EXPLORER PCA ERA

Soft gamma repeaters (SGRs) are associated with slowly rotating, extremely magnetized neutron stars (NSs; see reviews by Woods & Thompson 2006; Mereghetti 2008). They are sometimes found in young supernova remnants and are characterized by recurrent emission of short duration, ∼0.1 s (Kouveliotou 1995), bursts of soft gamma-rays/hard X-rays with spectra described by optically thin thermal bremsstrahlung (OTTB) at kT ∼ 20–40 keV (Goğus et al. 2001). Recent studies at lower energies, <15 keV, have found that an OTTB model is no longer accurately fitted to the spectra and there is a rollover which can be best fitted with two blackbodies or alternatively a cutoff power law (Feroci et al. 2004; Olive et al. 2004; Nakagawa et al. 2007; Israel et al. 2008; Lin et al. 2011; van der Horst et al. 2012). There is evidence that these bursts are the result of starquakes that occur when the NS crust fractures due to a buildup of stress associated with the evolution of the strong magnetic field, greater than 10¹⁴ G (Thompson & Duncan 1995).

In Thompson & Duncan's seminal 1995 paper first describing magnetars they give a theoretical description of the repeating bursts observed from SGRs. The ultra-strong magnetic fields rotating with the core of the NS are pulled through the crust, causing stress to build up. When the stresses become more than the crust can support it fractures. An electron/positron pair plasma is ejected from the star and captured by the magnetic field near the NS surface. This plasma then cools via emission of soft gamma rays and X-rays.

The statistical properties of SGR bursts have been shown to be similar to those observed for earthquakes (Cheng et al. 1996; Gutenberg & Richter 1956, 1965). Event energy distributions from SGR 1806−20 and SGR 1900+14 sources have been well fitted with a power law described by dN ∝ E^−γ dE and an exponent, γ, of 1.6–1.7 (Goğus et al. 1999, 2000). Many natural systems have been found to fit power laws (Aschwanden 2011). This power-law distribution of energy release was recognized to occur in many natural systems that exhibit nonlinear energy dissipation and is commonly referred to as a self-organized critical (SOC) system (Bak et al. 1987).

Here, we report on burst energy distributions using all of the data available from the Rossi X-ray Timing Explorer (RXTE) for two of the most active SGRs, SGR 1806−20 and SGR 1900+14, covering the period from 1996 December to 2011 February. The initial search found 3040 bursts from SGR 1806−20 and 1963 from SGR 1900+14. Differential and cumulative event fluence distributions are presented for each source. These were fitted with single power laws as reported by past authors (Laros et al. 1987; Woods et al. 1999; Goğus et al. 1999), but we also fitted single and broken power laws with exponential cutoffs and were able to improve upon the quality of fit for each source. We also use the large number of bursts observed to define periods of high and low burst activity. The burst fluence distribution for high and low burst phases was then analyzed. The contribution function was calculated for the burst fluence distributions. This function would be peaked at a characteristic fluence if one existed in the data set. This distribution shows the contribution of the different fluence bins to the total energy released by the bursts. In Section 2 the observations for each source are described, Section 3 covers analysis and the results, and Section 4 presents our conclusions.

SGR 1806−20 has been observed to exhibit sporadic bursting behavior since 1983 (Laros et al. 1987). The Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory launched in (April 1991) detected more sporadic bursting behavior. It entered an active phase in 1996. Two weeks of observations with RXTE/PCA led to the discovery of 7.47 s pulsations and confirmed its nature as a magnetar (Kouveliotou et al. 1998). This source remained relatively inactive until it released a giant flare in 2004 (Hurley et al. 2005). The luminosity of this flare had a peak of a few times 10⁴⁷ erg s⁻¹ (Hurley et al. 2005; Palmer et al. 2005). The source remained active, emitting hundreds of smaller bursts for the next two years, although it generally decreased in activity over that time.

SGR 1900+14 became active in 1998 May after a period of long inactivity (Kouveliotou et al. 1993). It then emitted a giant flare in 1998 August (Hurley et al. 1999). The persistent emission from this source shows pulsations with a period of 5.2 s, matching the period of pulsations observed in the tail of the 1998 giant flare (Cline et al. 1998; Hurley 1999; Feroci 2001). The source has remained active over the last decade but no further giant flares have been observed.

The PCA on board RXTE observed SGR 1806−20 and SGR 1900+14 for a total of more than 800 hr, or 3 Ms, each. An automated burst search, similar to the searches by Woods et al. (1999) and Goğus et al. (1999), was performed for all of the available data. We used standard-1 (2–60 keV) data constrained to observations 5° above Earth's horizon. Each 0.125 s bin was searched. A background count rate was estimated using 5 s of data 3 s before and after the bin being searched. Bins in excess of 125 counts bin⁻¹ were assumed to contain burst emission and were excluded from the background estimate. A burst was defined as any continuous set of bins in which the count rate exceeded 5.5σ the average local background rate. The count fluence was then estimated by integrating the background-subtracted counts for all bins included in the burst. Bursts which happen very close in time were counted as a single burst if their fluence did not drop below the 5.5σ of the average local background rate and counted as multiple bursts when they did. There were a small number of bursts which saturated the RXTE/PCA and were left out of our study because the burst fluence cannot be accurately calculated for these events. We report the fluence in PCA counts PCU⁻¹ because no spectral analysis was done in this work. A conversion factor, 2 × 10⁻¹² erg cm⁻² counts⁻¹, can be used to determine the burst fluence in erg cm⁻². This was reported by Goğus et al. (1999, 2000) based on BATSE spectral measurements.

We fitted the data for each source using differential and cumulative distributions. The data were initially fitted with a single power law but for both types of distribution the fit parameters indicated that the likelihood of the model representing the data was very low, with reduced χ² values between 3 and 5 and a Kolmogorov–Smirnov (K-S) probability of zero for both sources. Examining the fluence distributions of each source (Figures 1 and 2), it is apparent that at the lower and upper ends of the distribution there are more components to the fit. We then fitted a broken power law and exponential cutoff using the cumulative distributions. The cumulative distribution retains all of the original information from the data set and more clearly shows the excess and falloff from the power law. The method and results for each source, distribution, and different fits are described in the following section.

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3.1. Differential Distributions of Burst Fluence

3.2. Cumulative Distributions of Burst Fluence

3.3. Contribution Function Distribution

To better understand the nature of these events and how the energy release is distributed, we examined the contribution function, (dN/d log E) E, for the fluence distributions. Using the differential distribution we calculated the contribution function and plotted it against d log E. This distribution should peak at the characteristic fluence of the intrinsic distribution, see Figure 3. Instead we observe a distribution well fitted by a single power law over four orders of magnitude, with exponents of 1.37 ± 0.03 and 1.34 ± 0.05 for SGR 1806−20 and SGR 1900+14, respectively. This further supports the idea that the falloff observed in the cumulative fluence distribution is not related to the characteristic fluence of the sources. Both distributions indicate that the largest portion of energy release occurs in the highest fluence bursts instead of the more numerous low fluence bursts.

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3.4. Event Distributions as a Function of Burst Activity

The large number of detected bursts allows us to distinguish between different levels of burst activity for each source. Figure 4 shows the burst rate for all observations of each source. We define high burst activity as a burst rate exceeding the average rate for all observations, approximately 1 burst ks⁻¹ of observing time for each source. Cumulative fluence distributions were made for separate periods of burst activity for each source and fitted with a single power law and a broken power law with exponential cutoff as described in Section 3.2. The burst-rate-dependent cumulative distributions are shown in Figure 5. The exponents for each source are the following: SGR 1806−20 high phase is 1.56 ± 0.02 and low phase is 1.59 ± 0.03; SGR 1900+14 high phase is 1.55 ± 0.02 and low phase is 1.57 ± 0.02. The fit parameters and goodness-of-fit values are summarized in Table 1. The power-law exponent for each phase is consistent with that of the total bursts indicating that the burst fluence statistics are independent of the level of burst activity over the time for which we have observations with RXTE/PCA, approximately 15 years. The fact that the excess of events at low fluence is dominant in the low burst rate regime is supportive of the idea that this excess is due to random fluctuations in the background, as suggested in Section 3.2.

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The collected RXTE/PCA observations for SGR 1806−20 and SGR 1900+14 provide thousands of bursts for each source to perform statistical analysis on the fluence distributions. We fitted the cumulative distributions for SGR 1806−20 and SGR 1900+14 with a single power law, broken power law, and both with exponential cutoffs. The distributions were best fitted with a broken power law with exponential cutoff but there is not a significant statistical difference between that and the broken power law without a cutoff. Fitting all the features of the distribution allowed us to improve the uncertainty on the fit parameters for a single power law over three orders of magnitude, giving γ = 1.54 ± 0.01 and γ = 1.56 ± 0.02 for SGR 1806−20 and SGR 1900+14, respectively.

The contribution function was calculated for each source and was found to be well fitted by a single power law over four orders of magnitudes of fluence. The function is clearly not peaked; thus we do not observe a characteristic fluence in these distributions. It also shows how energy release in repeating bursts is dominated by the emission from high fluence events instead of the more numerous low fluence events.

The burst activity for each source varies significantly over the ∼3 Ms of observations. We found the power-law fits for data at high and low burst rate and find that the exponents for different levels of activity are consistent with the exponent for the total event distribution. This indicates that the fluence of individual bursts is independent of burst activity; however the rate of bursts can vary significantly over time.

The power-law fits to the event fluence distributions when all the events are included as well as the rate-dependent distributions, especially when considered over three orders of magnitude, provide strong evidence that the repeating bursts from SGRs are the result of an SOC system. The independence of the power-law fit from burst rate is another indicator of SOC behavior. An SOC system requires a constant source of energy; in SGRs this can be attributed to the ultra-strong magnetic fields. The undoubtedly complex nature of the interactions occurring in the crust of an NS combined with this constant source of power in the magnetic field then explains why we observe SOC behavior from SGRs.

We thank Ken Gayley for his suggestion to calculate the contribution function and for his help in doing so. We also thank Joanne Hill, Randall McEntaffer, and Craig Kletzing for their comments. Fotis Gavriil also offered important advice for this work.