Instrumental Tip-of-the-iceberg Effects on the Prompt Emission of Swift/BAT Gamma-ray Bursts

Gamma-ray bursts (GRBs) are the most powerful explosions in the universe, ejecting a fraction of the Sun's rest mass energy in a matter of seconds. The most popular framework describing the GRB phenomenon assumes an accretion disk is formed around a compact object—either a rapidly spinning magnetar or a stellar-mass black hole—which has been recently produced by the core collapse of a massive star (Colgate 1968; Woosley et al. 1993; Galama et al. 1998; Hjorth et al. 2003) or the coalescence of two compact objects (Abbott et al. 2017; Eichler et al. 1989; Narayan et al. 1992; Tanvir et al. 2013). The accretion disk flows onto the compact object and powers a bipolar jet, accelerating particles (e.g., electrons, positrons, baryons) to highly relativistic speeds (Cavallo & Rees 1978; Rees & Meszaros 1992). As the highly energetic particles cool within the jet, gamma rays are produced via emission mechanisms such as synchrotron, Comptonization, inverse Compton, and photospheric processes, among others; this is called the prompt-emission phase of GRBs (Rees & Meszaros 1994; Piran 1999, 2004). The relativistic flow continues to propagate until the jet sweeps up enough circumburst and interstellar medium to quickly decelerate in a relativistic collisionless shock; this is the afterglow phase (Sari et al. 1998; Wijers & Galama 1999). Prompt emission is characterized by a bright flare of gamma rays that may last anywhere between a fraction of a second to hundreds of seconds and is mostly observed in the ∼kiloelectronvolt to ∼megaelectronvolt range, but can sometimes be observed down to optical wavelengths and up to gigaelectronvolt gamma rays (Akerlof et al. 1999; Hurley et al. 1994). The afterglow phase can be observed for hours to, occasionally, hundreds of days across the entire electromagnetic spectrum, down to radio frequencies and up to gigaelectronvolt gamma rays (Costa et al. 1997; Frail et al. 1997; van Paradijs et al. 1997; Atkins et al. 2000).

The duration of GRB prompt emission is traditionally measured using the T₉₀ algorithm, the duration which encompasses 5%–95% of the observed gamma-ray photon fluence within the 50–300 keV band in the observer frame (Kouveliotou et al. 1993). There is an observed bimodality in the T₉₀ distribution separated into short GRBs (SGRBs, T₉₀ ≲ 2 s) and long GRBs (LGRBs, T₉₀ ≳ 2 s) (Kouveliotou et al. 1993). Coincidental detections between compact-binary mergers and SGRBs (Abbott et al. 2017; Tanvir et al. 2013) and between stripped-envelope core-collapse supernovae and LGRBs (Colgate 1968; Galama et al. 1998; Hjorth et al. 2003)provide a natural explanation for the observed dichotomy. Therefore, it is common to use T₉₀ measurements to infer GRB progenitor systems (e.g., either a collapsar or a compact-binary merger, T₉₀ ≥ 2 s and T₉₀ ≤ 2 s, respectively). However, the T₉₀ is not the intrinsic duration of a GRB: instrumental effects and observing conditions lower the signal-to-noise ratio (S/N) of an observed GRB, leading to T₉₀ measurements shorter than the true duration (Hakkila et al. 2000). These effects are instrument dependent (e.g., instrument energy bandpass, time resolution) and lead to differences in the T₉₀ distribution made with observations from different telescopes (see Figure 7 of Lien et al. 2016; Paciesas et al. 1999; Sakamoto et al. 2011; Bromberg et al. 2012; Svinkin et al. 2016; Tsvetkova et al. 2017; von Kienlin et al. 2020). The percentage of GRBs measured to be SGRBs by the Compton Gamma-Ray Observatory Burst And Transient Source Experiment (CGRO/BATSE), Fermi Gamma-Ray Space Telescope Gamma-ray Burst Monitor (Fermi/GBM), and Swift/Burst Alert Telescope (BAT) all differ from one another (i.e., ∼26%, ∼17%, and ∼10%, respectively; Paciesas et al. 1999; Lien et al. 2016; von Kienlin et al. 2020). It has even been argued that the separation time between SGRBs and LGRBs should vary depending on the instrument used (Bromberg et al. 2012). Furthermore, T₉₀ distributions do not typically include measurement uncertainties, which have a significant influence on the shape of the distributions and the separation of the SGRB and LGRB populations. A more robust method to determine the progenitor system is to use both spectral information and the T₉₀ measurement of a GRB, as SGRBs are typically observed with harder spectra than LGRBs (Dezalay et al. 1992; Kouveliotou et al. 1993). There have been proposals to establish a new classification system for GRBs by separating them into Type I and Type II GRBs (e.g., GRBs with compact-merger progenitors and those with supernova progenitors, respectively), which separate themselves when considering specific combinations of their observables (Gehrels et al. 2006; Zhang 2006; Lü et al. 2010; Minaev & Pozanenko 2020).

The trigger methods of an instrument also impact observed T₉₀ distributions. Frontera et al. (2009) found a discrepancy between the number of SGRBs detected with the Gamma-Ray Burst Monitor (GRBM) aboard BeppoSax compared to the number detected by CGRO/BATSE. For the majority of the mission, the BeppoSax/GRBM trigger system used a 1 s integration time to search for SGRBs, leading to a low triggering efficiency for SGRBs (Frontera et al. 2009).

Littlejohns et al. (2013) simulated a sample of low-redshift GRBs observed by Swift/BAT at higher redshifts to witness the evolution of their measured durations. The authors found that while time dilation always lengthens light-curve duration, measured durations are strongly impacted by the loss of burst structure into background noise as the S/N decreases. It was also shown that the relation between measured duration and redshift is highly dependent on the structure of the burst.

Measurements of GRB durations are sensitive to the observing conditions and the distance to the object. For instance, Kocevski & Petrosian (2013) investigated how accurate the T₉₀ measured by CGRO/BATSE was as a proxy for the intrinsic duration of a GRB. To do so, they simulated GRBs with fast rise exponential decay (FRED) light curves and folded them through BATSE instrument response functions. They found that the lack of very high T₉₀ values due to time dilation for high-redshift GRBs may be explained by low S/N; in some cases as much as 90% of the emission is buried into the noise, leading to T₉₀ measurements that significantly underestimate the intrinsic durations of the bursts in the observer frame.

It is recommended to use both spectral and temporal information to predict GRB progenitor systems, yet this does not always result in a clear answer (Kouveliotou et al. 1993). Only by directly observing a signal from the progenitor system (i.e., the supernova from a collapsar or the gravitational-wave signal from a compact-binary merger) can the type of progenitor be confirmed. GRB200826A is a SGRB characterized by a sharp pulse (T₉₀ ∼ 1.1 s, z = 0.748) and no evidence of any dim, long-lasting emission; this would infer a compact-binary merger progenitor (Mangan et al. 2020). However, the spectral behavior and energetics of the event were consistent with LGRBs from collapsar progenitors (Zhang et al. 2021). Additionally, the host galaxy is a low-mass, star-forming galaxy, typical for LGRBs (Rossi et al. 2021). Follow-up observations reveal excess emission in the afterglow light curve that cannot be explained as kilonova emission, but is consistent with supernova emission, which confirms that the progenitor system was a collapsar (Ahumada et al. 2021). Lü et al. (2014) have suggested that the "amplitude" of the GRB prompt emission, defined as the ratio between the measured peak flux and the flux background, is a necessary criterion to include to classify GRBs in order to distinguish between long/soft and short/hard GRBs. They also find that most SGRBs are likely not the "tip-of-the-iceberg" of LGRBs, but also show that most LGRBs would appear as rest-frame SGRBs above a certain redshift.

In this study we investigate the accuracy of T₉₀ measurements made by Swift/BAT as estimates of the intrinsic GRB prompt-emission durations. In Section 2, we describe Swift/BAT and introduce the instrument parameters which most significantly influence S/N. In Section 3, we describe the GRB sample used for our analysis. In Section 4, we outline our analysis methods. In Section 5, we discuss our results and their implications on the Swift/BAT GRB population.

Swift was launched on 2004 November 20. Swift is a space-based multiwavelength observatory comprised of three instruments: a wide-field gamma-ray detector (BAT), a narrow-field X-Ray Telescope (XRT), and a narrow-field Ultra-Violet/Optical Telescope (UVOT; Gehrels et al. 2004; Barthelmy et al. 2005; Burrows et al. 2005; Roming et al. 2005).

Swift/BAT is a coded-mask aperture instrument with a 1.4 steradian field of view when half-coded (i.e., ∼10% of the sky) and is able to localize sources to within a few arcminutes (Barthelmy et al. 2005). The coded-mask aperture allows for imaging of photons between 15 and 150 keV, but the telescope is able to observe noncoded photons up to ∼350 keV. In this work we investigate how the observing conditions of Swift/BAT influence the accuracy of T₉₀ measurements. Namely, we investigate the effects due from changes in the active number of enabled detectors, the angle of the source from the detector bore sight, and average background level. These three parameters were found to have the strongest impact on duration measurements made by Swift/BAT; each parameter is described below.

2.1. Detector Plane versus Time

At the start of the mission, Swift/BAT had 32,768 CdZnTe detectors (each 4 × 4 × 2 mm); however, as the instrument has aged, some detectors have become permanently noisy and are therefore turned off; this results in the number of enabled detectors steadily decreasing (see Figure 1(a)). In 2019, the yearly averaged number of enabled detectors (NDETS) was ∼16,000. In 2020, due to a series of controlled reboots performed on the BAT instrument, the yearly averaged NDETS increased to ∼18,000. Although we display the yearly averaged NDETS in Figure 1(a), some observations have reached NDETS levels as low as ∼10,000. As the number of enabled detectors reduces, so too does the instrument sensitivity (see Figure 4 in Lien et al. 2014).

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2.2. Incident Angle from Detector Bore Sight

The coded-aperture mask technique is useful in X-ray and gamma-ray astronomy because it allows an instrument to have a large field of view while maintaining imaging capabilities for improved source localization (Barthelmy et al. 2005); however, the sensitivity of coded-mask instruments quickly decreases as the incident angle of the source with respect to the telescope bore sight, θ_inc, increases (see Figure 2 in Lien et al. 2014). The coded-aperture method defines the partial coding fraction (PCODE) as the fraction of the detector illuminated by a source through the mask. It is correlated to the source incident angle, but it also accounts for instrument geometry; PCODE = 1 corresponds to an on-axis observation and a fully illuminated detector plane, PCODE = 0 indicates an incident angle of ≳70°. The PCODE accounts for the noncircularity of the Swift/BAT field-of-view contours on the detector plane. The contours are not rotationally symmetric around the detector bore sight due to the geometry of the detector (Barthelmy et al. 2005). The PCODE reflects the effective area of the Swift/BAT detector plane in use during an observation.

The distributions of PCODE and θ_inc are displayed in Figure 2(a). The distributions are created from the PCODE and θ_inc values reported for all GRBs in the Swift/BAT GRB catalog data tables. The PCODE and θ_inc reported are the values taken at the time of the GRB trigger. We can see that the PCODE distribution is somewhat uniformly distributed, but has a peak at PCODE = 1. The θ_inc distribution is a combination of the cosine effect from projecting a three-dimensional sphere onto a two-dimensional plane, and the decrease in sensitivity at larger incident angles. In Figure 2(b) the PCODE and θ_inc values for all Swift/BAT GRBs are shown. From this plot we can see how the θ_inc distribution can spread out into the PCODE distribution we observe. A PCODE = 1 can be obtained even at θ_inc ∼ 20° depending on the ϕ angle of the source relative to the detector plane.

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2.3. Average Background Level

2.4. Trigger Methods

In order to investigate the effects that observing conditions have on GRB prompt-emission duration, we will apply a duration-measurement algorithm similar to the one employed by the standard Swift/BAT pipeline to a sample of light curves. In this initial study, we focus on light curves with a "simple-pulse" shape, where "simple-pulse" light curves are designated as either "FRED-like" if the light curve has a rise and fall similar to a FRED light curve or as "symmetric-like" if the light curve rises and falls more gradually and symmetrically. It should be noted that our definition of simple-pulse structure is not and need not be rigorous, but is used as a loose guide line to select bursts with relatively simple structure as compared to the more complex bursts (e.g., with multiple bright peaks or multiple emission periods). Although we use simple-pulse light curves, we have selected light curves with a few unique features in order to investigate how light-curve phenomenology plays a role in the accuracy of the T₉₀. In the next sections we describe how we generated or selected and prepared the synthetic and real light-curve samples.

3.1. Synthetic FRED Light Curves

To create ideal benchmark cases for our results, we created four synthetic FRED light curves. We use the Hakkila & Preece (2014) FRED function form:

$$\begin{eqnarray}&&I(t)=A\lambda {e}^{[-{\tau }_{1}/(t-{t}_{s})-(t-{t}_{s})/{\tau }_{2}]},\end{eqnarray} \tag{ 1 }$$

where A is the pulse amplitude, t_s is the pulse start time, τ₁ and τ₂ characterize the pulse rise and decay, respectively, and $\lambda \,={e}^{[2{({\tau }_{1}/{\tau }_{2})}^{1/2}]}$. The pulse peak time occurs at ${t}_{\mathrm{peak}}={t}_{s}+\sqrt{{\tau }_{1}{\tau }_{2}}$ (Hakkila & Preece 2014). The parameters used to create our benchmark FRED light curves are displayed in Table 1 and the corresponding light curves are shown in Figure 3. We vary the count rate in each time bin according to a Gaussian centered on the theoretical count rate with a standard deviation equal to the square root of the count rate (i.e., ${N}_{\mathrm{FRED}}(t)={Norm}(\mu \,=I(t),\sigma =\sqrt{I(t)})$). We analytically find the T₉₀ of each, where the T₉₀ is defined as the duration which encompasses 5%–95% of the total fluence (see the rightmost column in Table 1). For all four FREDs, we set the spectrum in the 15–350 keV band as a power law (PL) with a photon index of α = −1, a typical photon index found in Swift/BAT GRBs (Lien et al. 2016). For our sample of FRED light curves, we keep all parameters the same except the amplitudes. The amplitude values are selected to produce FRED light curves with mask-weighted count rates similar to those found for typical Swift/BAT GRBs.

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Table 1. Sample of Synthetic FRED Light Curves (Hakkila & Preece 2014)

Label	A	ts	τ1	τ2	Fluence	T90
	(counts s−1)	(s)			(erg cm−2)	(s)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
FRED1	20000	−0.1	1	4.5	1.44 × 10−5	14.14
FRED2	9000	−0.1	1	4.5	6.07 × 10−6	14.13
FRED3	5000	−0.1	1	4.5	3.64 × 10−6	14.17
FRED4	2500	−0.1	1	4.5	1.54 × 10−6	14.14

Note. A is the pulse amplitude, t_s is the pulse start time, τ₁ and τ₂ characterize the pulse rise and decay. The total fluence and T₉₀ of the synthetic light curves are reported in columns 6 and 7, respectively.

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3.2. Real GRB Light Curves

We select a sample of eight real Swift/BAT-detected GRBs observed between 2009 and 2015. Simple-pulse burst structure was determined by visual inspection upon observation with Swift/BAT. ⁸ We briefly describe the shape of each burst in the rightmost column of Table 2 and display the corresponding light curves in Figure 9. GRB data were taken from the online Swift/BAT Gamma-Ray Burst Catalog. ⁹

Table 2. Sample of LGRBs with a "Simple-pulse" Shape.

GRB Name	z	T90	Fluence	α	PCODE	θinc	S/N	Description
		(s)	(erg cm−2))
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
GRB160314A	1.726	8.73	3.75 × 10−07	−1.53	0.75	1969	14.18	Dim GRB
GRB150314A	1.76	14.8	5.13 × 10−05	−1.08	0.344	351	256	FRED-like with dim tail
GRB120119A	1.73	68.0	3.17 × 10−05	−1.38	1.02	513	45.46	Symmetric-like
GRB110422A	1.77	25.8	5.56 × 10−05	−0.831	0.227	447	27.95	Symmetric-like
GRB090510	0.903	5.664	1.46 × 10−06	−1.06	0.162	4607	145.49	Short, hard spike
								with soft tail
GRB071010B	0.947	36.124	6.21 × 10−06	−1.97	0.8438	2904	52.96	FRED-like with dim
								pretrigger emission
GRB051111	1.55	64.0	7.94 × 10−06	−1.32	0.594	272	37.09	Broad FRED-like
GRB050219A	0.211	23.8	4.53 × 10−06	−0.124	0.232	431	14.69	Symmetric-like

Note. All values reported in the table are from the online Swift/BAT Gamma-Ray Burst Catalog. The observatories and methods used to measure the redshift, z, for each burst are cited in the Swift/BAT GRB catalog. The T₉₀, fluence, and the spectral index, α, are all measured by Swift/BAT. The PCODE describes the effective area of the Swift/BAT detector plane in use during the observation. The PCODE is related to the incident angle of the source from the detector bore sight, θ_inc (see Figure 2). The observed rate S/N ratio (as opposed to image S/N) is given in the second-to-last column. A short description of the burst light curve is given in the final column. The light curves can be seen in Figure 9.

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Our simulations use the light curves of GRBs observed by Swift/BAT, meaning that they have already been affected by instrumental parameters; because of this our results should be considered self-consistent and not used to infer the intrinsic behavior for the GRBs they came from.

For our analysis we define ${T}_{90}^{\mathrm{BAT}}$ (T ${}_{100}^{\mathrm{BAT}}$) as the duration which encompasses 5%–95% (0%–100%) of the light-curve background-subtracted count fluence in the 15–350 keV band in the observer frame (i.e., the Swift/BAT band). ${T}_{90}^{\mathrm{BAT}}$'s calculated for template light curves (i.e., before folding the light curve with the instrument response function) represent the true ${T}_{90}^{\mathrm{BAT}}$ of the light curve and are thus designated ${T}_{90,\mathrm{true}}^{\mathrm{BAT}}$. ${T}_{90}^{\mathrm{BAT}}$'s measured for simulated light curves (i.e., after folding with the instrument response function) are designated as ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$.

We study how observing conditions affect the ${T}_{90}^{\mathrm{BAT}}$ of synthetic FRED light curves and real simple-pulse GRB light curves. To do so, we fold template light curves through Swift/BAT instrument response functions at varying observing conditions and use a Bayesian block method to measure their ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ values (Scargle 1998). A detailed description of our simulation method is given below. A simple schematic of the pipeline is shown in Figure 4.

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We generate template light curves from Equation (1) and from our sample of real Swift/BAT GRBs. Swift/BAT light-curve counts are reported as mask-weighted count units, which are defined as "background subtracted counts per fully illuminated detector for an equivalent on-axis source" ¹⁰ (Markwardt et al. 2007). This means counts per detector per sec may be negative when close to the background level (top plot in Figure 5). For our light-curve templates we only select the positive counts of the background-subtracted and detector-corrected emission that occurred during the T₁₀₀ interval reported by the Swift/BAT team; ¹¹ by doing so, we are assuming all the positive counts in a template light curve come from real burst emission. An example of this process used on the light curve of GRB050219A is shown in Figure 5. The template light curves (with units of photons det⁻¹ s⁻¹) are turned into template energy flux curves (with units erg det⁻¹ s⁻¹) by multiplying by the average energy per photon. The average energy per photon is found by taking the ratio of the integral of the spectrum across the 15–350 keV band and the total number of photons in the template light curve. This is necessary to convolve the template light curve with the instrument response function.

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Following the procedure in Lien et al. (2014), we simulate the light curve Swift/BAT would observe for any given energy flux light curve, spectrum, and set of instrument parameters (e.g., angle of incidence, number of activated detectors, background level). ¹² The best-fitting spectral function for most GRBs in the Swift/BAT GRB catalog is typically a PL but can occasionally be a cut-off power law (CPL) when the break energy is within or near the 15–350 keV band. Both of these spectral functions can be approximated by a Band function when considering the spectrum in a narrow energy band. In this work, we assume a Band function spectrum for all GRBs with the observed spectral index and, when observable, break energy (Band et al. 1993). For the spectrum of each burst we use the best-fit time-integrated spectral function and parameters reported in the BAT GRB catalog (Lien et al. 2016). One limitation of using the Band function is that the bolometric integration of the Band function evaluates to infinity if a low-energy PL index of ≤−2 is used. For this reason any burst used as a template in our pipeline with an observed PL index of α_PL ≤ −2 has its index set to α_BAND = −1.99. We do not include any GRBs with α_PL ≤ −2 in the sample used in this work.

We keep the spectrum constant throughout the duration of a GRB to reduce the computational resources required during simulations, meaning there is no time-evolution of the spectra, although the pipeline is able to use evolving spectra if desired. We have found that bursts with more complex structure than a FRED-like simple pulse (i.e., multipulsed or extended emission) are not well represented by a constant spectrum. For the simple-pulse sample used in this work, we find that using a constant spectrum produces results that do not differ significantly from results obtained using time-dependent spectra.

The Swift/BAT response function depends on the source incident angle and azimuthal angle in relation to the detector plane. For our simulations we split the detector plane into 31 regions, following the work of Lien et al. (2014; see their Figure 1). Each region is assigned a unique instrument response function that well represents the instrument response at that location on the detector plane. We label each region with a GridID number running from 1 to 33 (the grid spaces 06 and 28 are unused). The GridID serves as a proxy to specifying the burst incident and azimuthal angles (and, hence, also a proxy of the PCODE). For each simulation we specify a PCODE to use and we then find the GridID with the nearest PCODE value. The selected GridID designates which response function to use for the simulation. GRB spectra are convolved with Swift/BAT response functions in order to calculate observed count rates in each Swift/BAT energy channel. The count rates are then scaled by a factor to accurately reflect the instrument sensitivity at different numbers of enabled detectors (i.e., a factor of NDETS/32,768).

By multiplying the template energy flux light curves by the average rates found from the synthetic spectra, we create synthetic-source light curves. To create synthetic observed light curves which represent light curves that Swift/BAT would have observed for a particular set of observing conditions, we add a flat background to the synthetic-source light curves and, following the procedure used for the FRED light curves, we fluctuate the counts in each time bin according to a Gaussian distribution centered around the expected number of counts in order to simulate statistical noise fluctuations (i.e., ${N}_{\mathrm{obs}}(t)={Norm}({N}_{\mathrm{source}}(t),\sqrt{{N}_{\mathrm{source}}(t)})$).

Our simulations are evaluated using three NDETS values, three PCODE values, and three average background levels. The NDETS values we use are approximately the yearly average number of enabled detectors in 2004, 2013, and some particularly low levels during observations made in 2019 (i.e., NDETS = 30,000, 20,000, and 10,000, respectively). The PCODE values we select represent an on-axis observation, a typical off-axis observation, and an extreme off-axis observation (i.e., PCODE = 1, 0.522, and 0.101, corresponding to θ_incident = 0°, 44988, and 64286, respectively). The background levels we select represent a very low background, a typical background, and a high background for Swift/BAT (e.g., ∼1000 c s⁻¹, ∼9500 c s⁻¹, and ∼22,000 c s⁻¹, respectively; see Figure 1(b)).

We test whether Swift/BAT would trigger on these simulated observed light curves by approximating the true Swift/BAT trigger search following the procedure in Lien et al. (2014). To measure the duration of the simulated light curves, we use the FTOOLS function battblocks ¹³ , which uses a similar Bayesian block-searching analysis as the pipeline used by the standard Swift/BAT ground analysis to determine burst durations. To correctly scale the S/N and the associated uncertainty in each time bin, mask weighting must be applied to the synthetic observed light curves. Proper mask weighting involves complex ray-tracing, as is done for official BAT products (Markwardt et al. 2007); we avoid this computationally intensive process by applying a simple and empirical mask-weighting approximation,

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{MaskWeightedLC}\\ \,\,=\,\displaystyle \frac{(\mathrm{LC}-\mathrm{Background})}{\cos ({\theta }_{i})\ast \mathrm{NDETS}\ast \mathrm{PCODE}\ast f(\mathrm{PCODE})},\end{array}\end{eqnarray} \tag{ 2 }$$

where "LC" is the count rate in each time bin of the synthetic observed light curve, "Background" is the average background of the light curve, BGDLVL, and θ_i is the angle of incidence. There is an additional light-curve efficiency factor that roughly depends on the PCODE of the observed burst: this factor is due to the fast Fourier transform convolution of the mask and the detector plane. To properly calculate the factor the Swift/BAT standard pipeline uses complex ray-tracing algorithms. In order to avoid the computationally intensive calculations, we calculated this correction factor for a sample of 100 GRBs and empirically fit the factors with a 2nd-order polynomial as a function of the PCODE; we include this as correction f(PCODE) (see Figure 6). The best-fit polynomial we found is given by

$$\begin{eqnarray}&&f=0.618\ast {\mathrm{PCODE}}^{2}-1.214\ast \mathrm{PCODE}+1.121.\end{eqnarray} \tag{ 3 }$$

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We then apply the battblocks algorithm to the mask-weighted light curves in order to obtain duration measurements for the synthetic observed light curves, ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$. We do not account for high-energy photons penetrating through instrument structure. While this may have an influence on bursts with particularly hard spectra, this is a small effect in any case.

The results of the simulations outlined in Section 4 show that the T₉₀ of simple-pulse GRB prompt emission measured by Swift/BAT are highly impacted by observing conditions. As observing conditions become worse, (i) T₉₀ measurements become increasingly biased toward shorter durations, and (ii) the measurement uncertainties become larger.

We report the ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ distributions for several sets of observing conditions for all synthetic and real GRBs in our sample in Appendix B. As the S/N of a simulated light curve decreases the bias on the ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ increases toward shorter durations, yet there does not appear to be a quantifiable trend as it is highly entangled with the shape of the light curve (see Section 5.1 and Appendix D). Light curves simulated with typical observing parameters for Swift/BAT (e.g., PCODE =1, 0.522; NDETS = 20,000; BGDLVL = 95,000 counts s⁻¹) were typically consistent in only ∼25%–45% of simulations (see Table 3).

Table 3. Fraction of Simulated Light Curves for which the Bayesian Block Algorithm Was Able to Obtain Duration Measurements

GRB Name	f(measurable)	f(consistent, 3σ)	f(consistent, 1σ)	T90,true	Ave. ${T}_{90,\mathrm{sim}}$	90% CI (s)
				(s)	(s)	68% CI (s)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
FRED1	0.914	0.826	0.271	14.14	11.62	[4.008, 15.108]
(1.44 × 10−5 erg cm−2)						[6.008, 14.108]
FRED2	0.787	0.828	0.329	14.13	10.86	[5.008, 14.108]
(6.07 × 10−6 erg cm−2)						[6.008, 14.108]
FRED3	0.709	0.618	0.259	14.17	10.22	[4.008, 15.108]
(3.64 × 10−6 erg cm−2)						[5.008, 14.108]
FRED4	0.571	0.468	0.224	14.14	8.64	[4.008, 14.108]
(1.54 × 10−6 erg cm−2)						[5.008, 12.108]
GRB160314A	0.289	0.440	0.346	8.64	6.95	[0.942, 9.442]
						[2.042, 9.042]
GRB150314A	0.990	0.120	0.069	16.0	11.14	[4.003, 19.103]
						[6.003, 15.103]
GRB120119A	0.911	0.182	0.074	83.0	47.41	[10.014, 107.314]
						[11.014, 89.214]
GRB110422A	0.999	1.000	0.880	25.0	24.35	[17.033, 27.133]
						[24.033, 26.133]
GRB071010B	0.799	0.516	0.472	36.0	20.988	[4.007, 39.208]
						[5.008, 38.208]
GRB051111	0.704	0.472	0.383	65.0	41.491	[7.017, 77.317]
						[8.017, 75.317]
GRB050219A	0.811	1.000	0.767	24.0	21.787	[13.013, 25.113]
						[19.013, 24.113]
GRB150314A	0.989	1.000	0.260	11.0	11.149	[4.004, 12.104]
(no dim tail)						[11.004, 12.104]
GRB090510	0.652	0.432	0.402	5.69	2.70	[0.064, 6.064]
						[0.164, 5.864]

Note. In addition, we calculate the fraction of ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ values consistent with ${T}_{90,\mathrm{true}}^{\mathrm{BAT}}$ to within 3σ and 1σ limits for simulations using realistic parameter combinations (e.g., PCODE = 1, 0.522; NDETS = 20,000; BGDLVL = 95,000 counts s⁻¹). The majority of bursts have f(consistent, 1σ) ∼25%–45%. GRB110422A is an exception, which we believe is due to the sharp shoulders seen on either side of the light curve. The Bayesian block analysis we use reports Gaussian uncertainties on duration measurements. In column 5, we report the T_90,true calculated for the 1 s resolution light curve used in the simulations. In column 6, we report the average ${T}_{90,\mathrm{sim}}$ calculated for all simulated light curves that were measurable by the Bayesian block algorithm. Lastly, in column 7, we report the 90% and 68% confidence interval (CI) for the sample.

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In the following sections we first discuss the measurement bias of ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ and the fluence as a function of S/N. We then discuss how low-intensity tails of GRB emission can be easily missed due to high background levels. Lastly, we discuss the possibility that some SGRBs observed by Swift/BAT have a chance of being collapsar events, which are typically associated with LGRBs.

5.1. Bias of ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ and Fluence Measurements as a Function of S/N

For analytical FRED light curves, the fraction of duration measurements made on simulated light curves which are consistent to within 1σ of the analytical duration of the FRED light curve, f(consistent, 1σ), decreases steadily as the fluence of the synthetic light curve decreases (see Table 3). This trend is similar to what Kocevski & Petrosian (2013) found for FRED light curves folded with the CGRO/BATSE instrument response function. Yet, there are no clear trends between S/N and the measurement bias of ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ for real GRB light curves (see Table 3 and distributions in Appendix B); this is consistent with the results of Littlejohns et al. (2013).

Of the three observing conditions we evaluated, lowering the PCODE of the source (i.e., increasing the source angle from the detector bore sight) causes the largest bias on duration measurements (i.e., lower ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$) and increases the uncertainty the most, followed by the average number of enabled detectors and background level. In Figure 7 we show that although the average ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ decreases as mask-weighted fluence decreases, distributions with similar fluence values show different structure depending on the observing conditions used in the respective simulations.

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In Figure 22 we display plots similar to the bottom plots shown in Appendix B, but made using the measured mask-weighted fluence of the simulated light curves in the 15–350 keV band, ${\text{}}{S}_{\mathrm{sim}}^{\mathrm{BAT}}$. The mask-weighting process means the fluence has already been background subtracted and corrected for PCODE. We see that the fluence distributions are more tightly constrained than the ${T}_{90,\mathrm{sim}}$ distributions for each combination of observing conditions. This is most likely because it is typically the dim emission at the beginning and end of a burst that is easily lost into the noise, while the bright main-emission periods of a burst remain visible. So, while the ${T}_{90,\mathrm{sim}}$ may have large variations, the fluence remains relatively similar for a particular combination of observing conditions. However, even though the mask-weighting process aims to correct the ${\text{}}{S}_{\mathrm{sim}}^{\mathrm{BAT}}$ measurements for different observing conditions, the process cannot recover signal that is already lost; this is why we see that fluence decreases over one to two orders of magnitude with decreasing PCODE, depending on the GRB simulated. The fluence decreases by a factor of a few between NDETS = 30,000 and NDETS = 10,000. The complete figure set of fluence plots for all GRBs in our sample are available in the online journal; the remaining fluence plots are similar to the example shown in Figure 22.

5.2. Dim-tail Emission

5.3. Collapsars Observed as SGRBs due to Observing Conditions

SGRBs are typically associated with compact-merger progenitor events, but there may be instances of collapsar events which are measured as SGRBs due to measurement bias arising from poor observing conditions. The template light curve generated from GRB160314A (T₉₀∼8.7; see Figure 9) is measured to have ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}\lt 2\,{\rm{s}}$ in ∼1% of all simulations; for these instances the progenitor system would be ambiguous if only the duration was considered. The duration distributions show a bimodal behavior (see Figure 14); some distributions are centered around the intrinsic duration while others display a strong instrument bias where most durations are measured to be ∼2.5 s (see Figure 8). This may indicate that some collapsar events are measured as SGRBs due to instrument bias.

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There is evidence that some SGRBs contain dim-tail emission that, if included as prompt emission, would increase the duration above 2 s and thus affect its classification as a SGRB. Connaughton (2002) applied the same background-subtraction method they applied to LGRBs to a sample of 100 SGRBs observed with CGRO/BATSE and found possible dim extended emission lasting for hundreds of seconds after the short, hard spike. Although, due to the low flux of the tail emission, the author does not claim if this is the same emission component found for the LGRB sample or, alternatively, if this emission is simply due to afterglow emission (Connaughton 2002). This latter option is supported by a study from Lazzati et al. (2001) who found X-ray afterglow in 76 short CGRO/BATSE GRBs by summing the four channel BATSE light curves. The emission peaked ∼30 s after the short, hard spike of the prompt emission (Lazzati et al. 2001). There is theoretical support that afterglow emission from SGRBs will be separated from the prompt pulse by tens of seconds, while in LGRBs the afterglow will overlap the prompt emission (Sari & Piran 1999). The former option is supported by Dichiara et al. (2021), wherein the authors applied careful data reduction to eight Swift/BAT GRBs (all with T₉₀ < 2 s and z ≥ 1) and found that significant long, dim emission could be observed in four of the eight GRBs, which was not significant when using the standard Swift/BAT pipeline. This emission is found to be in excess of the X-ray afterglow emission and is therefore argued to be a prompt component. The authors show that the extended emission of GRB071227 would not be significant if the burst was at a higher redshift or was observed during a time of higher background (Dichiara et al. 2021).

We included GRB090510 (Figure 21) in our sample of real GRB light curves. The light curve comprises a short, hard spike (∼0.3 s) and a soft tail (∼5 s). When only considering Fermi/GBM observations, the burst looks to be a typical short, hard GRB (Guiriec et al. 2009; Ackermann et al. 2010), but when including Swift/BAT observations, which display dim but significant excess emission following the short pulse, and considering the initial rise in optical emission, the distinction between short or long GRB becomes more complex (De Pasquale et al. 2010; Guiriec et al. 2010).

Of the ∼65.2% simulated light curves that were bright enough to obtain Bayesian block measurements, ∼55% had ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}\lt 2$ s and the remaining had ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}\gt 2\,{\rm{s}}$. Although we do not know how many SGRBs may exhibit similar behavior, it may be true that there are other GRBs which appear to only have a hard, short spike, but in reality include a dim, soft tail, though due to poor observing conditions the tail was not able to be measured. To truly remove the degeneracy between SGRBs and LGRBs, more information must be included in addition to the observed burst duration (e.g., burst environment, spectral information, and instrument condition upon observation).

We summarize our findings as follows:

• 1.  
  The measured durations of simple-pulse GRB prompt-emission light curves observed with Swift/BAT are highly impacted by observing conditions. We see that, due to observing conditions, burst duration measurements commonly vary by ∼80% and fluence measurements can vary across two orders of magnitude.
• 2.  
  As instrument sensitivity decreases (i) T₉₀ measurements become increasingly biased toward shorter durations, and (ii) the uncertainty of the measurements become larger.
• 3.  
  We have shown that the PCODE has the strongest influence on measured duration and fluence, followed by the number of enabled detectors and then background level.
• 4.  
  Light-curve shape has a strong influence on the accuracy of a T₉₀ measurement, even between similar S/N events. Consequently, it is difficult to quantify the trend between the S/N and the accuracy of the T₉₀.
• 5.  
  For most GRBs in our sample, measured durations were consistent with their respective intrinsic durations only ∼25%–45% of the time.
• 6.  
  Poor observing conditions, such as low PCODE, low NDETS, or high backgrounds, can cause source light curves with T_90,true > 2 s to be observed with T_90,measured < 2. This finding brings into question the viability of classifying all progenitor systems of SGRBs as merger events.

Based on our results, it is clear that the shape of a light curve highly impacts how accurate the observed duration is compared to the intrinsic burst duration. It will be worth investigating a larger sample of real light curves. Cosmological distance effects will be presented in a future paper.

We note that some of our parameter combinations are not likely to occur. In reality, the background stays near constant at ∼0.3 counts s⁻¹ per detector. A background of 1000 counts s⁻¹ will most likely not occur in reality, but it is a good reference point to compare to for this study. Additionally, a PCODE of 0.1 is uncommon. Although it is not expected currently, NDETS = 10,000 may be a reality in the future as the detector plane of Swift/BAT continues to degrade. In Table 3 we report the fraction of simulations with T₉₀ measurements consistent with the intrinsic light curve T₉₀, using only simulations with typical observing conditions (e.g., PCODE = 1, 0.522; NDETS = 20,000; BGDLVL = 95,000 counts s⁻¹). These fractions cannot be applied as correction factors to the Swift/BAT GRB population because the values of f(consistent,1σ) range from ∼7% to ∼88%, indicating that light-curve shape has a significant impact on the measured duration.

The durations of GRBs are important quantities that help infer progenitor systems and constrain physical processes of the bursts, yet the duration measurements are highly impacted by observing conditions. A proper understanding of the instrumental effects on measurements is necessary to correct for measurement bias. In any case, additional physical information must be used to accurately identify the progenitor system as a compact-binary merger or collapsar (e.g., burst environment, gravitational-wave measurements, and spectral behavior).

The authors would like to thank the anonymous reviewer for their very constructive and insightful comments. This work was in part funded by the Swift Guest Investigator program, Cycle 13 (80NSSC17K0336). All data used in this work were taken from the online Swift/BAT Gamma-Ray Burst Catalog.

Figure 9 displays the mask-weighted light curves for the eight real simple-pulse GRBs we used as light-curve templates in our simulations. Additional information on each GRB is presented in Table 2.

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The measured ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ for FRED template light curves are displayed in Figures 10–13 and for real GRB light curves in Figures 14–21. In each figure, the top plot displays the template light curve used in the simulations (blue line) along with the ${T}_{90,\mathrm{true}}^{\mathrm{BAT}}$ of the template light curve (vertical red-dashed lines). Each horizontal orange bar is a single ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ measurement; the bars are ordered from longest to shortest duration (bottom to top). The number of orange bars is equal to the number of simulations able to be measured by the Bayesian block algorithm (e.g., N_bars = f(measurable) ∗ 27,000). The bottom-left and right plots each display distributions of ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ at particular instrumental parameter combinations. The two plots contain ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ distributions made for simulations using different numbers of enabled detectors, i.e., simulations in the left plot used NDETS = 30,000 and the right plot 10,000. The distributions shown on each plot are shaded to indicate the average background level used during the simulation, i.e., dark blue ∼1000 c s⁻¹ and light blue ∼9500 c s⁻¹. Each plot displays the distributions at three different PCODE values indicated along the horizontal axis, i.e., PCODE =0.101 (θ_incident = 64286), PCODE = 0.522 (θ_incident = 44988), and PCODE = 1.0 (θ_incident = 00). The vertical axis on the left displays the ratio of the ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ to ${T}_{90,\mathrm{true}}^{\mathrm{BAT}}$; this can be also thought of as the ratio between one of the orange bars and the vertical red-dashed lines. The vertical axis on the right shows the duration measurement in seconds. When a distribution is tightly centered on ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$/T ${}_{90,\mathrm{true}}^{\mathrm{BAT}}$ = 1 (horizontal red-dashed line), the measured ${T}_{90,\mathrm{sim}}^{\mathrm{BAT}}$ of the simulated light curve accurately represents the ${T}_{90,\mathrm{true}}^{\mathrm{BAT}}$ of the template light curve.

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For any combination of observing conditions where a distribution is not present in the figures below, then none of the simulations made for that combination of parameters resulted in a light curve that was bright enough for the Bayesian block algorithm to provide a duration measurement. In these cases, the GRBs would not have been observed.

The two plots in Figure 22 contain fluence distributions (the mask-weighted fluence in the 15–350 keV band) made from simulations using different numbers of enabled detectors, i.e., simulations in the left plot used NDETS = 30,000 and the right plot 10,000. The distributions shown on each plot are shaded to indicate the average background level used during the simulation, i.e., dark blue ∼1000 c s⁻¹ and purple ∼9500 c s⁻¹. Each plot displays the distributions at three different PCODE values indicated along the horizontal axis, i.e., PCODE = 0.101 (θ_incident = 64286), PCODE = 0.522 (θ_incident = 44988), and PCODE = 1.0 (θ_incident = 00). The vertical axis on the left displays the fluence value. The fluence plots for all GRBs in the sample can be viewed in the online journal.

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View figure set (12 panels)

Tarball of figure set images

For any combination of observing conditions where a distribution is not present in the figures below, then none of the simulations made for that combination of parameters resulted in a light curve that was bright enough for the Bayesian block algorithm to provide a duration measurement. In these cases, the GRBs would not have been observed.

D.1. Synthetic FRED

D.2. Real GRBs: FRED-like

D.3. Real GRBs: Symmetric-like