Fermi-GBM GRBs with Characteristics Similar to GRB 170817A

Fermi-GBM is one of two instruments on the Fermi Gamma-ray Space Telescope, launched in 2008. GBM is made up of two types of scintillation detectors: 12 NaI(Tl) detectors, sensitive from 8 keV to ∼1 MeV, and two BGO detectors, sensitive from 200 keV to 40 MeV. The NaI(Tl) detectors are arranged in four groups of three on the corners of the spacecraft so that they view the whole unocculted sky. The BGO detectors are located on opposite sides of the spacecraft to enable an all-sky view. GBM produces triggered and continuous data types. A trigger is defined as a significant increase above background, detected on-board by the GBM flight software in one of several preset energy ranges and timescales (for a summary of the current settings of the GBM trigger criteria see Bhat et al. 2016). Triggered data types, available since launch, include accelerated CTIME data (binned to 64 ms, 8 energy channels) and accelerated CSPEC data (binned to 1.024 s, 128 energy channels) for 10 minutes and Time Tagged Event data (individual events at 2 μs resolution, 128 energy channels) for 5 minutes after a trigger. The continuous data types used in this analysis are CTIME (256 ms, 8 energy channels, available since launch) and Continuous Time Tagged Event (CTTE) data (2 μs, 128 energy channels, available since a flight software update in 2012 November). For a complete description of the GBM instrument and data types, see Meegan et al. (2009).

Here we describe the first search we performed, which only uses parameters from the GBM GRB catalog. The 10 yr catalog (A. von Kienlin et al. 2019, in preparation) comprises 2357 GRBs, 1959 long GRBs (lGRBs, ∼83%), 395 sGRBs (∼17%), and 3 GRBs with no measured duration. In order to identify those GRBs with similar temporal characteristics as GRB 170817A, we first put a constraint on the burst duration (${T}_{90}$, calculated in the 50–300 keV energy range, Kouveliotou et al. 1993) requiring that 0.5 s < ${T}_{90}$ < 3.5 s. These limits were created by adding a time window of ±1.5 s around the known duration of GRB 170817A (${T}_{90}$ = 2.0 ± 0.5 s). This condition is fulfilled for 312 GRBs, i.e., ∼13% of GRBs of the 10 yr catalog. This is a slightly lower fraction than the one obtained using the traditional division at 2 s between the short and long GRB populations. Moreover, we imposed additional temporal restrictions by employing the ${T}_{50}$ duration measure as a selection tool for the brightest part of the observed GRB emission in the 50–300 keV energy range, which is mostly showing up as a main pulse. Imposing a constraint of (${T}_{50,\mathrm{start}}$−${T}_{90,\mathrm{start}}$)/${T}_{90}$ < 0.2 on the relative start times of ${T}_{50}$ and ${T}_{90}$ primarily selects GRBs with the main pulse being located at the beginning of the GRB emission, like for GRB 170817A with a relative start time difference of 0.06. Together with a second constraint on the duration ratio of 0.1 < ${T}_{50}$/${T}_{90}$ < 0.7 we targeted to find GRBs where the ratio of the main pulse duration compared to the overall length is comparable to the case of GRB 170817A with ${T}_{50}$/${T}_{90}$ = 0.63 or even smaller, providing search results with a more extended tail. In addition, we limited the 64 ms peak flux to be smaller than 10 ph cm⁻² s⁻¹, thus allowing the identification of GRBs with peak fluxes up to values about twice as high as GRB 170817A (3.7 ± 0.9 ph cm⁻² s⁻¹). This search resulted in the identification of 107 good candidates.

This first result highlights a relevant limitation of the search method applied. One could further restrict the parameter range to better agree with the measured values of GRB 170817A, but this would concurrently limit any variation in the observed GRB characteristics. Furthermore, the aforementioned method has a fundamental drawback; by selecting quantities that are calculated in the 50–300 keV energy band, like ${T}_{90}$ and ${T}_{50}$, we might be missing those events where the soft component is contributing below the 50 keV threshold.

This led us to test an alternative search method, employing Bayesian Block analysis, which is described in Section 2.3.

We found that the most appropriate selection method is a two-step procedure, in which first GRBs with a duration of less than 5 s are prefiltered using Bayesian block analysis, followed by a dedicated manual selection. The Bayesian block analysis on its own produced a sample too large to be useful as a standalone method.

We relaxed the constraint on ${T}_{90}$ used in the previous Section 2.2 to ${T}_{90}$ < 5 s driven by the wish not to exclude potential candidates with a distinct soft tail and to include short duration events like GRB 150101B. Furthermore, we dropped any constraint on the peak flux or the fluence so as to not exclude brighter events. Applying this less restricting selection criterion, we obtain a sample of 558 GRBs detected during the time period of the 10 yr trigger catalog. Aiming for the automatic detection of the main and soft emission periods of candidate GRBs, we performed Bayesian Block analysis on this sample of short GRBs over three energy channels using the triggered detectors.

The Bayesian Block analysis technique delineates a light curve into piece-wise constant Poisson rate episodes (Scargle 1998). The algorithm (applied to an interval) decides between a constant rate model and a model with two constant rates, using a change point to describe an interval. It is an iterative process that when applied, continues until a stopping condition is met. The P parameter (prior) for the stopping condition indicates the chance probability of needing an additional change point. The analysis of Scargle et al. (2013) suggests that P ∼ 10⁻² is generally a good value to use.

As the main pulse of GRB 170817A was dominant over the 50–300 keV energy range¹³ and the soft episode was strongest below 50 keV, we consider three energy ranges for our analysis: 8–50, 50–300, and 300–1000 keV. We run the Bayesian Block algorithm over the light curves within these energy ranges (see Figure 1 for an example), designating the main pulse as the brightest nonbackground Bayesian Block interval in the 50–300 keV light curve. As we are looking at triggered GRBs, at least one Bayesian Block will necessarily exist in this energy range. If there are nonbackground blocks before the peak, those would be assigned to the main pulse as well. If the Bayesian Block model in the 8–50 keV light curve identifies emission that lasts longer than the main emission episode in the 50–300 keV range, then we attribute this as possible soft emission. In some cases, the Bayesian Block algorithm failed, because it did not detect the GRB over the 8–50 keV channel.

Zoom In Zoom Out Reset image size

The calculation of the hardness ratio (ratio of photon counts in 50–300 and 8–50 keV ranges) for the main and tail emissions obtained by the Bayesian Block method is also invoked as an additional criterion in our analysis. In order to identify sGRBs with characteristics similar to GRB 170817A, we required the main peak hardness ratio to be greater than 1 (HR_main > 1) and the soft tail hardness ratio to be smaller than 1 (HR_soft < 1). In this way, we identify 327 candidates out of our initial sample of 558 GRBs. However, this sample is contaminated by bursts showing a clear hard-to-soft evolution and by several bursts displaying a relatively high flux in the 50–300 keV range, comparable to the observed flux in the 8–50 keV range. Thus it was necessary to further inspect it, using an additional manual selection process that obeyed the following criteria:

• 1.  
  A significantly luminous initial peak, which is brighter over 50–300 keV than the 8–50 keV energy range.
• 2.  
  A weak tail, which is bright over the 8–50 keV energy range and disappears at higher energies.
• 3.  
  A discernible change of the light curve, giving some indication of two emission mechanisms. This criteria was used to avoid continuous hard-to-soft spectral evolution, which is extremely common in GRB pulses.

The manual check resulted in 17 candidates (including GRB 170817A and GRB 150101B, which were easily identified by this method). Visually inspecting the sample of GRBs, not selected by the constraint on the HR of the main and tail emission, we found no likely additional candidates, confirming the Bayesian Blocks method as a good prefilter. These 17 candidates still do not represent the final sample, due to two important, additional selection criteria that need to be fulfilled:

• 1.  
  The localization of the main and soft emission episodes must coincide.
• 2.  
  The spectral characteristics of the soft tail must be similar to that of GRB 170817A.

The fulfillment of these criteria is checked and presented in the next two sections.

The Bayesian Block method identifies temporally coincident excesses; however, we cannot determine a connection through temporal coincidence alone. The GBM background is dominated by real signals from galactic transients, solar flares, magnetospheric particle precipitation events, etc. Therefore, we must also verify that both components arise from the same location. GBM can perform degree-level accuracy localizations of signals using a standard technique originally developed for BATSE and adapted for use to localize all GBM triggers. Provided a manual selection identifying the signal and a background model, the localization algorithm compares the relative count rates observed in the detectors and estimates the most likely arrival direction by performing a chi-squared minimization over an 1° grid on the sky and three spectral templates. The spectral templates are Band functions (Band et al. 1993), representing spectrally hard, normal, and soft GRBs as observed by GBM. The main peak of each GRB was localized utilizing all three templates, while the soft tail was localized using only the softer spectrum. The localization also include an additional systematic component determined as a core-plus-tail model, with 90% of GBM GRBs having a 37 systematic error and a tail of greater than 10° (Connaughton et al. 2015).

Using by-eye selections of source windows, independent of those found through the Bayesian Block analysis, we separately localized the main peak and the subsequent softer emission for all GRB candidates in our sample. For 15 out of the 17 candidates, we derived consistent localizations. Two candidates were withdrawn at this step of the analysis as the soft tail could not be localized.

The spectral analysis of the 15 remaining candidate bursts was performed using RMfit.¹⁴ The assumed photon model (i.e., comptonized (Comp), power-law (PL), BB, etc.) is folded through the detector response to produce a model counts spectrum, which is then compared to the observed counts spectrum. A nonlinear least squares minimization method is then performed in counts spectrum space to produce a spectral fit. Since the detection efficiency of the NaI(Tl) detectors decrease for large incidence angles, we chose detectors with source angles ≤60 (Bissaldi et al. 2009), as is standard GBM procedure. More on this and other important steps in the spectral analysis of the bursts presented in this paper can be found in Gruber et al. (2014).

The results of the spectral analysis are summarized for 15 GRBs in Table 1. These include the results for GRB 170817A and GRB 150101B. For each of the GRBs listed in the table, the individual rows show the results of the spectral analysis over the time intervals of the main and tail emission. The exception is GRB 170111B, where we show spectral analysis of the soft pretrigger emission in addition to the other results. For the main emission episode, only the values for E_peak and the index are shown (first row for each GRB), derived from fits with the Comp model, which was in all cases statistically preferred compared to fits with the PL or BB model. This allows us to determine if the main peak is spectrally harder when compared to the tail emission. The spectral analysis results for the tail emission, shown for each GRB in the second and third rows, compare the Comp or PL fit results with the one derived from a fit with a BB model. We used the difference of the Castor C-Statistic (C-Stat, see Goldstein et al. 2017 for a comparison of C-Stat values for different models based on simulations) per degree of freedom (DOF) in order to assess which model fits the data best, or equally well (model name highlighted in bold face). In cases where the fit parameters of the Comp model were not constrained, results using the simpler PL model are presented. The last four columns list the energy flux (EF), fluence (${\mathscr{F}}$) and fluence ratio ${{\mathscr{F}}}_{T}$/${{\mathscr{F}}}_{P}$ for the selected tail model and peak (main) model mission respectively. In the case of GRB 170111B, the fluence ratio is calculated individually for the pretrigger and tail emission, in addition to the sum of both soft emission periods, listed in the middle row.

Table 1.  Spectral Analysis Results for 15 Candidate GRBs

GRB Name	Time Int	Model	Epeak	Index	kT	C-Stat/DOF	Phot. Flux	Energy Flux (EF)	Fluence (${\mathscr{F}}$)	${{\mathscr{F}}}_{T}$/${{\mathscr{F}}}_{P}$
	(s)		(keV)		(keV)		(ph cm−2 s−1)	×10−7	×10−7
								(erg cm−2 s−1)	(erg cm−2)
	−0.128:0.256	Comp	1473 ± 275	−0.75 ± 0.08	⋯	366.8/359	10.8 ± 0.6	40.14 ± 0.20	15.4 ± 0.8
GRB 081209A	0.384:0.768	PL	⋯	−2.13 ± 0.35	⋯	368.8/360	⋯	⋯	⋯
	0.384:0.768	BB	⋯	⋯	5.9 ± 1.4	369.8/360	1.8 ± 0.5	0.60 ± 0.17	0.23 ± 0.07	0.015
	0.000:0.128	Comp	811 ± 31	−0.19 ± 0.04	⋯	533.7/486	100.3 ± 1.6	468.0 ± 8.3	59.9 ± 1.1
GRB 090228A*	0.256:0.512	Comp	92 ± 13	−0.91 ± 0.22	⋯	512.7/486	9.7 ± 0.6	7.48 ± 0.67	1.91 ± 0.10	0.032
	0.256:0.512	BB	⋯	⋯	17.0 ± 0.8	571.7/487	⋯	⋯	⋯
	−0.064:0.384	Comp	927 ± 177	−0.54 ± 0.10	⋯	697.7/606	8.6 ± 0.3	33.61 ± 1.70	15.1 ± 0.76
GRB 100328A	1.024:1.344	Comp	34 ± 7	−0.12 ± 1.30	⋯	652.9/606	⋯	⋯	⋯
	1.024:1.344	BB	⋯	⋯	8.2 ± 1.2	653.4/607	2.7 ± 0.4	1.14 ± 0.20	0.36 ± 0.06	0.024
	−0.384:0.256	Comp	248 ± 71	0.36 ± 0.79	⋯	390.5/360	1.8 ± 0.3	4.21 ± 1.10	2.69 ± 0.70
GRB 100719C*	0.256:0.640	PL	⋯	−1.57 ± 0.19	⋯	369.9/361	2.07 ± 0.52	2.95 ± 0.90	1.13 ± 0.35	0.42
	0.256:0.640	BB	⋯	⋯	25.3 ± 6.2	375.1/361	⋯	⋯	⋯
	−0.256:0.256	Comp	341 ± 320	−1.04 ± 0.39	⋯	487.0/486	2.5 ± 0.4	4.04 ± 0.15	2.07 ± 0.77
GRB 101224A	1.280:2.048	PL	⋯	−2.09 ± 0.39	⋯	565.3/487	⋯	⋯	⋯
	1.280:2.048	BB	⋯	⋯	8.2 ± 2.2	567.2/487	0.85 ± 0.26	0.36 ± 0.12	0.28 ± 0.09	0.14
	0.000:0.128	Comp	328 ± 67	−0.34 ± 0.26	⋯	326.2/363	10.7 ± 1.0	25.57 ± 3.50	3.27 ± 0.45
GRB 110717A	0.384:0.768	PL	⋯	−2.45 ± 0.66	⋯	418.4/364	⋯	⋯	⋯
	0.384:0.768	BB	⋯	⋯	7.1 ± 2.2	417.9/364	1.3 ± 0.4	0.49 ± 0.18	0.19 ± 0.07	0.06
	−0.128:0.256	Comp	144 ± 18	0.53 ± 0.60	⋯	395.7/365	2.8 ± 0.4	4.11 ± 0.53	1.58 ± 0.20
GRB 111024C	0.768:1.409	PL	⋯	−2.02 ± 0.49	⋯	408.7/366	⋯	⋯	⋯
	0.768:1.409	BB	⋯	⋯	8.7 ± 2.6	406.6/366	0.9 ± 0.3	0.39 ± 0.15	0.25 ± 0.10	0.16
	−0.128: 0.384	Comp	133 ± 20	0.66 ± 0.68	⋯	542.9/489	2.7 ± 0.4	3.72 ± 0.53	1.90 ± 0.27
GRB 120302B	0.640:1.792	PL	⋯	−2.38 ± 0.43	⋯	556.7/490	⋯	⋯	⋯
	0.640:1.792	BB	⋯	⋯	6.9 ± 1.4	552.2/490	1.1 ± 0.3	0.40 ± 0.09	0.46 ± 0.10	0.24
	−0.128:0.384	Comp	526 ± 114	−0.21 ± 0.25	⋯	523.9/464	3.8 ± 0.3	13.66 ± 1.40	6.99 ± 0.72
GRB 120915A	0.640:1.280	PL	⋯	−1.89 ± 0.45	⋯	475.6/465	⋯	⋯	⋯
	0.640:1.280	BB	⋯	⋯	10.2 ± 2.7	471.6/465	0.8 ± 0.2	0.38 ± 0.13	0.24 ± 0.08	0.034
	−0.512:1.024	Comp	91 ± 20	−0.80 ± 0.35	⋯	448.5/363	2.7 ± 0.3	2.12 ± 0.30	3.26 ± 0.46
GRB 130502A	2.048:3.072	Comp	54 ± 21	−1.26 ± 0.59	⋯	393.9/363	⋯	⋯	⋯
	2.048:3.072	BB	⋯	⋯	10.1 ± 1.2	403.5/364	1.8 ± 0.3	0.88 ± 0.14	0.90 ± 0.14	0.28
	−0.064:0.128	Comp	280 ± 58	−0.78 ± 0.16	⋯	815.0/727	8.7 ± 0.6	14.85 ± 1.70	2.85 ± 0.33
GRB 140511A	0.128:0.384	Comp	29 ± 42	−1.79 ± 0.63	⋯	727.7/727	⋯	⋯	⋯
	0.128:0.384	BB	⋯	⋯	6.7 ± 1.0	728.7/728	2.6 ± 0.4	0.94 ± 0.15	0.24 ± 0.04	0.084
	−0.016:0.000	Comp	524 ± 176	−0.80 ± 0.20	⋯	638.2/885	28.4 ± 2.6	70.58 ± 8.40	1.13 ± 0.13
GRB 150101B	0.000:0.064	PL	⋯	−2.42 ± 0.21	⋯	723.1/886	⋯	⋯	⋯
	0.000:0.064	BB	⋯	⋯	6.0 ± 0.6	713.3/886	9.2 ± 1.1	3.07 ± 0.37	0.20 ± 0.02	0.18
	−0.768:−0.192	Comp	49 ± 7	−0.08 ± 0.70		708.5/633	⋯	⋯	⋯
	−0.768:−0.192	BB	⋯	⋯	10.8 ± 1.0	709.8/634	2.5 ± 0.3	1.31 ± 0.15	0.75 ± 0.09	0.20
GRB 170111B	−0.128:0.384	Comp	154 ± 22	−0.62 ± 0.19	⋯	697.0/633	6.3 ± 0.4	7.42 ± 0.70	3.80 ± 0.36	0.25
	0.768:0.960	Comp	35 ± 13	−1.12 ± 1.03	⋯	608.5/607	⋯	⋯	⋯
	0.768:0.960	BB	⋯	⋯	8.1 ± 1.0	611.8/608	2.6 ± 0.5	1.08 ± 0.22	0.21 ± 0.04	0.06
	−0.512:0.512	Comp	197 ± 89	−0.84 ± 0.39	⋯	527.3/506	1.6 ± 0.2	2.11 ± 0.56	2.16 ± 0.57
GRB 170817A	0.512:2.048	PL	⋯	−1.99 ± 0.26	⋯	639.0/507	⋯	⋯	⋯
	0.512:2.048	BB	⋯	⋯	11.2 ± 1.5	622.4/507	0.9 ± 0.2	0.49 ± 0.09	0.75 ± 0.14	0.35
	−0.032:0.032	Comp	639 ± 220	−0.61 ± 0.22	⋯	697.9/717	10.8 ± 1.0	34.29 ± 3.80	2.19 ± 0.24
GRB 180511A	0.032:0.128	PL	⋯	−1.97 ± 0.45	⋯	671.6/718	⋯	⋯	⋯
	0.032:0.128	BB	⋯	⋯	11.1 ± 3.0	667.4/718	1.9 ± 0.6	1.00 ± 0.33	0.10 ± 0.03	0.046

Note. GRBs marked with stars were rejected (for details see Section 2.5).

Download table as:  ASCIITypeset images: 1 2

We considered GRBs as possible candidates, in which the tail emission was fitted equally well or better by a BB compared to the PL or Comp models, giving an indication of the tail emission having thermal characteristics. Since only one GRB/GW event has been identified up to now and no commonly agreed theoretical guidance is available, we set a tentative limit to the BB temperature kT for a candidate GRB being similar to GRB 170817A. In this study, we set this BB temperature limit at about twice the value of GRB 170817A, i.e., kT ≲ 20 keV. Using this approach, we exclude candidate GRB 100719C (see row 4 of Table 1). Moreover, we also excluded GRB 090228A (see row 2 of Table 1), because it is showing a lower value of C-Stat for the Comp model than for the BB model. This hints to the possibility that the tail emission is not similar to the BB tail of GRB 170817A. We have not removed more GRBs from the candidate list, so as not to restrict the full range of candidates, some of them being clear candidates and others being more doubtful, e.g., we kept GRB 130502A in the list, although it has a slightly larger value of C-Stat for the BB model compared to the Comp model. Additionally, we will also not provide a ranking of our candidates at this stage until the detection of new GRB/GW events have consolidated the behavior of these phenomenon. This final step leaves us with 13 candidates, including GRB 170817A and GRB 150101B. The light curves for this final list of candidates are shown in Figures 8 and 9. The final limits of the main pulse and soft tail were determined by considering the temporal bins with sufficient flux above the background for spectral analysis. These are not necessarily the same as the Bayesian Block intervals.

In order to put the candidate list into context with the whole GBM GRB database, we list the standard burst catalog parameters, like the corresponding trigger ID, the trigger time in UTC, ${T}_{90}$, ${T}_{50}$, the localization, the total fluence during the ${T}_{90}$ time interval and the 64 ms peak flux in Table 2. The second last column in this table shows which of the GRBs were detected or observed by other instruments and the corresponding references are listed in the last column.

The six candidate GRBs detected after 2012 and GRB 140129A (trigger ID: bn140129499), a withdrawn candidate from the localization analysis (Section 2.4) were further investigated by applying the GBM Targeted Search (Blackburn et al. 2015) to verify the results from the Bayesian Block and spectral analysis as well as provide additional characterization of the spectral components. The Targeted Search was developed to find gamma-ray transients in the GBM data that lie below the on-board triggering threshold. It is used to follow up GW triggers from LIGO/Virgo (Burns et al. 2018) and has been demonstrated to recover Swift short GRBs within the GBM field of view (Kocevski et al. 2018). Due to improvements detailed in Goldstein et al. (2016), particularly that of the background estimation method, the Targeted Search can yield improved localizations over those found by techniques relying on manual selections of source and background. This search was utilized to confirm whether both spectral components (main peak and soft tail), were consistent with the same location. Furthermore, we attempted to localize the candidate soft tail of GRB 140129A with the Targeted Search due to its sensitivity to weak events, a task that we could not accomplish manually. The Targeted Search is based on the analysis of CTTE data, which are available only after 2012 November. Consequently, this method could not be applied to the earlier seven candidate events in our sample.

The Targeted Search does not look for detector-coherent signals in counts space alone. The search also considers the deconvolved spectrum of the observed photons once folded through the GBM detector responses. It assumes a set of four spectral templates each of which are folded through the 14 GBM detector responses, allowing for a search in deconvolved flux. The templates describing spectrally soft and medium GRBs are those mentioned in Section 2.4; however, the hard template is modeled as a PL with an exponential high-energy cutoff and parameters better suited for short GRBs (Goldstein et al. 2016). Motivated by the detection of the soft, thermal tail of GRB 170817A, a fourth BB template with a temperature of 10 keV was added (GBM Collaboration 2019, in preparation). The BB template has not previously been used for signal detection, and thus we do not attempt to quantify the significance of the BB components with the Targeted Search. We apply it here for confirmation of spectral analysis and as follow-up characterization.

For each of these GRBs, the Targeted Search processed a 15 s window centered on the GBM trigger time, searching timescales ranging from 16 ms to 8.192 s by powers of 2. In each case, the main peak was found to be the event with the highest signal-to-noise ratio (S/N) within the search window. We identified the thermal component as the most significant BB bin found within the time range used in the spectral analysis. A summary of the search results, including start times, durations, and localizations for both peaks and tails, is shown in Table 3. The soft tails are weaker compared to the main peaks. However, the BB components of GRB 130502A and GRB 170111B were found to have signal-to-noise ratios of 8.54 and 7.77, respectively (see Table 3), both of which are comparable to the main peaks of the subthreshold short GRBs (Kocevski et al. 2018).

The Targeted Search localizations of the main peak and soft tail for two candidate GRBs are shown in Figure 2. We quantify the spatial overlap between the two localizations as

$$\begin{eqnarray}&&{ \mathcal S }=\displaystyle \frac{{\sum }_{i=1}^{N}{P}_{1i}{P}_{2i}}{{\sum }_{i=1}^{N}{P}_{1i}{P}_{2i}+{\sum }_{i=1}^{N}{P}_{1i}u+{\sum }_{i=1}^{N}{{uP}}_{2i}},\end{eqnarray} \tag{ 1 }$$

where P₁ (P₂) is the localization probability map for the main peak (soft tail), i is the HEALPix (Gorski et al. 2005) pixel index (corresponding to a sky location vector), and u is the uniform probability for each pixel on the sky. Pixels of sky positions occulted by the Earth were excluded. Excluding GRB 140129A, the localizations for all soft tails identified with the Targeted Search were consistent with those of the main peaks, and this is reflected in the spatial probabilities listed in Table 3. For GRB 140129A, the inconsistency in the localization of both the main peak and soft tail, as well as their poor spatial agreement, confirmed initial indications that GRB 140129A is not a likely candidate. Additionally, the emission preceding the main peak of 170111B was located to a centroid of (R.A., decl.) = (249.9, 54.7), verifying its spatial association with the burst.

Zoom In Zoom Out Reset image size

Furthermore, the Targeted Search also produces spectrally separated waterfall plots that can act as proxies for detector light curves, with the addition of preliminary spectral information. For each timescale searched, the plot shows every data bin colored by the best-fit spectral template, where the color intensity is related to the S/N of that bin. We show these plots for GRBs with higher S/Ns, namely, GRB 130502A and GRB 17011B, in Figure 3. In both GRBs, the thermal tails are clearly identified. While the thermal tail of GRB 130502A appears as a distinct component separate from the main emission, the thermal tail of GRB 170111B occurs closer in time to the main peak. GRB 170111B also shows the soft peak preceding the main emission.

Zoom In Zoom Out Reset image size

The local galaxy density has a significant overdensity that appears as a plane on a two-dimensional map, the supergalactic plane. This structure is actually more complex, consisting of filaments, sheets, and knots, and is strongest at ∼40 Mpc and extends to ∼80 Mpc (Lahav et al. 2000). Since GRB 170817A is at 40 Mpc, it is possible that GRBs selected to be similar are mostly located close enough to show deviations from isotropy. However, GRB 150101B having a redshift of 0.134 (Levan et al. 2015) is significantly more distant. Figure 4 shows the locations of the final sample of 13 GRBs (Table 2) in supergalactic coordinates—the locations appear isotropic and there is no excess at the supergalactic plane. Quantitative tests of large-scale isotropy were made, checking the quadrupole moment about the supergalactic plane, $\langle {\sin }^{2}\mathrm{SGB}-\tfrac{1}{3}\rangle$, and two coordinate-system independent statistics, the Rayleigh–Watson dipole statistic ${ \mathcal W }$, and the Bingham quadrupole statistic ${ \mathcal B }$ (Briggs 1993; Briggs et al. 1996). All of these had values consistent with isotropy. Because the sample is very small, only a very strong anisotropy could have been detected.

Zoom In Zoom Out Reset image size

Figure 5 shows the hardness–duration plot from the 10 yr GBM GRB catalog. The spectral hardness was obtained using the standard duration analysis performed in the catalog (Bhat et al. 2016). In this case, the hardness is defined as the ratio of the deconvolved counts in two energy bands (10–50 keV and 50–300 keV) obtained during the ${T}_{90}$ time interval. We use 10 keV as the lower limit instead of 8 keV used in Section 2.3 to facilitate comparison with previous catalogs. The locations of the final sample are shown on this diagram as red marks. GRB 170817A and GRB 150101B are highlighted by the purple stars and GRBs (with ${T}_{90}$ < 5 s) with a redshift by black stars, respectively. It emerges that the 13 GRBs in our sample are distributed in two small groups; one which is located at the soft tail below a hardness ratio value of one for a duration range between 1 and 4 s (7 GRBs including GRB 170817A). The second group consists of six GRBs (including GRB 150101B), each with a duration of less than 0.6 s. The latter are distributed over a hardness range between 0.7 and 6 and exhibit larger errors due to the fact that the automatic hardness calculation barely registers the pulse of the GRB because it is relatively short. For better assessment, we inspect the peak energy of this group—used as a proxy for the hardness ratio. We find that the main pulse of the short group of candidates (see Table 1) has systematically higher peak energies compared to the longer population. For the same reason we assign GRB 150101B, which shows a hardness below one, to the second group owed to its high peak energy. Hence, we rather consider the two groups by a slanted cut than by a single limit in hardness or T90. Looking more carefully at individual GRBs within the short group we find that the four sGRBs at the top of the diagram (hardness >2) are the cases where the catalog ${T}_{90}$ does not include the soft tail emission. This can be checked by comparing the ${T}_{90}$ time range, marked by two vertical dashed lines in Figures 8 and 9 with the time interval used for spectral analysis highlighted as red bins. For GRB 081209A, GRB 100328A, GRB 110717A, and GRB 120915A, we find no overlapping time interval leading to an increased hardness compared to the other GRBs where at least some of the ${T}_{90}$ range is overlapping the soft tail emission.

Zoom In Zoom Out Reset image size

We have explored correlations between parameters of the main pulse and soft tail. These included photon and EFs, fluence and characteristic energy (kT and E_peak). We find a significant, Spearman rank correlation coefficient of C = 0.67 in the photon fluxes. The p-value, or the probability that C > 0.67 correlation occurs by chance is 0.012. A PL fit to the photon flux gives ${P}_{\mathrm{Main}}\propto {P}_{\mathrm{Tail}}^{0.70\pm 0.16}$ (see Figure 6, left).

Zoom In Zoom Out Reset image size

We find no significant correlation between the fluence and characteristic energies either for the whole sample or within the two subgroups. We plot the soft tail's temperature as a function of the main peak in the right panel of Figure 6.

The correlation in the photon flux points to the fact that the luminosities of the main episode and the soft tail may be linked rather than the total energetics.

To further characterize the relation of the main pulse to the tail, we inspect the light curve using pulse-fitting techniques. We find cases where the two episodes are clearly separated, and some that overlap (see Figures 7–9).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

GRB pulse shapes can be well described by analytical functions (Norris et al. 1996, 2005). We fit a function composed of two pulses to the light curve in the 8–300 keV energy range, in order to study the properties of the main pulse and the soft emission. In Norris et al. (1996) a single pulse shape is given by $I{(t)=A\exp (-(({t}_{\mathrm{peak}}-t)/{\sigma }_{\mathrm{rise}})}^{2})$ for t < t_peak and $I{(t)=A\exp (-((t-{t}_{\mathrm{peak}})/{\sigma }_{\mathrm{decay}})}^{2})$ for t > t_peak, where A is the amplitude at the peak time of the pulse, t_peak, σ_rise and σ_decay are the characteristic rise and decay times of the pulse respectively.

The minimum variability timescale, dt_min, describes the shortest coherent variation in the light curve, and can be used to infer the radius of the emission region. For the candidates, we determine dt_min based on the method of Golkhou et al. (2015). As the main pulse carries most of the flux, the variability timescale informs us whether there are any significant structures shorter than the typical timescale of the pulse (e.g., the rise time). Based on the temporal parameters of the main pulse, we find that short-hard candidates with the exception of GRB 150101B have significant variation within the main pulse, i.e., they are composed of multiple overlapping pulses. We indicate the properties in this subsection in Table 4.

Table 4.  Temporal Parameters of the Candidates All in Units of ms

GRB name	${\sigma }_{{t}_{\mathrm{rise},\mathrm{main}}}$	dtmin	tpeak,soft–tpeak,main	Main/Tail Relation
GRB 081209A (v)	25 ± 3	<14.9	133 ± 14	joined
GRB 100328A (v)	77 ± 21	<10.6	1153 ± 65	separated
GRB 101224A	23 ± 23	47.4 ± 7.6	1360 ± 625	separated
GRB 110717A (v)	36 ± 11	11.4 ± 3.0	712 ± 2097	separated
GRB 111024C	33 ± 17	40.7 ± 8.8	106 ± 20	separated
GRB 120302B	16 ± 19	<119.6	1545 ± 134	separated
GRB 120915A (v)	312 ± 75	40.6 ± 13.2	632 ± 717	separated
GRB 130502A	169 ± 63	220.7 ± 34.0	2092 ± 765	separated
GRB 140511A	23 ± 7	<94.4	385 ± 424	joined
GRB 150101B	6 ± 1	7.9 ± 0.7	52 ± 11	joined
GRB 170111B	110 ± 36	<63.4	865 ± 71	separated
			−502 ± 104a	separated
GRB 170817A	263 ± 103	124.6 ± 6.4	1201 ± 774	joined
GRB 180511A (v)	15 ± 4	<5.3	94 ± 65	joined

Notes. The (v) mark indicates candidates, where the variability timescale is less than the rise time with more than 2σ significance, indicating pulse substructure.

^aResult for the pretrigger soft emission of GRB 170111B.

Download table as:  ASCIITypeset image

All of these bursts can be described within the search criteria of the sample. They are all GRBs with a duration of less then five seconds, most of which can be described as a spectrally hard burst followed by thermal X-ray emission. The exception is GRB 170111B, which is the only burst to exhibit soft, thermal emission about 0.5 s before the main burst. The soft emission episodes for the final list of GRBs are seen prominently in Figures 8 and 9 and have BB temperatures of around 5–10 keV. The E_peak values for the main burst episode varies from around 100 to 1000 keV.

Only two bursts in our sample have recorded redshifts; GRB 150101B and GRB 170817A. To-date, these two bursts are among the closest known short-GRBs with redshifts to have been detected by Fermi-GBM. These redshifts are 0.134 and 0.010 for 150101B and 170817A, respectively. The temporal arrangement between the main episode of the short GRB and the thermal emission is mostly what defines the morphology and duration of each burst. For a handful of bursts in the final sample, the soft component is found to be a temporally separate event from the main episode at high significance (GRB 100328A, GRB 101224A, GRB 120302B, and GRB 170111B). For the rest of the bursts there is no clear separation between the main pulse and the soft tail. We have to emphasize that we did not see any stark difference in our measured parameters between bursts with resolved soft components, and those that have no clear temporal separation.