THE THIRD SWIFT BURST ALERT TELESCOPE GAMMA-RAY BURST CATALOG

Each year, the Swift team schedules special observations of the Crab Nebula to perform an on-orbit calibration of the BAT for both energy and position measurements. During the calibration observations, the BAT observes the Crab Nebula at different incident angles to check that the measurements show consistent results.

In 2015, five observations with different incident angles were performed: (1) on-axis, (2) off-axis with θ = 30°, ϕ = −90°. (3) off-axis with θ = 30°, ϕ = 90°, (4) off-axis with θ = 45°, ϕ = 0°, and (5) off-axis with θ = 45°, ϕ = −180°. θ is the polar angle measured from the BAT pointing direction, and ϕ is the azimuth angle.

Figures 1 and 2 show the results of the spectral fits with different incident angles from year 2005 to 2015. The Crab spectrum is fitted with a simple power-law model (see definition in Equation (1)). The photon indices of the simple power-law model ${\alpha }_{\mathrm{PL}}$ are plotted in Figure 1, while the fluxes are presented in Figure 2. Results show that the photon index and the flux measured at different locations on the BAT detector plane can vary by up to ∼±5% and ∼±10%, respectively, from the canonical values of Crab photon index of −2.15 and flux of 2.11 × 10⁻⁸ erg cm⁻² s ⁻¹ (Jung 1989; Rothschild et al. 1998).

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Wilson-Hodge et al. (2011) suggests that the flux of the Crab Nebula can fluctuate on a timescale of months to years, with the value changes as much as ∼10% in the BAT energy range from 2008 to 2010. However, as seen in Figure 2, the systematic errors for the flux measurements at large incident angles can be as large as ∼10%. This is because of the unknown systematic uncertainties included in the BAT energy response function. Thus, it can be difficult to place tight constraints for flux variations less than ∼10%, if the spectral analysis is involved in the BAT data. Note that the BAT Crab light curve presented in Wilson-Hodge et al. (2011) is based on the survey data process which extracts the counts directly from the sky images. The BAT calibration data base is last updated in 2009 (Sakamoto et al. 2011b).

Figure 3 shows the differences between the true Crab position (R.A. = 83633, decl. = 22014) and the Crab positions calculated using observations from the five different incident angles taken in 2015. Results show that the Crab position measurements can change up to ∼2 arcmin (with respect to the assumed "true" location) when measuring with different incident locations. However, 90% of the measurements are within 0.93 arcmin from the "true" location.

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Based on the BAT log files, BAT spends ∼78% of the time performing observations and searching for GRBs. Figure 4 shows the fraction of the time when BAT was capable of triggering bursts from year 2005 to 2015. BAT is unable to trigger a burst mainly due to spacecraft slewing and when the spacecraft passes through the SAA. Figure 5 shows the fraction of time during spacecraft slews and SAA. There are ∼12% of spacecraft slew time. This fraction gradually increases with time as Swift observes more and more Target-of-Opportunity (ToO) targets. Record shows that the spacecraft spends ∼9% of the time in SAA. Note that this is the SAA time as defined for BAT operations, which is determined based on instant count rate and backlog in the ring buffer. XRT and UVOT adopt a more strict criteria for SAA using the location, and thus have a larger SAA time fraction in general. As shown in the figure, the fraction of the BAT SAA time decreases slightly from 2005 to 2015. This is because the solar activity increases during these years, which results in a slightly lower particle density in the SAA region. Since BAT uses the count rate to define the SAA time, the fraction of SAA time decreases as fewer cosmic-ray particles appear in the SAA region.

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All the BAT event data used in this analysis are downloaded from HEASARC.¹⁹ We use the standard BAT software (HEASOFT 6.15²⁰ ) and the latest calibration database (CALDB²¹ ) to perform analysis for event data. Specifically, we use the script bateconvert for energy calibration, and batgrbproduct²² to perform a series of standard analyses of the event data, which includes filtering out hot pixels of the detectors, occultation time periods, refined-position analysis, duration estimation, making light curves with different time segments and bin sizes, and generating spectra. We adopt the default options of batgrbproduct, except the minimum partial coding fraction (pcodethresh), which is set to 0.05 instead of 0.0.

The burst durations estimated by batgrbproduct include T₁₀₀, T₉₀, and T₅₀, which correspond to the durations that contain 100%, 90%, and 50% of the burst emission, respectively. Specifically, the start and end times of T₉₀ in this standard pipeline are defined as the times when the fraction of photons in the accumulated light curve reaches 5% and 95%.²³ Similarly, the start and end time of T₅₀ is defined as the times when the accumulated light curve reaches 25% and 75%. These definitions for T₉₀ and T₅₀ are commonly adopted for quantifying burst durations by other teams, including BATSE, BeppoSAX, and Fermi (Koshut et al. 1996; Paciesas et al. 1999; Frontera et al. 2009; von Kienlin et al. 2014). In this paper, we follow the convention and use the T₉₀ = 2 s as the separation between the long and short GRBs categories (Kouveliotou et al. 1993). Specifically, the bursts that are referred to as short GRBs in this paper have T₉₀ ≤ 2 s, without taking into account of the uncertainty in T₉₀.

The burst refined positions are generally also found by batgrbproduct by running batcelldetect on the image with the burst emission. This image will end before the spacecraft slews if T₁₀₀ lasts beyond the slew time. These refined positions are not used in any of the further analyses, such as calculating the mask-weighted light curve and spectrum. However, we do use the signal-to-noise ratio reported with these refined positions to determine whether the burst could be a questionable detection. For a few dozen bursts, the signal-to-noise ratio associated with the refined positions found by this auto pipeline is lower than 7 (the typical image-trigger threshold). However, most of these cases are due to a long quiescent period of the burst emission before the spacecraft slews. We thus rerun the search for detections for these bursts using images created with the time interval and energy range determined by the flight software. If the signal-to-noise ratio is still below 7 and there is not an accompanying an XRT afterglows, we will mark it as a "tentative detection" in Table 9. The readers are advised to treat these bursts with special caution.

For spectral analysis, we use the commonly adopted X-ray fitting package, XSPEC.²⁴ When the spectrum covers time periods including spacecraft slew time, we generate multiple response files in this period in order to create an "average" response file for the whole period. Swift slews at a rate of ∼1° per second (Markwardt et al. 2007) and hence the telescope motion can be safely ignored within 5 s (Sakamoto et al. 2011a). Therefore, we create a response file for each five seconds during slew time, and a response file for each time segment when the spacecraft is settled. We create an average response file for the whole time period using the HEASARC tool addrmf, with weighting factors equal to the fraction of photon counts in the specific time periods of each response file.

Following the BAT2 catalog, we fit the GRB spectra with two different models: simple power law (PL) and cutoff power law (CPL). The simple power-law model is described by the following equation,

$$\begin{eqnarray}&&f(E)={K}_{50}^{{\rm{PL}}}{\left(\displaystyle \frac{E}{50\mathrm{keV}}\right)}^{{\alpha }^{{\rm{PL}}}},\end{eqnarray} \tag{ 1 }$$

where f(E) is the photon flux at energy E, α^PL is the PL index, and K^PL₅₀ is the normalization factor at 50 keV, with units of photons cm⁻² s⁻¹ keV⁻¹. The cutoff power-law model is expressed as,

$$\begin{eqnarray}&&f(E)={K}_{50}^{{\rm{CPL}}}{\left(\displaystyle \frac{E}{50\mathrm{keV}}\right)}^{{\alpha }^{{\rm{CPL}}}}\exp \left(\displaystyle \frac{-E(2+{\alpha }^{{\rm{CPL}}})}{{E}_{{\rm{peak}}}}\right),\end{eqnarray} \tag{ 2 }$$

where α^CPL is the CPL index, ${K}_{50}^{\mathrm{CPL}}$ is the normalization factor at 50 keV, with units of photons cm⁻² s⁻¹ keV⁻¹, and E_peak is the peak energy in the $\nu {F}_{\nu }$ (i.e., ${E}^{2}f(E)$) spectrum, where ${F}_{\nu }={Ef}(E)$ is the energy flux density.

The BAT spectra produced using the mask-weighting techniques have Gaussian statistics (Markwardt et al. 2007). Therefore, we use the "fit" command in XSPEC with the default "statistic chi" option, which finds a fit with the maximum likelihood for Gaussian data (in other words, finds a fit with a minimum χ²; see detailed descriptions in the Appendix B of the XSPEC manual²⁵ ).

We use the "error" command in XSPEC to estimate the 90% confidence region for each parameter. This command changes the assigned parameter values until it finds a value that gives a fit with statistics differing by a number Δ from the best-fit statistics. When the data follow a Gaussian distribution, Δ follows a ${\chi }^{2}$ distribution. In our case, we use the default Δ = 2.706, which is equivalent to the 90% confidence region in the χ² distribution. Based on the XSPEC manual, the "error" command is one of the more reliable and recommended methods for constraining uncertainties, and it is not as computationally expensive as the Monte Carlo techniques (see detailed descriptions in the Appendix B of the XSPEC manual²⁵). However, in order to use the "error" command to estimate the uncertainties of the implicit parameters, such as the fluxes, one would need to re-write the function to make flux one of the parameters (instead of the normalization factor K), and re-do the fit. Therefore, for the flux error estimation, we use the "cflux" and "cpflux" command in XSPEC, which performs this conversion for energy flux and photon flux, respectively. Ideally, if XSPEC does find the global minimum, all these fits should find the same solution. However, if XSPEC only finds a local minimum, fitting using the different forms of the same function can converge to different solutions. Thus, we cross check the fits that use different forms of the same functions and only accept the fits if they find solutions that are consistent with each other (i.e., the fitted values have overlapping uncertainty ranges).

Note that in order to set up an automatic pipeline for all the bursts, we accept the solutions found by the "fit" command after about 100 iterations. We cannot rule out the possibility that this is a local minimum. Sometimes XSPEC finds better fits when going through the search with the "error" command. However, we always discard these new fits to make sure the uncertainties for all the parameters are estimate based on the same best fit, and to prevent XSPEC from going into an infinite loop if it keeps finding new fits when constraining parameter errors.

As mentioned in Sakamoto et al. (2011b), most of the GRB spectra in the BAT energy range can be well-fitted by the simple PL model, and show no significant improvement in their fit when changing to the CPL model. We adopt the same criteria as the one in Sakamoto et al. (2011b) and determine when CPL is a better fit when Δχ² ≡ χ²_PL − χ²_CPL > 6 (and when there is no problem in the CPL fit; see the criteria for acceptable fits below).

In the following list, we summarize the criteria we use to decide whether a fit is acceptable:

• 1.  
  All the parameters (normalization factor, photon index, photon and energy fluxes for different energy bands, and E_peak for the CPL fit) and their errors are constrained.
• 2.  
  The parameters (photon index and E_peak) found by fitting different forms of the same functions are consistent with each other (i.e., the 1-sigma uncertainty regions overlap). We compare the fits that are used to constrain the photon and energy fluxes in different energy bands with the original fit for constraining the normalization factor and photon index.
• 3.  
  The normalization factors and fluxes for different energy bands are not consistent with zero (i.e., the lower limit found is greater than zero).
• 4.  
  The lower limit is not larger than the upper limit (this should always be satisfied in principle, but we place this criteria regardless just in case).
• 5.  
  The "probability of the null hypothesis" from the resulting XSPEC fit (estimated based on the χ² distribution) needs to be larger than 0.1. That is, the null hypothesis needs to be consistent with the data within 90% of confidence range.
• 6.  
  If Δχ² ≡ χ²_PL − χ²_CPL > 6 and the fit satisfies all the criteria above, we adopt the CPL fit in the following discussions and mark these bursts as better-fitted by the CPL model in the summary tables (Appendix A).

Section 4.3.3 contains further discussions regarding the bursts with unacceptable spectra under these criteria. Note that spectral fits from both the simple PL and CPL are presented for all GRBs in the summary tables (Appendix A) regardless of whether or not they satisfy these criteria. The names of GRBs with their best-fit models are given in separate lists in Section A.

We perform spectral analyses for the following four types of spectra: (1) Time-averaged spectra, which are the spectra created using the T₁₀₀ duration,²⁶ (2) The 1 s peak spectra, which cover the 1 s peak time selected by battblocks, (3) The time-resolved spectra, which are a series of spectra for each burst created based on the sub-time-segments within T₁₀₀ that are selected by battblocks. Ideally, these sub-time-segments pick out the sub-structure in the light curve variations, but the selections are not always perfect. (4) The 20 ms peak spectra, which cover the 20 ms peak time selected by battblocks using the 4 ms binned light curve. This is not one of the standard products included by batgrbproduct, however, we create this additional peak time and spectral analyses for those extremely short GRBs in particular. Due to the extremely short time interval, we generate a spectrum with only 10 energy bins (equally spaced in the log-scale from 14.0 to 149.99 keV), following the pipeline in the BAT2 catalog.

There are 81 GRBs found in ground analysis, including 25 discovered during spacecraft slews. That is, these GRBs did not pass the on-board trigger criteria, but were identified by miscellaneous ground processing, such as searching in the BAT data for those GRBs triggered by other spacecraft, and/or searching for possible GRBs during spacecraft slews (since BAT cannot trigger during this time). Most of these bursts are found in either the "failed event data" or the "slew event data." The "failed event data" are ∼10 s long event data that are downlinked when a burst passes the first-stage detection threshold (i.e., the rate-trigger criteria), but failed to pass the second-stage trigger criteria (i.e., the image-trigger criteria; see Barthelmy et al. (2005) for more information of the two-stage trigger criteria for BAT). The "slew event data" are event data collected during spacecraft slews. GRB 150407A, GRB 140909A, GRB 110604A, GRB 070125, and GRB 060123 were only found manually in images created by the flight software, and no event data are available.

When at least some event data exist for a ground-detected burst, we re-analyze the burst using standard BAT data analysis scripts, bateconvert and batgrbproduct, as mentioned in Section 3.1. To perform the analysis, batgrbproduct requires some information from the prompt data collected through the Tracking and Data Relay Satellite System (TDRSS), which includes the burst observation ID, trigger number, trigger time, the R.A. and decl. of the burst found in the onboard analysis, background duration used for the trigger, and information of whether this is a rate or image trigger. For bursts triggered onboard, the TDRSS data are downlinked to the ground within seconds to minutes of the trigger time. However, only limited data are transfered due to the downlink bandwidth. The complete data are downlinked to ground stations ∼hours later. Since ground-detected GRBs are not triggered onboard, they do not have TDRSS data. We thus manually create fake TDRSS messages that contain the relevant information required by batgrbproduct.

Bursts that have "failed event data" are assigned with unique trigger numbers because they have passed the rate trigger criterion. We use these trigger numbers in the fake TDRSS messages. Bursts found using the "slew event data" do not have a unique trigger number. Hence, we use the observation ID corresponding to the relevant slew event data as the trigger number in the fake TDRSS message. For the burst position, we use the best position reported in a GCN circular, which was found by previous manual analysis using the BAT data, or from the follow-up XRT/UVOT observations if the afterglow was detected (for simplicity, we do not use position from ground-based follow-up). The burst position is the only important information in the TDRSS data that is used for the actual analysis. Other information, such as the background duration, are only used in the summary report produced by batgrbproduct, and thus we use arbitrary numbers in the fake TDRSS messages.

Because the "failed event data" are much shorter than regular event data, it is common that the burst duration lasts longer than the ∼3–10 s event data range. In such cases, we use the un-maskweighted count rate data (the so-called "quad-rate data"²⁷ to be specific, which is the raw count rate binned in 1.6 s).

Many of the ground-detected bursts have very low partial coding fractions, we follow the same guidelines described in Section 3.3 for analysis of these bursts. There are 15 ground-detected bursts that were outside of the BAT calibrated field-of-view (i.e., the region where the FLUX mask²⁸ is applicable) in the whole event data range. These bursts require using DETECTION mask²⁸ for finding burst durations and refined positions, and the spectral analyses are unavailable. There are 2 ground-detected bursts requiring DETECTION mask for finding the burst refined positions, the rest of the analyses are done using the FLUX mask.

Similar to the onboard triggered bursts, any ground-detected GRBs without an XRT afterglow and with signal-to-noise ratio less than 7 is marked as a "tentative burst." However, the limited event data and the lack of flight trigger information make it difficult to determine the time interval and energy range that enclose the maximum burst emission to estimate the signal-to-noise ratio. A trial-and-error approach might find a higher signal-to-noise ratio, but it also increases the expected number of false detections, which are hard to quantify in a manual process. We therefore estimate the signal-to-noise ratio from the image created in 15–350 keV in the time interval of T₁₀₀ range if possible, or the whole event-data range if T₁₀₀ extends beyond that. If the T₁₀₀ range includes some spacecraft-slewing periods, we create a mosaic image with small time steps (usually ∼0.5 s). Moreover, we note that for many ground-detected bursts, the lack of XRT afterglows might be due to delayed observations, since the bursts was discovered on the ground after full data downlinks, and manually submitting a ToO observation request. It is hard to make a robust conclusion on this issue, however, since the information is lost forever.

There are some bursts that are detected at the very edge of the BAT field of view, and thus have a very low partial coding fraction. We examine every burst with a partial coding fraction lower than 10%. If the standard analysis method fails to perform part or all of the analysis due to the small partial coding fraction, we redo the analysis using the "DETECTION" mask aperture setting. In comparison to the default setting of the "FLUX" mask aperture, the DETECTION mask aperture is the full aperture that includes the largest solid angle and most illuminated detectors. However, it also includes regions with shadows from the mounting brackets, and thus will reduce the accuracy of flux measurements and is only recommended to use for finding bursts (Markwardt et al. 2007). We only use DETECTION mask for finding burst refined position and estimating burst duration if necessary. We only perform spectral analysis for the part of the light curve that is available with the FLUX mask setting.

There are 62 bursts with partial-coding fractions lower than 10% (including the ground-detected GRBs). We examine and assign these bursts into three groups with different analysis approaches:

• 1.  
  FLUX mask is okay: the batgrbproduct pipeline completes the analysis with the default FLUX mask setting, and there no need to perform further analysis. There are 28 bursts in this category.
• 2.  
  DETECTION mask needed only for finding refined position: the pipeline successfully performs most of the analysis except finding the refined position. We redo the search for the refined position with the DETECTION mask setting. There are 13 bursts requiring such analysis.
• 3.  
  DETECTION mask needed for finding burst duration and refined position: There are 21 bursts with either part or all of the burst durations outside of the BAT calibrated field of view (i.e., the region included in the FLUX mask). For these bursts, we use the DETECTION mask for estimating the burst durations and refined positions. The spectral analysis is only available for the time period when the burst is in the BAT calibrated field of view.

Occasionally, the standard analysis can fail or generate erroneous results for several reasons. For example, peculiar background behavior, such as rapid background rise when the telescope enters the SAA, can cause incomplete background subtraction and result in wrong estimations of burst durations. Additionally, if some bright X-ray sources appear in the same field of view as the burst, the background subtraction can be incorrect since the mask-weighting technique assumes the burst to be the brightest source in the BAT field of view. Thus, the light curve might be contaminated by these bright sources. Furthermore, sometimes there are gaps in the event data due to downlink problems. Therefore, we examine the result of each GRB by eye and add comments for those bursts that require special treatment. For problems that appear in more than one GRB, we make the comments in standard format, in order to enable automatic searches afterwards. We also mark the short GRBs with extended emission. However, we do not adopt any quantifiable criteria for determining short GRBs with extended emission. We simply follow the discussions from previous GCN circulars and eye inspections from the light curves.

The adopted comments in standard format include:

• 1.  
  The event data are not available.
• 2.  
  The event data are only available for part of the burst duration.
• 3.  
  battblocks failed because of the weak nature of the burst.
• 4.  
  GRB found by the ground process (failed event data).
• 5.  
  GRB found by the ground process (slew event data).
• 6.  
  DETECTION mask with pcodethresh = 0.0 is used for finding the refined position.
• 7.  
  DETECTION mask with pcodethresh = 0.0 is used for everything except spectral analysis.
• 8.  
  Refined positions found by mosaic image (DETECTION mask with pcodethresh = 0.01, time bin = XX s, and energy band = XX-XX keV).
• 9.  
  Spectral analysis is not available.
• 10.  
  Spectral analysis is only available for part of the burst duration.
• 11.  
  The detector plane histogram data are used for the spectral analysis.
• 12.  
  T100, T90, and T50 are lower limits.
• 13.  
  T100, T90, and T50 might be lower limits.
• 14.  
  Only part of the event data are used in order to have a more reasonable estimation of burst durations.
• 15.  
  Burst durations are found using quad-rate data from $T{0}_{{\rm{GCN}}}-\mathrm{XX}$ s to T0_GCN+XX s.
• 16.  
  Burst durations are found using FRED-model fitting.
• 17.  
  Tentative detection.
• 18.  
  Short GRB with extended emission.
• 19.  
  Maybe short GRB with extended emission.
• 20.  
  Refined position calculated with time interval and energy band determined by the flight software (T0 to T0+XX s; XX-XX keV).
• 21.  
  Spectral analysis failed, likely because the burst is too weak.
• 22.  
  Obvious data gap within the burst duration.

In the following sub-subsections, we summarize further discussion of the common problems.

GRBs without event data or event data range shorter than the burst duration. There are only two bursts, GRB 041219A and GRB 071112C, which were triggered on-board and have no event data due to downlink problems. For GRB 071112C, the burst duration is found by applying battblocks on the quad-rate data. The spectral analysis is not available, because the closest survey data bin lasts from ∼T0 – 120 s to $\sim T0+10\,{\rm{s}}$, which includes more background period than the burst duration. For GRB 041219A, all the analyses are not available due to the lack of event data, rate data, and survey data, because this burst occurred at the very beginning of the mission.

There are 77 bursts that have burst durations that last longer than the event data. For the 35 ground-detected bursts that last longer than the available ∼10 s of event data, we apply battblocks on quad-rate data (un-maskweighted) to estimate burst durations. However, for the bursts triggered on-board, we add the comment "T100, T90, and T50 are lower limits," instead of using the quad-rate data for quantifying the burst durations. This is because the on-board triggers have much longer event data. Thus, the bursts that extend beyond the event data ranges are usually those with fairly long durations, and quantifying the durations using un-maskweighted rate data becomes more inaccurate due to changes of the background levels. The spectral analyses for these bursts with incomplete event data are only available for the part of the burst emission that occurs within the event data range.

GRBs with unusual background changes or background problems. Unusual background changes are most likely to occur when the spacecraft is entering or leaving the SAA. During these times, the background count rates can increase/decrease by ∼ few × 10⁴ count s⁻¹ within a few hundreds of seconds, and cause problems in background subtraction and burst-duration estimations. We examine the burst light curves individually. When the burst duration seems to be incorrect, we re-do the analysis with a modified light curve that excludes the peculiar background period (when possible, i.e., when the problematic background period is far enough from the burst emission) to check if the burst duration changes significantly by excluding the problematic part of the data. It was necessary to recalculate the burst durations of 53 GRBs using only part of the event data.

GRBs with bright x-ray sources in the field of view. Other bright X-ray sources in the field of view that have similar or higher signal-to-noise ratios as the GRB can cause problems in background subtraction and give incorrect estimations of the GRB counts. We thus list the bursts with bright X-ray sources in their field of view in Table 36 in Appendix A. The analysis results for these bursts need to be treated with caution, particular the reliability of potential weak emissions in the light curves, and suspicious bumps or dips in the spectra. Extra manual analyses to remove the bright sources might be needed to obtain more reliable results.

We adopt the following criterion for selecting bursts with bright X-ray sources in their field of view: (1) If the burst has signal-to-noise ratio SNR_GRB ≥ 10.0, the X-ray sources in the field of view need to have signal-to-noise ratios SNR_source ≥ (0.9 × SNR_GRB), and (2) if the burst has signal-to-noise ratio SNR_GRB < 10.0, the X-ray sources in the field of view need to have signal-to-noise ratios SNR_source ≥ (SNR_GRB − 1.0). There are 315 bursts that satisfy this criterion, indicating that for a large fraction of the BAT-detected bursts (∼31%), extra caution is needed when determining the reality of weak emissions in the light curves.

GRBs with data gap. For the bursts triggered onboard, there are only 12 GRBs that have data gaps in the T100 range. Most of the data gaps are around one or two seconds. The only one with a large data gap of 58 s is GRB 080319B because it happened shortly after the "A" burst and had some problem in data collection. The 12 GRBs are: GRB 151027A, GRB 131002A, GRB 130907A, GRB 111209A, GRB 111022B, GRB 110709B, GRB 090516, GRB 081017, GRB 080928, GRB 080319B, GRB 060526, and GRB 041224.

Tentative detections. There are some events with marginal BAT detections (<7σ; see Sections 3.1 and 3.2 for details of how the detection significance is estimated). We mark these as "tentative detections" in Table 9 if there was no XRT afterglow detected. There are 16 bursts that are marked as tentative detections. These bursts should be treated with caution, as some of them might be due to noise fluctuation even though they have a given GRB name. However, we note that 10 out of 16 tentative detections are lacking XRT information due to observational constraints, and thus are difficult to determine the true nature of the event with the BAT detections alone. Information from other instruments (e.g., Fermi, Konus-Wind, etc.) might provide further clues to identify the burst nature. We leave the judgement to the readers because it differs on a case-by-case basis.

3.4.1. Comparison with the BAT2 Catalog

The BAT has detected 1006 bursts to date (until GRB 151027B), including 925 GRBs triggered on-board and 81 bursts found by ground analyses (within which 25 events are found during spacecraft slews). As mentioned in Section 1, although GRB 151027B is the officially announced 1000th GRB detected by Swift, there are 1006 in our list due to a slightly different criteria of counting the BAT-detected GRBs. Table 1 lists the average number of GRB detected each year and the number of active detectors of BAT. Both the total number of GRB detections (i.e., including ground-detected GRBs) and the number of GRB triggered onboard are included in the table.²⁹ The averaged number of active BAT detectors per year is gradually decreasing because some detectors get noisier and are thus turned off. Results show that the number of GRB detections per year remains similar throughout the ten years of Swift observations, despite the continuously decreasing number of active BAT detectors. Table 2 summarizes the number of bursts in the commonly adopted categories (long, short, short GRBs with extended emission, etc). In this paper, the term "ultra-long burst" refers to GRBs with the observed durations longer than 1000 s (the usual BAT event data range), and we only considered duration measured using the BAT emission.

The sky distribution (in Galactic coordinate) of all the BAT-detected GRBs are plotted in Figure 6, with blue stars representing short GRBs, red square showing the short GRBs with extended emission (E.E.), and green triangle marking the bursts with duration longer than 1000 s (i.e., longer than the event data range).

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There are 990 GRBs that have available burst durations. However, there are 9 bursts that do not have available errors associated with the T₉₀, because the burst durations are determined by the FRED-model fit. For the 16 GRBs without T₉₀ measurements, 10 of them are missing burst durations because battblocks failed to find the burst durations due to the weak nature of the bursts, and the rest of the 6 GRBs are those without event data. In addition, there are 52 bursts that have incomplete GRB durations, i.e., the reported burst durations are lower limits, mostly because the burst durations last longer than the available event data time range. Two of these bursts, GRB 101225A and GRB 060218, have unusually long burst durations without obvious structure in the light curve, and thus are also in the list of GRBs for which battblocks failed to find the burst durations.

The upper panel of Figure 7 shows the T₉₀ distribution of 940 bursts that have burst durations successfully determined. That is, we exclude bursts with incomplete T₉₀, and/or bursts without T₉₀ that are found by battblocks or FRED-model fit. There are 850 GRBs with T₉₀ > 2 s (long GRBs), and 90 GRBs with T₉₀ ≤ 2 s (short GRBs). When folding in the appropriate lower/upper limit, there are 17 long bursts with the T₉₀ lower limit shorter than 2 s, and 5 short bursts with T₉₀ upper limit longer than 2 s. For comparison, the histogram of T₉₀ upper limits and T₉₀ lower limits are also plotted in the figure. Results show that the uncertainties in T₉₀ measurements do not have significant effect on the overall T₉₀ distribution.

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The T₉₀ distribution remains very similar to the one shown in the BAT2 catalog, and thus is still significantly different from the distributions of GRBs detected by other instruments, such as Fermi and BATSE, as mentioned in the BAT2 catalog. The middle and bottom panels of Figure 7 shows the T₉₀ distributions for GRBs detected by Fermi and BATSE for comparison. T₉₀ of the Fermi GRBs are obtained from the Fermi GBM burst catalog³⁰ (Gruber et al. 2014; von Kienlin et al. 2014), and T₉₀ of the BATSE GRBs are from The Fourth Gamma-ray Bursts Catalog (Paciesas et al. 1999). Compared to the short GRB fraction in the Swift/BAT GRB sample (∼9%), the fractions of short bursts are larger in both the Fermi GRB sample (∼17%) and the BATSE sample (∼26%).

4.3.1. Time-averaged Spectra

After applying the criteria described in Section 3.1, there are 877 bursts that have acceptable spectral fits in their time-averaged spectra (spectra made by photons in the T₁₀₀ range), in which 90 bursts are better fitted by the CPL model.

GRB classification of spectral characteristics: short-hard bursts versus long-soft bursts. In addition to the short and long categories using the burst durations, previous studies from GRBs detected by multiple instruments, including BATSE, Fermi, and Swift, have found that short bursts tend to be harder than long GRBs (e.g., Kouveliotou et al. 1993; Qin et al. 2000; Řípa et al. 2009; Sakamoto et al. 2011b; Qin et al. 2013; von Kienlin et al. 2014).

Figure 8 shows an updated version of the hardness ratio (i.e., the fluence in 50–100 keV divided by fluence in 25–50 keV) versus T₉₀ to include all the new BAT-detected GRBs since the BAT2 catalog. The fluences are estimated from the better-fitted spectral model (see criterion described in Section 3.1). We only included bursts with acceptable spectral fits and with available values of T₉₀ and T₉₀ errors. In addition, we exclude bursts with incomplete T₉₀ (i.e., the burst durations are lower limits) and those bursts with T₉₀ consistent with zero (i.e., the lower limit of T₉₀ is equal or less than zero). There are 815 bursts included in this plot. There are 86 bursts that are better fitted by the CPL model in this plot (marked in red).

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This plot is very similar to the one presented in the BAT2 catalog. The conventional two GRB classes, short-hard bursts and long-soft bursts, can be roughly identified in this plot, though the separation of the two groups is not very obvious. The particularly soft short burst with the hardness ratio of 0.47 and T₉₀ of 0.132 s is GRB 140622A. Despite the unusually soft spectrum, the fast fading XRT light curve of this burst is consistent with the normal behavior of a short burst (Burrows et al. 2014; Sakamoto et al. 2014). Moreover, the redshift of z ∼ 0.96 measured from the emission lines from the possible host galaxy (Hartoog et al. 2014) suggests that this is not a Galactic source and is unlikely to be a soft gamma repeater (e.g., Mereghetti 2008).

To further explore the difference in spectral hardness of the short and long bursts, we plot the histogram of the photon index α for the bursts that are better fitted by the simple PL model in Figure 9. The upper panel shows the distribution for all 787 GRBs that have acceptable spectral fits and are better fitted by the simple PL model. The middle and bottom panel show the distributions for long and short GRBs, respectively. We need the T₉₀ information to distinguish short and long bursts. Thus, GRBs without available values of T₉₀ and/or T₉₀ errors are excluded from these two panels. Moreover, GRBs without complete burst durations (only lower limits reported) are also excluded. The figure shows that the short bursts are slightly harder (i.e., higher α_PL) than long bursts, but the difference is not significant. There are 671 long GRBs, and 58 short GRBs in these two panels.

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BAT Sensitivity on GRB Detections

The BAT detector is a photon-counting instrument (Barthelmy et al. 2005), and thus the sensitivity roughly increases with $\sqrt{T}$ (T is the exposure time), as the signal-to-noise ratio increases as $1/\sqrt{N}$ (N is the number of photons) and the number of photons N increases as time T (for BAT, the photon N is dominated by background photons, and thus roughly increase linearly with T).

Figure 10 shows this effect by plotting the correlation between the energy/photon fluxes of the BAT-detected GRBs versus the burst durations T₉₀.³¹ The fluxes are estimated by the best-fit model (either the simple PL or the CPL). The bursts that are better fitted by the CPL model are marked in red. The figure shows a clear correlation of the minimum fluxes of the detected GRBs and the burst durations. This correlation of the energy flux and T₉₀ is very similar to BAT sensitivity (as a function of exposure time) derived in Baumgartner et al. (2013) (Equation (9)), despite that in Baumgartner et al. (2013) the sensitivity is derived for non-GRB sources with Crab-like spectra, and for a signal-to-noise ratio of $5\sigma$ (instead of the ∼6.5 to 7σ threshold used for GRB detections). However, note that this plot includes only the GRBs with "acceptable spectral fits" (as defined by criteria described in Section 3.1). Thus, this plots might exclude dim bursts that do not have data with low enough uncertainties to constraint the fits.

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In addition, due to the complexity of the BAT trigger algorithm, this correlation between the minimum detectable fluxes with the burst durations should only be treated as an approximation. For example, the burst durations are not usually identical to the actual exposure time used by the trigger algorithm for detecting the burst, because the trigger algorithm might not correctly bracket the burst period. Thus, this correlation does not necessary mean that GRBs with fluxes above this line will be certainly detected, since the foreground period of the trigger algorithm needs to first correctly select the optimal period that maximizes the signal-to-noise ratio (Lien et al. 2014). Moreover, if the GRB flux decays significantly with time so that the average flux decreases faster than T^−1/2, there would be no gain in the signal-to-noise ratio by increasing the exposure time.

The figure also shows that bursts that are better fitted by the CPL model tend to have higher fluxes. This is because a burst needs to be bright enough to obtain a decent spectrum (i.e., with smaller uncertainties in each energy bin) that is capable of distinguishing the two models.

Figure 11 shows the distribution of energy fluxes (left panel) and photon fluxes (right panel) for all the 877 bursts with acceptable spectral fits. The fluxes are estimated from the best-fit model (either the simple PL for CPL). The distributions for both the energy and photon fluxes are roughly Gaussian, with an average of 5.90 × 10⁻⁸ erg s⁻¹ cm⁻² and 0.75 ph s⁻¹ cm⁻² for the energy and photon fluxes, respectively. Again, because we only plots those bursts with acceptable spectral fits, the weak bursts with lower fluxes are likely to be removed from this sample.

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BAT selection effects on GRB spectral shapes. Both the theoretical predictions from the synchrotron shock model (Rees & Meszaros 1992; Preece et al. 1998, and reference therein) and empirical fits from observations with instruments that have wide-energy coverages (e.g., BATSE and Fermi) suggest that the GRB spectrum (photon flux as a function of photon energy) can be roughly described by a power-law decay at lower energy, followed by some steepening after the energy E_peak, the peak energy in the νF_ν spectrum, where F_ν is the energy flux density.

The BAT has a relatively narrow energy range. Therefore, it can be difficult to constrain E_peak with BAT data alone. In fact, the E_peak distributions from the BATSE and Fermi GRB samples suggest that the E_peak distribution peaks at around few hundreds keV (see Figure 12). Moreover, even for those bursts with E_peak occurring within the BAT energy range, the narrow energy coverage also requires a spectrum to have less uncertainty in order to be able to constrain E_peak.

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In the current BAT GRB sample, there are 90 bursts with acceptable spectra that are better fitted by the CPL model. The E_peak and photon index α_CPL distributions for these events are plotted in the left and right panel of Figure 13, respectively. The black and red lines show the distributions using the lower and upper limits. As expected, all of the values of E_peak lie in the range of ∼10 to ∼300 keV, which is within the BAT energy range. However, these might not be the only bursts in the BAT sample that have E_peak within the BAT energy range. It is possible that some other bursts also have E_peak in this range, but are not bright enough to present good spectra that can distinguish the two models (Sakamoto et al. 2008). The E_peak distribution peaks at ∼80 keV (the center of the bin with the largest number of bursts), which is similar to the one presented in the BAT2 catalog, but is significantly different than the distributions from GRBs detected by other instruments, as shown in Figure 12 (Sakamoto et al. 2011b; Goldstein et al. 2013; Gruber et al. 2014; von Kienlin et al. 2014). The difference is likely due to instrumental biases with each instrument sensitives to a different energy range.

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Both the BAT1 and BAT2 catalog have shown that most of the BAT-detected GRBs have spectral hardnesses that are consistent with the spectral hardnesses calculated from a Band function fit with ${E}_{{\rm{peak}}}^{{\rm{obs}}}$ in the range of the BAT energy band. Here we updated the same plot that shows the spectral hardness as in the BAT1 and BAT2 catalog with the new GRB detections, as shown in the left panel of Figure 14. In addition, we also plot the spectral hardness in flux instead of fluence in the right panel of Figure 14. As usual, we only include in these plots bursts with acceptable spectral fits and complete burst durations with valid numbers of T₉₀ and T₉₀ errors. There are 756 long bursts (red dots) and 59 short bursts (blue dots) in these plots. Similar to the BAT1 and BAT2 catalog, we plot the lines using the Band function with E_peak of 15 keV (dashed line) and 150 keV (dashed–dotted line), respectively. Both lines are calculated using canonical values of α = −1, β = −2.5. Each line traces the fluence ratios from the same α, β, and E_peak, with a range of normalizations. Results show that ∼80% of the bursts lie between the two lines (when including the errors of the burst fluences), indicating that most of the BAT-detected bursts have fluence ratios that are consistent with the ones from the Band function with E_peak lying within the BAT energy range. In other words, it is possible that these bursts have E_peak within the BAT energy range, though most of the spectra do not have small enough uncertainties to constrain the E_peak.

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Furthermore, Sakamoto et al. (2008) studies the potential confusion between the simple PL, CPL, and Band function (Band et al. 1993) spectral fit in the BAT observations using simulated spectra. These authors found that most of the BAT-detected GRBs probably have E_peak within the BAT energy range, and derived an equation to estimate E_peak (for the Band function) using the photon index from the simple PL fit. Figure 15 shows E_peak distribution from the E_peak estimator derived in Sakamoto et al. (2008). Results show that majority (∼78%) of the GRBs detected by BAT might have E_peak within the BAT energy range. This fraction is very similar to the fraction (∼80%) of the bursts that fall between the lines in Figure 14, which traces the fluence ratios with E^obs_peak = 15 keV and 150 keV, respectively. Because the E_peak estimator only works for GRBs that have E_peak within 15–150 keV, all the bursts estimated to have E_peak below or above this energy range are placed in single bins in light red.

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For bursts with similar total energies, it is reasonable to expect that BAT is most sensitive to those events that have E_peak within the instrument's energy range, because in such cases most of the energy of these bursts are distributed in the detectable energy range. However, it is also possible to have a burst with E_peak outside of the BAT energy being detectable because it has higher fluxes overall, and it is not completely trivial how much the energy budget arrangement is sensitive to different spectral shapes. To quantify the energy budget in the BAT energy range, we calculate the energy flux in 15–150 keV for a range of E_peak and photon indices in the CPL model, but with a fixed total flux (i.e., we assume a flux of 7.21 × 10⁻⁷ erg s⁻¹ cm⁻² from 1 to 10,000 keV, which is a relatively typical flux for GRB and it can be easily scaled up or down for bursts with different total flux/normalization). Figure 16 shows the contour plot of how flux changes as a function of E_peak and photon indices. We make the contour plot with the CPL model rather than the Band function simply because the Band function has one more parameter, which makes it difficult to present in a two-dimensional plot. Moreover, since we are focusing on the flux in the narrow BAT energy range, the CPL model should be a good-enough approximation. We show an extremely wide range of α_CPL in this plot for demonstration. However, observations from BATSE, Fermi, and Swift suggest that the value never exceeds 1 (Sakamoto et al. 2011b; Goldstein et al. 2013; Gruber et al. 2014; von Kienlin et al. 2014). Moreover, theoretical predictions from the synchrotron shock model enforce that α_CPL < −2/3 (Rees & Meszaros 1992; Preece et al. 1998, and references therein). Therefore, one can see in the plot that in the reasonable range of α_CPL from ∼−2 to ∼1, GRBs with normal energy output are indeed most likely to be detected by BAT if they have E_peak in the BAT energy range. For GRBs with much higher E_peak, they would need to be roughly one or two orders of magnitude brighter in order to be detected, and the consequences become more significant at larger α_CPL.

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When comparing Figures 13 and 9 for the spectral index distributions from the simple PL and CPL fits, one would notice that in general the spectral indices from the CPL fits are higher than those from the simple PL fits. This can be explained if most of the bursts actually have E_peak within the BAT energy range. In such cases, the photon index from a simple PL fit will be an average of the true power law index before and after E_peak, and thus will be lower than the real first slope of the spectrum.

For those bursts that are better fitted by the CPL model, all except two have their lower limit of α_CPL greater than −2/3. Therefore, almost all the bursts are consistent with the synchrotron shock model. The only two GRBs with the lower limits higher than −2/3 are GRB 050219A and GRB 130420B, and the α_CPL range for these two bursts are (−0.41, 0.18) and (−0.61, 0.44), respectively. All the bursts with acceptable fits that are better fitted by the simple PL model also have spectral indices that are consistent with the the synchrotron shock model. However, the comparison using the simple PL fit might not be physically meaningful, if the simple PL model does not represent the true underlying spectral shape due to the uncertainty in the data.

4.3.2. Peak Spectra

For the 1 s peak spectra, there are only 728 bursts that have acceptable spectral fits due to the smaller number of photon counts in the 1 s duration. Within these bursts with acceptable spectral fits, there are 68 GRBs that are better fitted by the CPL model.

There are 51 bursts with T₁₀₀ shorter than one second. For these extremely short bursts, the 1 s peak flux is likely to include some background intervals, and the 20 ms peak flux discussed below (and reported in Section A.4) is probably better represent the true peak flux. Nonetheless, we still present the 1 s peak flux for GRBs with T₁₀₀ < 1 s here for completeness, and also because of the uncertainties in the burst duration measurements.

Comparison with the time-averaged (${T}_{100}$) spectra. There are 542 bursts that are better fitted by the simple PL model for both the T₁₀₀ spectra and the 1 s peak spectra; 22 bursts that are better fitted by the CPL for both of the T₁₀₀ spectra and the 1 s peak spectra; 42 bursts that are better fitted by the PL model for the T₁₀₀ spectra but change to the CPL fit for the 1 s peak spectra; and 50 bursts that are better fitted by the CPL model for the T₁₀₀ but switch to the simple PL fit for the 1 s peak spectra. Those bursts that switch between models for the two different spectral fits usually either have Δχ² ∼ 5 (close to our threshold for adopting the CPL model at Δχ² = 6) for one of the spectra, or the fits have fairly low null probability (close to our threshold of 0.1 for rejecting the fit). Note that only one burst with T₁₀₀ < 1 s (GRB 081101) is better fitted by different models for the time-averaged spectrum and the 1 s peak spectrum. To be specific, the time-averaged spectrum for this burst is better fitted by the CPL model, while the 1 s peak spectrum is better fitted by the simple PL model, likely because the 1 s peak spectrum includes a larger interval than the true T₁₀₀ range and thus is contaminated by some background photons.

Figure 17 compares the photon indices α_PL from the T₁₀₀ and 1 s peak spectral fits. The results show that the fits from two different kinds of spectra gives similar α_PL. Several studies have shown that it is not uncommon that the spectral evolution follows the shape of the light curve (e.g., Zhang et al. 2007, 2011). Therefore, one might expect that the 1 s peak spectrum is harder (i.e., has larger α_PL) than the time-averaged spectrum. Due to the large uncertainties in the values of α_PL, it is difficult to determine whether such trend exists. However, we do notice this trend of spectral evolution for some brighter bursts with decent spectrum (see the "Spectral Evolution" plot in the individual burst webpage³² ).

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BAT detection limit with the 1 s flux. Similar to Figure 10, we plot in Figure 18 the 1 s peak energy flux (left panel) and the photon flux (right panel) as a function of T₉₀ to show the BAT detection limit with the 1 s flux. As expected, there is no obvious correlation between the minimum 1 s peak energy/photon flux with respect to T₉₀. Also, results show that the BAT sensitivity to 1 s flux is ∼3 × 10⁻⁸ erg s⁻¹ cm⁻² (or ∼0.3 s⁻¹ cm⁻² for photon flux), which are similar to the detection limit shown in Figure 10. Similar to Figure 10, the bursts that are fitted-better by the CPL model have higher minimum fluxes.

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20 ms peak fluxes for short GRBs. Because most of the short bursts are shorter than one second, we also generate peak spectra for the 20 ms duration to have values that better represent the peak fluxes for short bursts. As mentioned in Section 3.1, the 20 ms peak spectra are made with larger energy bins and only ten energy bands, to have reasonable number of counts in each energy bin. However, despite the larger energy bins used, there are only 226 bursts with acceptable spectral fits for the 20 ms spectral analyses, which is significant lower than those from the 1 s peak spectral analyses and the time-averaged T₁₀₀ spectral analyses. Only five GRBs (GRB 140209A, GRB 110715A, GRB 101023A, GRB 060117, and GRB 050525A) have the 20 ms spectrum better fitted by the CPL model.

Figure 19 shows the correlation between the photon indices α_PL from the 20 ms peak spectral analyses and the time-averaged T₁₀₀ spectral analyses. Comparing the the similar plot made for the 1 s peak spectral fits, the correlation between the α_PL from the 20 ms peak and T₁₀₀ spectra are less significant. Results also show that the long and short bursts follow similar trend.

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4.3.3. GRB that Do Not have Acceptable Spectral Fits

Figure 20 shows the histogram of the partial coding fraction for long, short, and ground-detected GRBs. The bursts found by ground-analyses during spacecraft slews are not included, because the partial coding fraction changes constantly for these events. There are no short GRBs triggered on-board with partial coding fraction less than 0.2, which is equivalent to an incident angle of ∼50^o.

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Short GRBs with extended emissions have raised special interests among the GRB community, partially due to their mixed characteristics between the short and long bursts (e.g., Gehrels et al. 2006; Norris & Bonnell 2006; Troja et al. 2008; Kaneko et al. 2015). We therefore include a special section of short GRBs with extended emission. We also present both a more secure list of these bursts (Table 3), plus a list of possible short GRBs with extended emission (Table 4).

Table 3.  List of Definite Short GRBs with Extended Emission (E.E.)

GRB Name	Short Pulse Start	Short Pulse End	E.E. End	Short Pulse	E.E.
	(s)	(E.E. Start) (s)	(s)	αPL	αPL
GRB 150424A	−0.060	0.468	95.012	$-{0.78}_{-0.06}^{+0.06}$	$-{2.10}_{-0.54}^{+0.46}$
GRB 111121A	−0.336	1.000	138.264	$-{0.99}_{-0.08}^{+0.08}$	$-{1.83}_{-0.15}^{+0.15}$
GRB 090916	−0.040	0.392	68.520	$-{1.58}_{-0.27}^{+0.27}$	$-{1.37}_{-0.37}^{+0.38}$
GRB 090715A	−0.200	0.800	48.936	$-{1.02}_{-0.20}^{+0.21}$	$-{1.54}_{-0.62}^{+0.62}$
GRB 090531B	0.252	1.300	56.132	$-{0.99}_{-0.16}^{+0.16}$	$-{1.69}_{-0.28}^{+0.27}$
GRB 080503	−2.192	0.600	221.808	$-{1.32}_{-0.43}^{+0.45}$	$-{1.89}_{-0.12}^{+0.12}$
GRB 071227	−0.144	0.908	150.552	$-{1.01}_{-0.23}^{+0.24}$	$-{2.23}_{-0.49}^{+0.41}$
GRB 070714B	−0.792	1.976	74.640	$-{0.96}_{-0.08}^{+0.08}$	$-{1.92}_{-0.49}^{+0.43}$
GRB 061210	−0.004	0.080	89.392	$-{0.69}_{-0.12}^{+0.12}$	$-{1.80}_{-0.37}^{+0.34}$
GRB 061006	−23.288	−22.000	137.720	$-{0.91}_{-0.07}^{+0.08}$	$-{2.06}_{-0.23}^{+0.22}$
GRB 051227	−0.848	0.828	122.732	$-{0.94}_{-0.23}^{+0.25}$	$-{1.48}_{-0.27}^{+0.27}$
GRB 050724	−0.024	0.416	107.140	$-{1.51}_{-0.14}^{+0.14}$	$-{2.05}_{-0.26}^{+0.25}$

Note. The times listed in the table are relative to the burst trigger time.

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All of the short GRBs with extended emissions listed in Table 3 that occurred before 2009 are included in the BAT2 catalog. Note that we do not apply any quantitative criteria for selecting these short GRBs with extended emissions. Most of the bursts before 2009 are adopted from the BAT2 catalog, which was classified by Norris et al. (2010). However, the bursts after 2009 are chosen based on reports in GCN circulars. We also double check by eye inspection for all GRBs to (1) make sure no other obvious GRBs with similar features are missed in previous GCN circulars, and (2) those bursts reported as short GRBs with extended emissions do show such a feature.

The possible short GRBs with extended emission listed in Table 4 are GRBs with similar structure as those listed in Table 3. They are selected because some literature (mostly the GCN circulars) mentioned potential extended emissions. However, these are not included in Table 3 because of at least one of the following reasons: (1) The short pulse is slightly longer than 2 s. (2) The extended emission is not picked out by the auto-pipeline (battblocks). (3) The extended emission is weak, and there are some significant fluctuations in the background and/or bright X-ray sources in the field of view, which may cause extra residuals when performing the mask-weighting. (4) The bursts was found by ground analyses and there is not sufficient event data. The corresponding comments for each burst are presented in the table. Note that although GRB 081211B is a ground-detected burst (during a spacecraft slew) with only ∼120 s of event data, several GCN circulars suggest that this burst is possibly a short GRB with extended emission, with the short spike detected by Konus-Wind while the burst was outside of the BAT field of view (Golenetskii et al. 2008/GCN 8676; Perley et al. 2009/GCN 8914). In fact, there is also a visible short spike at ∼T0–150 s in the BAT raw light curve. However, due to the lack of event data at that time, we cannot confirm whether this short pulse is related to the GRB.

There are five bursts (GRB 091117, GRB 100724A, GRB 100625A, GRB 101219A, and GRB 090621B) for which the GCN circular mentioned an indication of extended emission, but further analysis suggests that the extended emissions of GRB 091117, GRB 100724A, GRB 100625A, and GRB 101219A are below ∼3σ even when choosing an optimal time periods and optimal energy bands. GRB 090621B shows no extended emission until ∼T0 + 150 s, when a low-significant bump occurred and last ∼50 s. Thus, we conclude that these extended emissions are likely not real.

Figure 21 shows the results of spectral fits from the simple PL model (α_PL) for both the short pulses (left panel) and the extended emission (right panel), for the confirmed short GRBs with extended emissions (Table 3). Because of the small sample of the short GRBs with extended emission, and all of these bursts have constrained α_PL but not necessarily have constrained parameters in the CPL model, we only show the simple PL model fits in this figure. Moreover, we include all the bursts, even if the do not satisfied some of the criteria listed in Section 3.1 (in fact, only a few simple PL fits here do not satisfied all the strict criteria in 3.1, such as the lower limit of one energy band is consistent with zero). The α_PL distributions for short and long GRBs are also plotted in gray bars in the left and right panel, respectively, to be compared with the distributions of short pulses and extended emissions. As mentioned in previous studies (e.g., Sakamoto et al. 2011b), the spectra of short pulses are harder than the extended emission in general, and resemble more of short GRBs, while the spectra for extended emission parts are softer and match better with the α_PL distributions of long GRBs.

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We include a list of GRBs with redshift measurements in this catalog (Table 37). The information in this list is collected from and cross-checked between other online lists (e.g., GRBOX by Daniel Perley,³⁴ online list by Jochen Greiner,³⁵ online table by Nathaniel Butler³⁶ ), the GCN circulars (Barthelmy et al. 1995), and papers. The redshift list with full references are included in Table 37.

To date (till GRB 151027B), there are 378 BAT-detected GRBs with redshift measurements (within which 18 redshifts are marked as potential questionable measurements). In Table 37, we mark the four common methods for redshift measurements: (1) absorption lines measurement from the GRB afterglow spectra (noted by symbol "ba"); (2) emission lines from the GRB host galaxy spectra (noted by symbol "he"); (3) photometric redshift from the GRB afterglow (noted by symbol "bp"); (4) photometric redshift from the GRB host galaxy (noted by symbol "hp"). Other less-common methods, such as the Lyα break, are described in short sentences in Table 37. If we noticed that some questions were raised about the GRB redshifts (e.g., the potential host galaxy might not be related to the burst), the redshift value in the table will be followed by a question mark, and these redshift values are not included in the following summarized numbers and plots.

There are 229 GRB spectroscopic redshifts from GRB afterglows, 96 spectroscopic redshifts measured from host galaxies, 17 photometric redshifts from GRB afterglows, and 12 photometric redshifts from host galaxies.

The redshift distribution of the BAT-detected GRBs is shown in Figure 22. The distribution of bursts found by the image trigger is plotted in red. Compared to GRBs detected by rate triggers, the image-triggered GRBs are more uniformly distributed throughout all redshifts. The image-triggered bursts compose of 20.0% of the events with redshift measurements, which is very similar to the fraction of image-triggered GRBs out of all BAT-detected bursts (17.5%).

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4.6.1. Energy Flux versus Redshift: Exploring Potential Selection Effects in Redshift Measurements with the BAT Trigger Characteristic

The energy fluxes in 15–150 keV as a function of redshift is plotted in Figure 23. There are 35 bursts with redshift measurements excluded from this plot, because those bursts do not have acceptable spectral fits. The image-triggered bursts are marked in red, and the GRBs with photometric redshifts are marked in blue, with the uncertainties shown when available. Note that these uncertainties are adopted from different sources (see Table 37) and might refer to different confidence ranges. Thus, the values here are only presented as rough references. As expected, image triggers find bursts with lower fluxes in general throughout the redshift range. The decline in the number of detections of high-flux bursts at higher redshift is likely due to the shrinking of the sample size of detected GRBs (it is less likely to detect bursts from the tail of the distribution). There is also a slight decrease in the detections of low-flux bursts at higher redshift, though the effect is not obvious until higher redshift (z ≳ 5), which might imply that the majority of the bursts (i.e., the center of the intrinsic flux distribution) does not lie far from the BAT sensitivity threshold.

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Figure 24 compares the distributions of the time-averaged (T₁₀₀) energy flux in 15–150 keV for the GRBs with redshifts and all GRBs (but only those bursts with acceptable spectral fits are included). The plot is shown in the normalized number of GRBs, since there are ∼3 times more bursts in the all-GRB sample than in the GRB-with-redshift sample. Results show that the two distributions are very similar, which implies that the successful redshift measurements from the ground-based follow-up facilities have no correlation with how bright the burst is in the BAT energy range.

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4.6.2. Burst Duration Versus Redshift

The missing time-dilation effect and the observational biases. Many studies have shown that the observed burst durations do not present a clear effect of time dilation for GRBs at higher redshift (e.g., Sakamoto et al. 2011b; Kocevski & Petrosian 2013; Littlejohns & Butler 2014). One likely explanation is the "tip-of-the-iceberg" effect, where a larger fraction of the burst emission becomes hidden underneath the background noise, as the brightness of the GRB decreases at higher redshift. Kocevski & Petrosian (2013) demonstrates this effect with a single-pulse structure and concludes that the observed duration can miss up to ∼80% of the true burst duration at high redshift z ∼ 5.

Figure 25 shows the comparison of the rest-frame T₉₀ and the observer-frame T₉₀ as a function of redshift z. The rest-frame T₉₀ is calculated simply by correcting the (1 + z) time dilation effect (i.e., rest-frame T₉₀ = (observer-frame T₉₀)/(1 + z)). Indeed, there is no obvious trend from time dilation. However, the observed T₉₀ seems to show some correlation between the minimum detectable T₉₀ with redshift. As discussed in Section 4.3.1, BAT can in general detect lower fluxes for bursts with longer burst durations. Therefore, one would generally expect that BAT can only detect longer bursts at higher redshift for GRBs with a specific intrinsic luminosity. In other words, the correlation between the minimum detectable flux (at 5σ) in the observed energy band F_band,obs and the exposure time T (Equation (9) in Baumgartner et al. 2013):

$$\begin{eqnarray}{F}_{{\rm{band,obs}}} & = & 1.18\,{\rm{m}}\,\mathrm{Crab}{\left(\displaystyle \frac{T}{1\mathrm{Ms}}\right)}^{-1/2}\\ & = & 2.86\times {10}^{-11}\,[\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}]{\left(\displaystyle \frac{T}{1\mathrm{Ms}}\right)}^{-1/2}\end{eqnarray} \tag{ 3 }$$

requires a longer exposure time to detect lower flux, and in the GRB case the maximum possible exposure time is determined by the burst duration. The observed flux in the observed energy band is correlated with the luminosity in the corresponding redshifted bandpass as

$$\begin{eqnarray}&&{F}_{{\rm{band,obs}}}=\displaystyle \frac{{L}_{{\rm{band,rest}}}}{4\pi {D}_{{\rm{L}}}^{2}},\end{eqnarray} \tag{ 4 }$$

where D_L is the luminosity distance and L_band,rest here refers to the luminosity in an energy band that corresponds to the observed energy band, not the bolometric luminosity (see detailed descriptions in Appendix B). Thus, for a specific luminosity, one can get the following correlation between the exposure time and the redshift,

$$\begin{eqnarray}&&{\left(\displaystyle \frac{T}{1\mathrm{Ms}}\right)}^{1/2}=2.86\times {10}^{-11}\,[\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}]\,\displaystyle \frac{4\pi {D}_{{\rm{L}}}^{2}}{{{\rm{L}}}_{{\rm{band,rest}}}}.\end{eqnarray} \tag{ 5 }$$

For simplicity, we approximate the exposure time by the burst duration, i.e., assuming T = T₉₀, and plot this relation as the blue-dotted lines in Figure 25 (for L_band,rest = 10⁵² and 10⁵³ erg s⁻¹, respectively). As expected, a larger luminosity corresponds to smaller burst duration throughout the redshift. As one can see in the plot, both of the blue-dashed lines lie below all but one of the detected burst with redshift measurements, leaving a relatively large empty space between the blue dotted line with L_band,rest = 10⁵² erg s⁻¹ and the detected bursts with the shortest durations at each redshift. Naively, one might expect that this indicates that there are no bursts with L_band,rest > 10⁵² erg s⁻¹, otherwise BAT should have detected them even if they have durations that lies below the blue dotted line. However, when we calculate the GRB luminosities in the following subsection (see Figure 28), more than one bursts have luminosities exceeding 10⁵² erg s⁻¹. Therefore, we are only missing bright "short" bursts that should have been detectable, and not all detectable bright bursts. Another possibility to explain these missing bright short bursts in the plot would be the missing redshift measurements. In other words, we might have detected these bright short bursts, but do not have redshift measurements and thus they are not included in this plot. Unfortunately, it remains difficult to distinguish these two possibilities due to the biases and incompleteness of redshift measurements.

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Long and short bursts with a rest-frame ${T}_{90}$. The GRB community has commonly used the observed burst duration to classify GRBs and to infer different physical origins, with the long GRBs related to deaths of massive starts, and short bursts linked to compact-object mergers. However, the burst duration in the observed frame is affected by several biases, such as the tip-of-the-iceberg effect mention above and the time-dilation effect, and thus might not represent the true duration of a burst. Although it is difficult to recover the intrinsic total burst duration from the tip-of-the-iceberg effect, we can easily correct the time-dilation effect and calculate the rest-frame T90 by dividing the observed T₉₀ by the (1 + z) factor. Figure 26 compares the rest-frame T₉₀ distribution and the observer-frame T₉₀ distribution. For the observer-frame T₉₀ distribution, we only include GRBs with redshift measurements, in order to have a fair comparison with the rest-frame T₉₀ distribution because there are more long bursts that have redshift measurements than short bursts. Results show that the "tail" of short bursts in the distribution become slightly less significant in the rest-frame T₉₀ histogram. There are 21 bursts with the observer-frame T₉₀ > 2 s, but have the rest-frame T₉₀ ≤ 2 s. However, this rest-frame T₉₀ distribution is still unlikely to represent the distribution of the intrinsic burst duration due to other observational biases.

4.6.3. Spectral Characteristics versus Redshift: Searching for Hints of the Intrinsic Spectral Shapes and Energy Outputs

Figure 27 shows the time-averaged (T₁₀₀) photon index α_PL (for those GRBs that are better fitted by the simple PL model) as a function of redshift z. Again, the bursts with photometric redshifts are marked in blue specifically, due to the larger uncertainties in their redshift measurements. Similar to the same figure shown in the BAT2 catalog, there is no clear correlation between α_PL and redshift. However, there are probably some instrumental selection biases for the photon indices of the BAT-detected GRBs. As discussed in Section 4.3.1, BAT is most likely to detect bursts with a certain range of α_PL that gives higher fluxes in the BAT energy range. Moreover, the burst needs to be bright enough to have a spectrum with uncertainties small enough to distinguish the simple PL and CPL model. Therefore, the distribution of α_PL might not represent the true intrinsic distribution.

Figure 28 shows the GRB luminosity in the observed 15–150 keV band as a function of redshift. Due to the limited energy range of the BAT, we can only constrain the energy emission within the BAT energy range. Extrapolating the spectral fits beyond the BAT energy range is probably not a good approximation because the turn-over point in the spectrum (i.e., E_peak) might happen somewhere above the BAT energy limit, and thus the total luminosity calculated by extrapolating the spectral fits from the BAT spectrum can be over-estimated. We therefore calculate the luminosity in the observed 15–150 keV (the BAT energy range). However, this luminosity will correspond to a different rest-frame energy range for a GRB at a different redshift. Specifically, the luminosity is calculated by the following equations:

$$\begin{eqnarray}{L}_{{\rm{band,rest}}} & = & {\displaystyle \int }_{{E}_{{\rm{rest}}}^{{\rm{\min }}}}^{{E}_{{\rm{rest}}}^{{\rm{\max }}}}{L}_{E,{\rm{rest}}}\,{{dE}}_{{\rm{rest}}}\\ & = & {\displaystyle \int }_{{E}_{{\rm{rest}}}^{{\rm{\min }}}}^{{E}_{{\rm{rest}}}^{{\rm{\max }}}}\displaystyle \frac{4\pi {D}_{L}^{2}}{1+z}\ {F}_{E,{\rm{obs}}}\,{{dE}}_{{\rm{rest}}}\\ & = & {\displaystyle \int }_{{E}_{{\rm{obs}}}^{{\rm{\min }}}}^{{E}_{{\rm{obs}}}^{{\rm{\max }}}}\displaystyle \frac{4\pi {D}_{L}^{2}}{1+z}\,{F}_{E,{\rm{obs}}}\,(1+z){{dE}}_{{\rm{obs}}}\\ & = & {\displaystyle \int }_{{E}_{{\rm{obs}}}^{{\rm{\min }}}}^{{E}_{{\rm{obs}}}^{{\rm{\max }}}}4\pi {D}_{L}^{2}\,{F}_{E,{\rm{obs}}}\,{{dE}}_{{\rm{obs}}}\\ & = & 4\pi {D}_{L}^{2}\,{F}_{{\rm{band,obs}}}\end{eqnarray} \tag{ 6 }$$

where ${F}_{{\rm{band,obs}}}={\int }_{{E}_{{\rm{obs}}}^{{\rm{\min }}}}^{{E}_{{\rm{obs}}}^{{\rm{\max }}}}{F}_{E,{\rm{obs}}}\ {{dE}}_{{\rm{obs}}}$ refers to the flux in the observed energy range, and L_band,rest corresponds to the luminosity in the rest-frame energy range ${E}_{{\rm{rest}}}^{{\rm{\min }}}={E}_{{\rm{obs}}}^{{\rm{\min }}}(1+z)$ to ${E}_{{\rm{rest}}}^{{\rm{\max }}}={E}_{{\rm{obs}}}^{{\rm{\max }}}(1+z)$. More detail descriptions can be found in Appendix B.

As expected, there is a clear correlation between the minimum luminosity of detected burst with redshift, which is mainly from the Malmquist bias. The black lines in Figure 28 demonstrate the effect of Malmquist bias due to the sensitivity of BAT. The solid line shows the minimum detectable luminosity in the observed 15–150 keV band assuming a T₉₀ of 100 s. The dashed black line shows the same detectable luminosity but assuming a redshift-dependent T₉₀ of 100/(1 + z) s. Note that this T₉₀ becomes shorter at higher redshift, contrary to the expectation of time dilation effect. As discussed in Section 4.6.2, there is no clear evidence of the time-dilation effect in the burst durations, which is likely because a larger fraction of the bursts are buried under noisy background as the burst become dimmer at higher redshift.

Figure 29 shows the normalized distributions of both the GRB Sun angle (red bars) and the BAT boresight Sun angle (blue bars) (i.e., the angle between BAT's pointing direction and the Sun). For the GRB Sun angles, a 1σ error estimated from the Poisson distribution (i.e., $\sqrt{N}$) for each bin is also plotted. The normalized numbers for the BAT boresight Sun angle are calculated from the Sun angle recorded every 5 s (excluding the time during SAA and spacecraft slews) from 2005 to August 2015. Thus, the number for the BAT boresight Sun angle represents the fraction of time that BAT spends at each Sun angle.

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Both distributions generally follow the sinθ shape (where θ is the Sun angle), which is expected from the amount of solid angle covered by the same angular range δθ (for example, there is more area covered within 80°–90° than from 170° to 180°). This relation of the solid angle versus Sun angle is shown as the black lines in the plots. The sharp drop off for the BAT boresight Sun angle at around 40° is due to the Sun constraints for the XRT, UVOT, and the star-tracker at ∼44°.³⁷ There are some GRBs detected with Sun angle less then ∼44° because the BAT has a large field of view. These bursts will have Sun constraints for prompt XRT and UVOT observations. This figure shows that the number of GRB detections generally follows the fraction of time that BAT spends at the location. The GRB detection rate seem to be slightly lower than average when BAT is pointing close to the Sun. However, this effect is not very significant and is still consistent with the BAT pointing time (the blue bars) within ∼2–3σ of the Poisson errors from the number of detections.

Similar to Figure 29, the distributions of the Moon angles for both the GRBs (red bars) and the BAT boresights (blue bars) are plotted in Figure 30. The number of GRB detections also follows the fraction of time that BAT spends at each Moon angle location, as expected. Again, the drop off at ∼20° in the distribution of the BAT boresight Moon angle is due to the Moon constraints for XRT, UVOT, and the star tracker at ∼19° (see footnote 37)).

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We perform a study of the false-detection rate in order to find a reliable criteria to search for weak emission. To quantify the false detection rate, we estimate the signal-to-noise ratio using background locations around GRBs. We choose the background locations to be ∼1° from the GRBs (so most of the time the background detection is from the same images as the GRB detections), and also ∼1° from other X-ray sources. We adopt the X-ray source list from Krimm et al. (2013).

We quantify the false-detection rate R_false in a particular energy band with a specific signal-to-noise ratio threshold as follows,

$$\begin{eqnarray}&&{R}_{{\rm{false}}}=\displaystyle \frac{N\,(\gt {\mathrm{SNR}}_{\mathrm{lim}})}{{N}_{{\rm{tot}}}},\end{eqnarray} \tag{ 7 }$$

where $N(\gt {\mathrm{SNR}}_{\mathrm{lim}})$ is the number of survey images with the background signal-to-noise ratio at the specific location higher than the assigned threshold. ${N}_{{\rm{tot}}}$ is the total number of survey images we included in the search, that is, the subset of all survey images that are close to GRB trigger times, as described above. Note that because of the different event data ranges for the earlier mission time and the later mission time, the false-detection rate study uses images that satisfy criterion 1 mentioned in previous section. The image exposure times can vary from ∼300 to ∼2500 s, with the majority of the exposure time around few hundred seconds. Ideally, one would require the observation time of each image to be identical to have a fair comparison of the signal-to-noise ratio in each image. However, because the survey process (Baumgartner et al. 2013) only produces one image for each observation (i.e., using the "SNAPSHOT" option in batsurvey³⁸), our estimation can only based on these images with different exposure times. To produce survey images with finer time bins in each observation (i.e., using the "DPH" option in batsurvey³⁸), one would need to re-process all survey data and the process will take ∼ months to years to finish, and hence would be beyond the scope of this paper.

We quantify the false-detection rate for a range of different signal-to-noise ratio thresholds (from ∼2.0 to ∼5.0) in different energy bands. The energy ranges we tried include the eight energy bands used by the survey process (14–20 keV, 20–24 keV, 24–35 keV, 35–50 keV, 50–75 keV, 100–150 keV,150–195 keV), the total energy band (14–195 keV), an energy band that combines the three soft bands (14–35 keV), and an energy band that covers the three energy bands with the largest effective area (35–100 keV).

Figure 31 shows an example of the resulting histogram of the signal-to-noise ratio at the background locations in images with energy 14–195 keV. Table 5 lists some of our calculations of false-detection rate in the most interesting ranges of signal-to-noise ratio threshold. The numbers in parenthesis following each false-detection rate are the expected numbers of false detections out of the whole image samples in our study (i.e., a total number of 19,182 images).

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We investigate the expected detection rate for each criteria, and select some potentially useful criteria to perform further tests by calculating the signal-to-noise ratios at the GRB locations. This gives us a total number of real detections plus false detections at each GRB location. We search through each criterion until we find one that gives the largest ratio of the number of detections at the GRB location ${N}_{\mathrm{GRB}\_\mathrm{locations}}$ (i.e., number of real plus false detections) over the number of detections at the background locations ${N}_{\mathrm{bgd}\_\mathrm{location}}$ (i.e., false detections). In other words, we demand the ratio

$$\begin{eqnarray}&&{r}_{{\rm{detect}}}\equiv \displaystyle \frac{{N}_{\mathrm{GRB}\_\mathrm{locations}}}{{N}_{\mathrm{bgd}\_\mathrm{location}}}=\displaystyle \frac{N(\mathrm{real}\,+\,\mathrm{false})}{N(\mathrm{false})}\end{eqnarray} \tag{ 8 }$$

to be as large as possible.

Table 6 presents a list of criteria that we tried, and the results of false-detection rates, actual number of detections at the GRB locations, and the number of detections at the background locations. Sometimes each location can have multiple detections at different times. Thus, the numbers in detected locations (i.e., each location only counted once even when they are detected at different times) are shown in the parenthesis. The criterion using images with the energy band 14–195 keV and signal-to-noise ratio threshold above 4.3 sigma turns out to be the one that has the highest r_detect. We thus adopt this criterion to search for possible emissions in survey data. Results are summarized and discussed in Section 6.⁴⁰

Table 9 contains some general information of the bursts. Information from these two tables are shown in one single list in the complete online version. They are divided into two tables in the abbreviated paper version due to the limited space.

Table 10 lists the start and end time of T₁₀₀, T₉₀, T₅₀, and the 1 s peak duration, relative to the BAT trigger time.

Table 11 summarizes the best-fit model for each burst. "PL" refers to simple power-law model; "CPL" refers to cutoff power-law model. If there is no acceptable spectral fit for the burst (see Section 3.1 for the criteria), the best-fit-model column is listed as "N/A."

Table 12 shows a list of parameters from the spectral fit using the simple power-law model.

Table 12.  The Format of the Table that Presents the Parameters from the PL Fit for the Time-averaged (T₁₀₀) Spectra

Column	Format	Unit	Description
GRBname	A9	⋯	GRB name.
Trig_ID	I11	⋯	Special ID associated with each triggers.
			For GRBs found in ground analysis,
			the ID are associated with the trigger ID of the failed event data,
			or the full observation ID of the event data for the analysis.
alpha	A13	⋯	αPL as defined in Equation (1).
alpha_low	A13	⋯	The lower limit of αPL.
alpha_hi	A13	⋯	The upper limit of αPL.
norm	A12	ph cm−2 s−1 keV−1	The normalization factor ${K}_{50}^{{\rm{PL}}}$, as defined in Equation (1).
norm_low	A12	ph cm−2 s−1 keV−1	The lower limit of ${K}_{50}^{{\rm{PL}}}$.
norm_hi	A12	ph cm−2 s−1 keV−1	The upper limit of ${K}_{50}^{{\rm{PL}}}$.
chi2	F6.2	⋯	χ2 from the fitting, reported by XSPEC.
dof	I2	⋯	degree of freedom from the fitting, reported by XSPEC.
reduced_chi2	F6.4	⋯	reduced χ2 (i.e., χ2 divided by the degree of freedom),
			reported by XSPEC.
null_prob	A12	⋯	The null probability of the model, reported by XSPEC.
enorm	F7.4	KeV	The normalization energy, which is set to 50 keV in our fits,
			as shown in Equation (1).
Exposure_time	A6	s	The time interval of the spectrum.
T100_start	A11	s	The start time of the spectrum,
			relative to the BAT trigger time.
T100_stop	A11	s	The end time of the spectrum,
			relative to the BAT trigger time.

Note. Note that this table includes the fit for every GRB, regardless of whether the fit is acceptable from the criteria listed in Section 3.1. A list of GRBs with acceptable fits can be found in Table 11.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 13 shows the photon fluxes in different energy ranges from the simple power-law fit.

Table 14 shows the energy fluxes in different energy ranges from the simple power-law fit.

Table 15 shows the energy fluences in different energy ranges from the simple power-law fit. The energy fluences are calculated by multiply the flux by T₁₀₀.

Similar to the tables for the simply PL fits, Tables 16 to 15 present the parameters, fluxes, and fluences for the CPL fits.apjaa2e74t17

Table 24.  The Format of the Table that Presents the Parameters from the CPL Fit for the 1 s Peak Spectra

Column	Format	Unit	Description
GRBname	A9	⋯	GRB name.
Trig_ID	I11	⋯	Special ID associated with each triggers.
			For GRBs found in ground analysis,
			the ID are associated with the trigger ID of the failed event data,
			or the full observation ID of the event data for the analysis.
alpha	A13	⋯	αCPL as defined in Equation (2).
alpha_low	A13	⋯	The lower limit of αCPL.
alpha_hi	A13	⋯	The upper limit of αCPL.
Epeak	A12	keV	Epeak as defined in Equation (2).
Epeak_low	A12	keV	The lowe limit of Epeak.
Epeak_hi	A12	keV	The upper limit of Epeak.
norm	A12	ph cm−2 s−1 keV−1	The normalization factor ${K}_{50}^{{\rm{CPL}}}$, as defined in Equation (2).
norm_low	A12	ph cm−2 s−1 keV−1	The lower limit of ${K}_{50}^{{\rm{CPL}}}$.
norm_hi	A12	ph cm−2 s−1 keV−1	The upper limit of ${K}_{50}^{{\rm{CPL}}}$.
chi2	F6.2	⋯	χ2 from the fitting, reported by XSPEC.
dof	I2	⋯	degree of freedom from the fitting, reported by XSPEC.
reduced_chi2	F6.4	⋯	reduced χ2 (i.e., χ2 divided by the degree of freedom),
			reported by XSPEC.
null_prob	A12	⋯	The null probability of the model, reported by XSPEC.
enorm	F7.4	KeV	The normalization energy, which is set to 50 keV in our fits,
			as shown in Equation(1).
Exposure_time	A6	s	The time interval of the spectrum.
Peak_start	A11	s	The start time of the spectrum,
			relative to the BAT trigger time.
Peak_stop	A11	s	The end time of the spectrum,
			relative to the BAT trigger time.

Note. Note that this table includes the fit for every GRB, regardless of whether the fit is acceptable from the criteria listed in Section 3.1. A list of GRBs with acceptable fits can be found in Table 20.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 28.  The Format of the Table that Presents the Parameters from the PL Fit for the 20 ms Peak Spectra

Column	Format	Unit	Description
GRBname	A9	⋯	GRB name.
Trig_ID	I11	⋯	Special ID associated with each triggers.
			For GRBs found in ground analysis,
			the ID are associated with the trigger ID of the failed event data,
			or the full observation ID of the event data for the analysis.
alpha	A13	⋯	αPL as defined in Equation (1).
alpha_low	A13	⋯	The lower limit of αPL.
alpha_hi	A13	⋯	The upper limit of αPL.
norm	A12	ph cm−2 s−1 keV−1	The normalization factor KPL50, as defined in Equation (1).
norm_low	A12	ph cm−2 s−1 keV−1	The lower limit of ${K}_{50}^{{\rm{PL}}}$.
norm_hi	A12	ph cm−2 s−1 keV−1	The upper limit of ${K}_{50}^{{\rm{PL}}}$.
chi2	F6.2	⋯	χ2 from the fitting, reported by XSPEC.
dof	I2	⋯	degree of freedom from the fitting, reported by XSPEC.
reduced_chi2	F6.4	⋯	reduced χ2 (i.e., χ2 divided by the degree of freedom),
			reported by XSPEC.
null_prob	A12	⋯	The null probability of the model, reported by XSPEC.
enorm	F7.4	KeV	The normalization energy, which is set to 50 keV in our fits,
			as shown in Equation (1).
Exposure_time	A6	s	The time interval of the spectrum.
Peak_start	A11	s	The start time of the spectrum,
			relative to the BAT trigger time.
Peak_stop	A11	s	The end time of the spectrum,
			relative to the BAT trigger time.

Note. Note that this table includes the fit for every GRB, regardless of whether the fit is acceptable from the criteria listed in Section 3.1. A list of GRBs with acceptable fits can be found in Table 27.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image