Fermi/GBM Observations of the SGR J1935+2154 Burst Forest

Because the detector-to-source angles change considerably during 130 s episode, we divided this data into two segments separated at $T_{0}+392$ s, taking into account the detector angles and the source lightcurve. We also calculated the field of view and spacecraft blockage (mainly by the Large Area Telescope) for each NaI detector during this time period. We used detectors having detector-to-source angles $<55^{\rm o}$ that were unblocked for each of the two segments (1. $T_{0}+310$ s to $T_{0}+392$ s and 2. $T_{0}+392$ s to $T_{0}+433$ s). These requirements constrained the detectors used for the analysis to NaI 6, 7, and 9 for Segment 1 and NaI 0, 1, 6, and 9 for Segment 2.

To model the background count rates, we first generated a Bayesian-block representation of the lightcurve (Scargle et al., 2013) using the TTE data of the triggered detectors (binned to 8 ms, 10–100 keV) and defined the background time intervals as the blocks longer than 4 s (hatched regions in Figure 1). The background count rates were then interpolated using the 8 ms lightcurve of the background time intervals in the energy range used in the spectral analysis (8–500 keV), by fitting a second-order polynomial function. We also cross checked our choice of the background time intervals by running the untriggered event search, which uses Poisson statistics to identify count rate increases, over the entire burst-forest period; none of the untriggered bursts identified were within our background time intervals.

Before proceeding with the spectral analysis, we evaluated the possibility of count saturation in the data due to the very high count rates recorded for some of the burst forest peaks. The TTE data suffers from a deadtime of 2.6 $\mu$s due to the fixed data-packet processing speed of 375 kHz on the spacecraft (Meegan et al., 2009). Consequently, bandwidth saturation of the data occurs when the collective count rates of all 14 GBM detectors (12 NaI + 2 BGO), exceed this limit. For the burst forest episode, the maximum count rate summed for all 14 detectors over all energy bands is $\sim 250$  kHz, which is well below this saturation limit. Additionally, we also evaluated the data for pulse pile-up effects, a phenomenon that inaccurately processes normally discrete spectral and temporal values when the “recovered” count rates exceed $\sim$10⁵ counts per second per detector (Chaplin et al., 2013; Bhat et al., 2014). The deadtime-corrected TTE count rates for the detectors used in this study do not exceed this limit, and thus we conclude that our data is unaffected by this behavior and our analysis of the burst forest is accurate.

We performed time-resolved spectral analysis ($8-$500 keV) using the RMFIT spectral analysis tool (version 4.3.2).¹¹1https://fermi.gsfc.nasa.gov/ssc/data/analysis/rmfit The energy range of 30-40 keV was excluded in our analysis to avoid possible contribution to the fit statistics due to the iodine $K$-edge at 33 keV. This exclusion, however, did not affect the analysis outcome. We fit each of the two time segments with four models commonly used to describe spectra of magnetar bursts: a power law with exponential cutoff (COMPT), a single blackbody (BB), a double blackbody (BB+BB), and a blackbody plus power law (BB+PL). The fit parameters were obtained by minimizing the log-likelihood (C-stat). The spectral fits were performed in various time resolutions: 4, 16, and 128 ms. The 4 ms and 16 ms spectral bins were created with a signal-to-noise (S/N) minimum of 25 in the brightest detector. We present in Table 1 the spectral parameters obtained with either COMPT, BB, or BB+BB fits for each time interval. We note here that based on the spectral fit results, we identified two distinct kinds of intervals, which we define as peaks and troughs. The former are invariably associated with the higher photon fluxes and can be best fit with either COMPT or BB+BB. The latter are associated with flux minima and are best fit with either COMPT or a single BB. Because the COMPT model provides reasonable fits for all spectra of the burst forest, we use the BB+BB and BB fits to define the peak/trough definition.

Throughout this Letter we have consistently used equal time bins of 128 ms for the peaks in all the figures, unless otherwise stated. However, for troughs, the requirement of a 25 S/N results in bins with variable time resolution. All these parameters are presented in Table 1. Finally, we find that the fluence during the entire duration of the burst forest was $F=(2.305\pm 0.001)\times 10^{-4}$ erg cm^-2 in the $8–500$ keV energy range; Segment 1 accounted for $(0.562\pm 0.002)\times 10^{-4}$ erg cm^-2 and Segment 2 for $(1.743\pm 0.002)\times 10^{-4}$  erg cm^-2.

The fit statistics that we employed for our spectral fitting (C-stat) does not provide the goodness of fit and cannot be directly used to identify the model that better describes each of the spectra. Therefore, we calculate for each spectral fit the Bayesian Information Criterion (BIC; Liddle, 2007) as follows:

Finally, within the trough spectra where BB is preferred, the $kT$ does not vary significantly. The weighted means of the BB $kT$ in the Segment 1 and 2 trough spectra are 8.0$\pm$0.5 keV and 7.8$\pm$0.3 keV, respectively. We assume, therefore, that this component is manifested as the low-energy $kT$ in the BB+BB spectra, and fix the low-energy $kT$ to the weighted mean values mentioned above. We then proceed to study the evolution of the high-energy $kT$. Although in some parts of the peaks the high-energy $kT$ is then found to be slightly lower ($\lesssim 2$ keV) than those found with the varying low-energy $kT$, we find that the overall high-$kT$ evolution does not change significantly from what is seen in Figure 4.

We expand below on the intriguing properties of Segment 2. Although the overall lightcurve of the burst forest by itself does not clearly exhibit periodic behavior consistent with the source’s spin, $P_{\rm spin}=3.24$ s, the source spectral properties are correlated with the spin period and the extrapolated pulse profile of the persistent emission observed with NICER at energies below 10 keV. The high-energy spectral component is clearly present in both COMPT and BB+BB fits within the burst peaks. We note that all transition times from BB+BB to the single BB thermal spectra correspond to a certain spin phase. In addition, the spectral hardness of the peaks is highest at the minima of the pulse phase, while the spectral parameters remain approximately constant during the trough intervals.

This strong correlation between the flux and the burst spectra, as well as the phases of soft X-ray emission, provides clues to the emission and viewing geometry for this magnetar. Because of the need to sustain bursts of duration 0.1 s for many light-crossing times ($<0.3$ms), it is widely believed that the bursts emanate from closed field line regions in the magnetosphere. The extrapolated NICER lightcurve represents the persistent emission from the stellar surface that likely emanates from locations relatively near the magnetic poles (Younes et al., 2020c). This is then more visible to an observer whose instantaneous perspective is more or less over the pole. As the high X-ray luminosity of the forest of bursts likely indicates highly optically thick conditions (e.g., Lin et al. 2011), their zones act to occult the surface emission at various rotational phases. Thus, it is highly likely that the soft X-ray pulse peak corresponds to a phase where the observer line of sight lies roughly over the poles; this is when the GBM burst spectra are at their softest in both COMPT and BB+BB fits. Yet, because the $<10\;$keV pulse fraction is modest (Younes et al., 2020c), the quasi-polar surface locales are probably at least partially visible for all burst phases. The key stellar parameters are the angle $\alpha$ between the magnetic and rotation axes, and the angle $\zeta$ between the observer direction and the spin axis. The soft X-ray pulse profile is most easily interpreted if $\alpha$ and $\zeta$ are both not too large, likely both less than around $50^{\circ}$; more precise determination of these angles requires detailed surface modeling (Younes et al., 2020a) and treatment of magnetospheric occultation, which is beyond the scope of this Letter.

The phase dependence of the burst spectra can then be interpreted, and constraints on the magnetar geometry can be discerned. Presume first that the various zones of burst activation span a full toroidal closed field line volume, with little or no bias in magnetic azimuth for the overall burst ensemble. Further, suppose that the hotter regions constitute a toroidal “belt” at low altitudes close to where the footpoints of the field lines (that define the toroidal surface) touch the stellar surface. According to Figure 8, this belt is roughly of effective surface area 3–30 km², a factor of 10–80 smaller than the cooler majority of the burst activation zone. For the rotational phases during which the polar surface is approximately visible to an observer, the hot zones are also readily visible along with large portions of the cooler outer toroid. There would also be other rotational phases where the observer’s view to the hotter burst locales is occulted by the optically thick cooler outer toroidal zones; these putatively correspond to the low flux phases evident in Figure 4 where the burst emission is cooler. Given that the hotter BB component is visible for around 60–70% of phases, the observer likely does not ever view the magnetar very close to the magnetic equator, when the hotter belt would be occulted by the cooler outer zones for larger portions of the rotation period. This translates to $\zeta$ not being very close to $90^{\circ}$, again probably less than $60^{\circ}$ or so.

A contrasting scenario would be to presume that the hotter BB regions are not adjacent to the surface but rather at higher altitudes, perhaps near the outermost portion of the toroid. In this circumstance, because Figures 7 and 8 indicate that the areas of the hotter zones for various bursts are on average a factor 20 or so smaller than those for the cooler BB spectral components, the hotter blackbody regions would generally be obscured by the larger opaque toroid for most rotational phases. This is contrary to the phase-dependent spectral landscape depicted in Figure 4. Yet, it is still possible to construct pathological morphology using disparate hotspot locales – for instance, placing the hotter BB zones on opposite faces (“upper” and “lower”) of the toroid and well removed from the magnetic equator. These would have to be activated in a geometrically non-random manner at preferred magnetic longitudes in order to maintain the presence of hotter BB components for the majority of rotational phases, which would considerably constrain physical mechanisms for burst activation.

This sketch of a geometrical interpretation suggests that locales for the hotter burst zones that are well removed from the surface are somewhat disfavored. Such locales are the preserve of the magnetic reconnection scenario for magnetar burst activation (Lyutikov, 2003) that serves as an analog of the picture for solar coronal mass ejections. They could still be accommodated, however, if the reconnection regions putatively triggering bursts do not sample magnetic longitudes in a uniform manner. In contrast, a hot near-surface belt for the active toroids is easier to render consistent with the data in Figures 4, 7 and 8. This is the expected locale for ignition of bursts by magnetar crustal fractures (Thompson & Duncan, 1995, 1996), likely involving hydromagnetic reconfigurations, and adjacent magnetospheric radiative dissipation. To discern between these two pictures requires more precise modeling of the emission geometry and its phase-dependent spectral signatures. The high quality of this burst storm dataset provides the basis for such a study, eliciting the prospect of discrimination between these burst activation scenarios.

Finally, compared with the COMPT-fit parameters presented in Lin et al. (2020), the spectra of the broad peaks (at the end of Segment 1 and the triple peaks in Segment 2) have harder $E_{\rm peak}$ and index values (Figure 2) than the time-integrated spectra of the bursts within the same active episode, observed before and after the burst forest. However, when the time-resolved spectra of the peaks are represented with thermal components (i.e., single BB or BB+BB), the luminosity during these peaks does not exceed the upper end of the typical magnetar burst luminosity range ($\lesssim 2.6\times 10^{41}$ erg s^-1; see Figure 8). A further study to compare the burst forest and the time-resolved spectral properties of bursts within the same activation period is planned.