GRB 200415A: A Short Gamma-Ray Burst from a Magnetar Giant Flare?

The multiwavelength light curves of this burst are shown in Figure 1 and derived from the photons collected by sodium iodide (NaI) detector n1 and bismuth germanium oxide (BGO) detector b0. The background is modeled via applying the "baseline" method (Zhang et al. 2018) to a wide time interval around the signal and subtracted in GBM light curves. The light curve obtained from HXMT-HE within 80–800 keV is added to the topmost panel in Figure 1. The correction of the aberration of light effect, which is 15.04 ms in terms of photon arrival time difference when they reached the GBM and HXMT-HE detectors, has been applied on the HXMT data. The count rates in the HXMT-HE light curve have also been corrected for the dead time and saturation (Xiao et al. 2020). The early 21 ms saturation time of HXMT-HE is shown with a gray shaded area in Figure 1. The light curves show a sharp peak at ∼T₀ with a duration of ${T}_{90}={5.88}_{-0.34}^{+0.23}$ ms (see Figure 2), which consists of an abrupt rise (∼2 ms) and a steep decay (∼8 ms). The sharp peak is followed by a soft tail (also see Figure 3) that extends to ∼T₀ + 0.2 s in lower energies.

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To determine the minimal time variability (${\rm{\Delta }}{t}_{\min }$), we employ the Bayesian block (Scargle et al. 2013) method on the photon events between 8 and 900 keV. The resulting blocks, as shown in the upper panel of Figure 3, can track the statistically significant changes in the light curve. The minimum bin size of the obtained blocks is 3.8 ms. We regard half of the minimum bin size as the minimal time variability of this burst (e.g., Vianello et al. 2018). We note that it is one of the smallest ${\rm{\Delta }}{t}_{\min }$ among all GRBs in Figure 4, where we plot a sample of short and long GRBs in the T₉₀–${\rm{\Delta }}{t}_{\min }$ plane obtained from Golkhou et al. (2015).

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The combined light curve obtained from the NaI detectors (n0, n1, n3, and n5), binned at 3.8 ms, is shown in the lower panel of Figure 3. It is also clear that the high-energy emission starts and ends at ∼T₀ – 0.005 and ∼T₀ + 0.2 s, respectively, which consists of a first spike and a weak tail. Such a time range will be used for the spectral lag calculations in Section 2.2 and the spectral analyses in Section 2.3.

Systematic time lags among light curves in different energy bands have been observed in large GRB samples (e.g., Yi et al. 2006; Ukwatta et al. 2010; Shao et al. 2017). A curvature effect has been suggested as a cause of spectral lags in GRB prompt emission (e.g., Ioka & Nakamura 2001; Norris 2002; Shenoy et al. 2013). However, it has recently been found that the observed spectral lags cannot be explained by the curvature effect alone, and they are also related to a curved photon spectrum, decreasing magnetic field, and large emission region undergoing a rapid bulk acceleration (Uhm & Zhang 2016). The existence of spectral lags supports that the prompt emission in GRBs is generated via a Poynting flux–dominated jet that abruptly dissipates magnetic energy at a large distance from the engine (Uhm & Zhang 2016). Compared to long GRBs, short GRBs show negligible lags (Bernardini et al. 2015). For GRB 200415A, we select the time interval from ${T}_{0}-0.005$ to ${T}_{0}+0.20\,{\rm{s}}$; then, we follow Zhang et al. (2012) to use the cross-correlation function (Norris et al. 2000; Ukwatta et al. 2010) to measure the time lags between any higher energy band and the lowest energy band in the GBM multiwavelength light curves, as shown in Figure 1. The uncertainties of time lags depend on the selected time interval and are estimated by Monte Carlo simulations (e.g., Ukwatta et al. 2010; Zhang et al. 2012). Interestingly, our results show that all of the lag values are very tiny (≲1 ms) and consistent with zero lag (Figure 5) when considering their uncertainties. Such a result is similar to previous studies (see, e.g., Zhang et al. 2009), where short GRBs were indicated with tiny lags. The tiny-lag result of GRB 200415A suggests that this event was likely not from a GRB jet but rather from a one-time fireball-like emission region. The spectral analyses in the next subsection confirm this suggestion.

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We perform both time-integrated and time-dependent spectral analyses between ${T}_{0}-0.005$ and ${T}_{0}+0.20\,{\rm{s}}$. This time interval is divided into 13 slices (see Table 1 or Figure 1) according to the brightness and the count statistical significance for spectral fitting (Zhang et al. 2018), in which three slices (covering the first spike, weak tail, and total emission) are used for time-integrated spectral analyses, and others are used for time-dependent spectral analyses. Within each slice, we extract the spectra of GRB 200415A from two NaI detectors (n1, n3) that are within a 60° angle with respect to the burst and BGO detector b0. Corresponding background spectra are acquired by applying the baseline method (Zhang et al. 2018) to the time interval from ${T}_{0}-20$ to ${T}_{0}+20\,{\rm{s}}$ for each energy channel. The response matrices of the detectors are generated using the response generator provided by the GBM Response Generator.¹⁵ Then we use McSpecfit (Zhang et al. 2018) to perform the spectral fitting. Several spectral models, including single power law (PL), cutoff power law (CPL), band function (Band), BB, and their combinations, are adopted. Additionally, a multicolor BB (mBB) model is also used in this study. Assuming that the distribution of the thermal luminosity with temperature follows the PL of index m, the mBB model can be formulated as (Hou et al. 2018)

$$\begin{eqnarray}&&N(E)=\displaystyle \frac{8.0525(m+1)K}{\left[{\left(\tfrac{{T}_{\max }}{{T}_{\min }}\right)}^{m+1}\mbox{--}1\right]}{\left(\displaystyle \frac{{{kT}}_{\min }}{\mathrm{keV}}\right)}^{-2}I(E),\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&I(E)={\left(\displaystyle \frac{E}{{{kT}}_{\min }}\right)}^{m-1}{\int }_{\tfrac{E}{{{kT}}_{\max }}}^{\tfrac{E}{{{kT}}_{\min }}}\displaystyle \frac{{x}^{2-m}}{{e}^{x}-1}{dx},\end{eqnarray} \tag{ 2 }$$

x = E/kT, and $K={L}_{39}/{D}_{{\rm{L}},10\,\mathrm{kpc}}^{2}$, with the luminosity L in units of 10³⁹ erg s⁻¹ and the luminosity distance ${D}_{{\rm{L}}}$ in units of 10 kpc.

Table 1.  Both Time-integrated and Time-dependent Spectral Fittings of GRB 200415A

Time Intervals	Best	Flux	mBB Parameters
(t1, t2) (s)	Model	(erg cm−2 s−1)	${{kT}}_{\min }$ (keV)	kTmax (keV)	m	pgstat/dof	BIC
(−0.005, 0.005)	mBB	${4.32}_{-0.62}^{+0.66}\times {10}^{-4}$	${39.40}_{-6.15}^{+6.25}$	${807.00}_{-113.78}^{+123.29}$	$-{0.33}_{-0.15}^{+0.17}$	278.5/350	302.01
(0.005, 0.200)	CPL	${2.79}_{-0.27}^{+0.32}\times {10}^{-5}$	${27.75}_{-5.48}^{+15.31}$	${399.87}_{-43.70}^{+81.42}$	${0.38}_{-0.40}^{+0.17}$	277.8/350	301.28
(−0.005, 0.200)	mBB	${4.53}_{-0.44}^{+0.45}\times {10}^{-5}$	${34.29}_{-4.79}^{+8.88}$	${542.61}_{-54.22}^{+71.79}$	$-{0.00}_{-0.23}^{+0.15}$	279.9/350	303.34
(−0.005, −0.003)	CPL	${1.99}_{-0.39}^{+0.50}\times {10}^{-4}$	${43.32}_{-3.98}^{+11.64}$	${402.21}_{-102.98}^{+814.98}$	$-{1.18}_{-0.58}^{+0.31}$	192.1/350	215.55
(−0.003, −0.001)	mBB	${4.10}_{-0.93}^{+1.58}\times {10}^{-4}$	${47.96}_{-5.94}^{+13.75}$	${539.31}_{-84.08}^{+501.25}$	$-{0.85}_{-0.57}^{+0.22}$	208.5/350	231.98
(−0.001, 0.001)	CPL	${6.61}_{-1.66}^{+2.19}\times {10}^{-4}$	${42.29}_{-4.45}^{+44.52}$	${789.59}_{-118.46}^{+343.87}$	${0.45}_{-0.67}^{+0.20}$	221.1/350	244.58
(0.001, 0.005)	BB	${1.79}_{-0.38}^{+0.46}\times {10}^{-4}$	${94.05}_{-29.75}^{+1.31}$	${533.12}_{-162.44}^{+257.78}$	$-{0.76}_{-0.30}^{+1.25}$	206.2/350	229.64
(0.005, 0.010)	BB	${1.17}_{-0.32}^{+0.37}\times {10}^{-4}$	${68.85}_{-19.77}^{+26.53}$	${298.35}_{-60.56}^{+281.16}$	${1.64}_{-1.81}^{+0.00}$	177.1/350	200.60
(0.010, 0.020)	CPL	${1.16}_{-0.20}^{+0.26}\times {10}^{-4}$	${77.42}_{-18.98}^{+16.68}$	${375.41}_{-19.63}^{+225.17}$	${0.63}_{-1.22}^{+0.18}$	218.4/350	241.91
(0.020, 0.040)	BB	${5.07}_{-0.75}^{+0.86}\times {10}^{-5}$	${98.56}_{-38.76}^{+1.44}$	${273.80}_{-1.52}^{+198.59}$	${0.81}_{-1.68}^{+0.18}$	194.2/350	217.66
(0.040, 0.080)	CPL	${3.76}_{-0.54}^{+0.66}\times {10}^{-5}$	${34.33}_{-18.48}^{+43.53}$	${269.64}_{-1.92}^{+187.74}$	${0.81}_{-1.65}^{+0.43}$	257.4/350	280.83
(0.080, 0.120)	BB	${8.38}_{-1.48}^{+1.80}\times {10}^{-6}$	${48.89}_{-5.89}^{+16.36}$	${221.49}_{-61.68}^{+697.44}$	$-{0.83}_{-0.96}^{+0.95}$	195.2/350	218.67
(0.120, 0.200)	PL	${3.78}_{-2.48}^{+2.93}\times {10}^{-6}$	Unconstrained

Time Intervals	CPL Parameters				BB Parameters
(t1, t2) (s)	Γph	Ep (keV)	pgstat/dof	BIC	kT (keV)	pgstat/dof	BIC
(−0.005, 0.005)	$-{0.28}_{-0.08}^{+0.06}$	${1118.09}_{-75.49}^{+113.39}$	300.2/351	317.79	${140.45}_{-6.83}^{+8.48}$	458.4/352	470.10
(0.005, 0.200)	$-{0.01}_{-0.08}^{+0.09}$	${826.43}_{-52.00}^{+59.65}$	279.1/351	296.68	${143.09}_{-5.38}^{+5.27}$	385.3/352	397.05
(−0.005, 0.200)	$-{0.14}_{-0.06}^{+0.06}$	${926.68}_{-52.33}^{+51.78}$	292.3/351	309.92	${142.12}_{-4.03}^{+4.36}$	533.5/352	545.27
(−0.005, −0.003)	${0.36}_{-0.31}^{+0.29}$	${393.53}_{-38.06}^{+72.77}$	196.6/351	214.18	${82.27}_{-6.53}^{+9.69}$	205.5/352	217.19
(−0.003, −0.001)	${0.03}_{-0.18}^{+0.22}$	${607.43}_{-75.55}^{+109.26}$	217.7/351	235.26	${97.81}_{-6.84}^{+10.26}$	237.5/352	249.27
(−0.001, 0.001)	$-{0.00}_{-0.16}^{+0.26}$	${1688.27}_{-224.37}^{+304.76}$	222.6/351	240.22	${299.57}_{-42.39}^{+0.40}$	241.2/352	252.97
(0.001, 0.005)	${0.60}_{-0.26}^{+0.46}$	${857.35}_{-132.59}^{+134.64}$	208.6/351	226.25	${182.53}_{-18.18}^{+27.82}$	212.4/352	224.10
(0.005, 0.010)	${1.67}_{-0.68}^{+0.88}$	${847.03}_{-121.32}^{+198.13}$	176.4/351	194.05	${233.18}_{-29.92}^{+32.22}$	177.0/352	188.73
(0.010, 0.020)	${0.53}_{-0.20}^{+0.30}$	${907.19}_{-89.61}^{+99.54}$	220.4/351	238.05	${202.23}_{-14.30}^{+21.71}$	227.9/352	239.66
(0.020, 0.040)	${0.63}_{-0.20}^{+0.38}$	${743.53}_{-75.94}^{+74.67}$	194.6/351	212.19	${168.98}_{-12.12}^{+15.06}$	198.8/352	210.55
(0.040, 0.080)	${0.31}_{-0.16}^{+0.23}$	${676.90}_{-58.29}^{+66.68}$	257.9/351	275.50	${139.89}_{-7.78}^{+10.02}$	273.9/352	285.62
(0.080, 0.120)	${0.65}_{-0.35}^{+0.52}$	${374.23}_{-46.83}^{+63.24}$	196.4/351	214.00	${85.80}_{-7.34}^{+10.20}$	199.0/352	210.70
(0.120, 0.200)	Unconstrained				Unconstrained

Note. The CPL model can be expressed as $N(E)={{AE}}^{{{\rm{\Gamma }}}_{\mathrm{ph}}}\exp [-E(2+{{\rm{\Gamma }}}_{\mathrm{ph}})/{E}_{{\rm{p}}}]$. The PL model gives an acceptable fit in the time slice between ${T}_{0}+0.12$ and ${T}_{0}+0.20\,{\rm{s}}$: ${{\rm{\Gamma }}}_{\mathrm{ph}}=-{1.44}_{-0.28}^{+0.11}$, pgstat/dof = 179.2/352, BIC = 190.96. Flux is derived based on the best model within 10–10,000 keV for each slice. Here the errors correspond to the 1σ credible intervals.

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Based on the Bayesian information criterion (BIC), we determine the best model for each time interval. The best-fit parameters of the CPL, BB, and mBB models for all time slices are listed in Table 1.

The time-integrated spectrum measured between ${T}_{0}-0.005$ and ${T}_{0}+0.005\,{\rm{s}}$, covering the first spike, can be best fitted by the mBB model with ${{kT}}_{\min }={39.40}_{-6.15}^{+6.25}$ and ${{kT}}_{\max }={807.00}_{-113.78}^{+123.29}$ keV, although the CPL model also gives an acceptable fit with photon index ${{\rm{\Gamma }}}_{\mathrm{ph}}=-{0.28}_{-0.08}^{+0.06}$ and peak energy ${E}_{{\rm{p}}}={1118.09}_{-75.49}^{+113.39}$ keV. The photon count spectra, modeled ${f}_{\nu }$ spectra, and corner diagrams for the parameter constraints of the two fits are shown in Figures 6 and 7, respectively. For the weak tail in the time range from ${T}_{0}+0.005$ to ${T}_{0}+0.20\,{\rm{s}}$, the CPL model provides the best fit with a relatively smaller peak energy, and the mBB model gives the second-best fit with a lower temperature. The total time-integrated spectrum measured between ${T}_{0}-0.005$ and ${T}_{0}+0.20\,{\rm{s}}$ can be described best by the mBB model with ${{kT}}_{\min }={34.29}_{-4.79}^{+8.88}$ and ${{kT}}_{\max }={542.61}_{-54.22}^{+71.79}$ keV, and the CPL model also gives an acceptable fit with photon index ${{\rm{\Gamma }}}_{\mathrm{ph}}=-{0.14}_{-0.06}^{+0.06}$ and peak energy ${E}_{{\rm{p}}}={926.68}_{-52.33}^{+51.78}$ keV. The BB model is significantly disfavored in the time-integrated spectra according to the BIC.

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To study the spectral evolution, we perform the time-dependent spectral analysis for each of the 10 slices mentioned above. The spectrum measured between ${T}_{0}-0.001$ and ${T}_{0}+0.001\,{\rm{s}}$ characterizing the hardest part of the burst can be fitted excellently by the CPL model with photon index ${{\rm{\Gamma }}}_{\mathrm{ph}}=-{0.00}_{-0.16}^{+0.26}$ and peak energy ${E}_{{\rm{p}}}={1688.27}_{-224.37}^{+304.76}$ keV. The mBB model gives a secondary fit with ${{kT}}_{\min }={42.29}_{-4.45}^{+44.52}$ and ${{kT}}_{\max }={789.59}_{-118.46}^{+343.87}$ keV. The best-fit models of the time-dependent spectra are generally the BB or CPL model, except for the second spectrum (mBB) and the last spectrum, which can be fitted by the PL model.

Following the first time-dependent spectrum, strong spectral evolution is observed until ${T}_{0}+0.2\,{\rm{s}}$, where the spectra are smeared into the background. Figure 8 shows the evolution of the parameters of the CPL, BB, and mBB models. For comparison, the light curve obtained by summing GBM detectors n1 and n3 is overplotted in several panels. It is clear that the behaviors of E_p and the temperature of this burst show an intensity tracking pattern (Golenetskii et al. 1983), even though there is a delay of ∼2 ms between the peaks of the flux and the spectral evolution. During the first spike, the rapid evolution of the peak energy and temperature imply that the emission source underwent an abrupt variation. Subsequent decay in the weak tail stage may indicate the cooling of the emission region. Such spectral evolution is consistent with a rapidly expanding then gradually cooling fireball-like emission source.

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Based on the spectral analyses, the average flux is derived from the best model within 10–10,000 keV for each slice, as shown in Table 1. The total fluence in the time range from ${T}_{0}-0.005$ to ${T}_{0}+0.20\,{\rm{s}}$ is ${9.29}_{-0.90}^{+0.92}\times {10}^{-6}\ \mathrm{erg}\,{\mathrm{cm}}^{-2}$. The peak flux of ${1.11}_{-0.11}^{+0.15}\times {10}^{-3}\,{\rm{e}}{\rm{r}}{\rm{g}}\,{{\rm{c}}{\rm{m}}}^{-2}\,{{\rm{s}}}^{-1}$ is approximately proportional to the average flux ${F}_{\mathrm{ave}}$ with a scale factor ${R}_{\mathrm{peak}}/{R}_{\mathrm{ave}}$, where ${R}_{\mathrm{peak}}$ is the 0.4 ms peak count rate. Assuming a distance of 3.5 Mpc, the corresponding isotropic energy and peak luminosity are estimated as ${E}_{\gamma ,\mathrm{iso}}={1.36}_{-0.13}^{+0.14}\times {10}^{46}$ erg and ${L}_{\gamma ,{\rm{p}},\mathrm{iso}}={1.62}_{-0.16}^{+0.21}\times {10}^{48}$ erg s⁻¹, respectively. The above values, along with some important temporal and spectral observational properties, are summarized in Table 2.

Table 2.  Observational Properties of GRB 200415A

Observed Properties	GRB 200415A
Abrupt rise time	∼2 ms
Steep decay time	∼8 ms
T90 (sharp peak only)	${5.88}_{-0.34}^{+0.23}$ ms
Total duration	∼200 ms
Γph at peak	$-{0.00}_{-0.16}^{+0.26}$
Ep at peak	${1688.27}_{-224.37}^{+304.76}$ keV
Time-integrated Γph	$-{0.14}_{-0.06}^{+0.06}$
Time-integrated Ep	${926.68}_{-52.33}^{+51.78}$ keV
Total fluence	${9.29}_{-0.90}^{+0.92}\times {10}^{-6}$ erg cm−2
Peak flux	${1.11}_{-0.11}^{+0.15}\times {10}^{-3}\ \mathrm{erg}\,{\mathrm{cm}}^{-2}\ {{\rm{s}}}^{-1}$
Possible host galaxy	Sculptor galaxy (NGC 253)
Distance	3.5 Mpc
Isotropic energy Eγ,iso	${1.36}_{-0.13}^{+0.14}\times {10}^{46}$ erg
Peak luminosity Lγ,p,iso	${1.62}_{-0.16}^{+0.21}\times {10}^{48}$ erg s−1

Note. The total fluence and peak flux are calculated in the 10–10,000 keV energy band. Here the time-integrated spectral parameters are measured over the total duration. All errors correspond to the 1σ credible intervals.

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Short GRBs have more photons at higher energy bands (Dezalay et al. 1991). This can be quantitatively represented by the ratio of observed counts in 50–300 keV (H) to 10–50 keV (S). We compute the spectral hardness (H/S) for the observed spike and tail individually. The spike is considered from ${T}_{0}-0.005$ to ${T}_{0}+0.008\,{\rm{s}}$, and the subsequent tail is considered from ${T}_{0}+0.008$ to ${T}_{0}+0.20\,{\rm{s}}$. The results are plotted in Figure 9 with a sample of short (blue circles) and long (red circles) GRBs obtained from Goldstein et al. (2017). Both the spike and the weak tail are slightly harder than most short GRBs with H/S ∼ 4.45 and 2.3, respectively.

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We extracted the Fermi-LAT data within a temporal window extending 1000 s after T₀. Then we performed an unbinned likelihood analysis. The data were filtered by selecting photons with energies in the range 100 MeV–300 GeV and within a region of interest (ROI) of 12° radius centered on the burst position. A further selection of zenith angle (100°) was applied to reduce the contamination of photons coming from the Earth limb. We adopt the P8R3_TRANSIENT020E_V2 response, which is suitable for faint detection. The probabilities of the photons being associated with the source are calculated using the gtsrcprob tool. The highest-energy photon is a 1.72 GeV event, which is observed 284 s after the GBM trigger. All LAT photon events are plotted in Figure 3, and the most significant five LAT photon events are listed in Table 3. For the time-integrated duration of 0–1000 s, the energy and photon flux in the 0.1–10 GeV energy range are $(3.78\pm 2.24)\times {10}^{-9}$ erg s⁻¹ cm⁻² and $(3\pm 1.74)\times {10}^{-6}$ photons s⁻¹ cm⁻², respectively. The spectral index is −1.47 ± 0.43 with a test statistic of detection of 26.

Assuming the association with the Sculptor galaxy is real, we can directly check if GRB 200415A exhibits differently when compared with other GRBs. To do so, we place GRB 200415A in the E_p–E_γ,iso diagram (aka the Amati relation), in which long and short GRBs typically follow different tracks. In Figure 10, we overplot the Amati relation using the GRBs with known redshift (Amati et al. 2002; Zhang et al. 2009). Short GRBs follow the track of logE_p,z = a + blogE_γ,iso, with the best-fitting parameters being a = −12.82 and b = 0.31, where E_p,z = E_p(1+z), while GRB 200415A, with different redshifts, follows the track shown with the red dashed line. Assuming a distance of 3.5 Mpc, it is clear that GRB 200415A significantly deviates from such a correlation. To be on the short GRB track, GRB 200415A would have to be much further, with $z\gtrsim 0.03$ (d ≳ 136 Mpc). Moreover, compared with the off-axis GRB 170817A, which is a nearby event at ∼40 Mpc, GRB 200415A obviously possesses a lower energy and a much higher E_p. On the other hand, by plugging in the properties of the giant outburst from SGR 1806–20, we find that GRB 200415A is very close to its location, which points toward the GF origin.

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It is natural to ask a question: if a compact star merger event, as an origin of typical short GRBs, happens at d = 3.5 Mpc, what would be the observational consequence, and how similar is it compared with GRB 200415A? Straightforwardly, considering a typical short GRB with ${E}_{\gamma ,\mathrm{iso}}={10}^{49}\mbox{--}{10}^{52}$ erg (Zhang et al. 2009; Gruber et al. 2014), the corresponding fluence at d = 3.5 Mpc is $\sim {10}^{-3}\mbox{--}{10}^{0}$ erg cm⁻², which is at least 3 orders of magnitude higher than the observed one in GRB 200415A. This suggests that GRB 200415A has to be an off-axis GRB so that the observed fluence can be significantly reduced due to the beaming effect if it is indeed from a compact star merger.

However, is an off-axis merger-type short GRB consistent with the observations of GRB 200415A? The isotropic equivalent energy of GRB 200415A is ∼10⁴⁶ erg, the E_p is ∼1 MeV, and its sharp peak duration is ∼6 ms. If it is a typical short burst seen off-axis, assuming the top-hat model, the relationship between duration (or peak energy) and the Doppler factor is approximately (Granot et al. 2002; Abbott et al. 2017)

$$\begin{eqnarray}&&\displaystyle \frac{{T}_{90,\mathrm{off}}}{{T}_{90,\mathrm{on}}}=\displaystyle \frac{{E}_{{\rm{p}},\mathrm{on}}}{{E}_{{\rm{p}},\mathrm{off}}}=\displaystyle \frac{D(0)}{D({\theta }_{{\rm{v}}}-{\theta }_{{\rm{j}}})}=a\approx 1+{{\rm{\Gamma }}}^{2}{\left({\theta }_{{\rm{v}}}-{\theta }_{{\rm{j}}}\right)}^{2},\end{eqnarray} \tag{ 3 }$$

where Γ is the Lorentz factor of the jet, D is the Doppler factor, and ${\theta }_{{\rm{j}}}$ and ${\theta }_{{\rm{v}}}$ are the jet opening angle and viewing angle, respectively. Note that the ratio of duration applies to the case of a single pulse (Zhang et al. 2009) or one central engine activity, and this burst is the case. For multipulse bursts, if the duration of one pulse is much larger than the duration of the central engine activity, this ratio also approximately applies. The isotropic equivalent energy scales as ∝a⁻² for ${\theta }_{{\rm{j}}}\lt {\theta }_{{\rm{v}}}\lt 2{\theta }_{{\rm{j}}}$ and ∝a⁻³ for ${\theta }_{{\rm{v}}}\gt 2{\theta }_{{\rm{j}}}$ (Ioka & Nakamura 2018). Assuming that the on-axis isotropic energy is the typical value of ${E}_{\gamma ,\mathrm{iso}}={10}^{50}$ erg for short bursts, we have $a\sim 100$ for ${\theta }_{{\rm{j}}}\lt {\theta }_{{\rm{v}}}\lt 2{\theta }_{{\rm{j}}}$ or $a\sim 20$ for ${\theta }_{{\rm{v}}}\gt 2{\theta }_{{\rm{j}}}$. So, the on-axis duration and peak energy would be ${T}_{90}=0.06{(a/100)}^{-1}$ or $0.3{(a/20)}^{-1}$ ms and ${E}_{{\rm{p}}}=100(a/100)$ or $20(a/20)$ MeV. These values are obviously atypical and have never been observed in existing short GRB samples.

Another possibility is that GRB 200415A is off-axis from a structured jet that includes a uniformly bright core surrounded by a PL or Gaussian decaying wing (Rossi et al. 2002; Zhang & Mészáros 2002). In this model, the energy/luminosity, Lorentz factor, and E_p all depend on the angle from the jet axis. The high E_p (∼1 MeV) and unusually low E_γ,iso (∼10⁴⁶ erg) observed in GRB 200415A require that the energy profile is quite steep while the E_p profile is flat. Such conditions are at odds with most studies of GRB jets, although they cannot be fully ruled out.

A similar case to GRB 200415A is GRB 170817A when considering the nearby distance and the explanation using a structured jet model (e.g., Meng et al. 2018), which was associated with the gravitational-wave event GW170817 that originated from a compact star merger. It is interesting to compare the two events. The isotropic energy of GRB 200415A is similar to that of GRB 170817A (also ∼10⁴⁶ erg). Therefore, the jet kinetic energies should be analogical for both events if the radiation efficiency is the same. We can further speculate that the progenitors of the two bursts are also similar. The GRB 170817A was followed by a "kilonova" that was observed about half a day after the burst (Coulter et al. 2017) and lasted for tens of days, while to date, no follow-up emission in any bands has been reported for GRB 200415A, which is 1 order of magnitude closer than GRB 170817A. Note that the emission of kilonovae is approximately isotropic, so different viewing angles do not affect the detection of kilonovae. If GRB 200415A was from a structured jet seen off-axis, its afterglow with a long time rise should also have been observed, like GRB 170817A, due to its similar jet energy and nearer distance. Thus, the nondetection of the kilonova and afterglow of GRB 200415A does not favor it as a typical short GRB.

In summary, if the association of the host galaxy is real, it is unlikely that GRB 200415A was generated from a compact star merger event.

For quite some time, GFs from SGRs in nearby galaxies have been proposed to serve a few misclassified short GRBs (Ofek et al. 2006, 2008; Frederiks et al. 2007a; Mazets et al. 2008). The claims are mainly based on the consistency with the energies of GFs and the associations with some nearby galaxies (e.g., M31; Ofek et al. 2008). In fact, the total energy (∼10⁴⁶ erg) of GRB 200415A and its location near the Sculptor galaxy are in agreement with such a scenario. In this section, we perform additional statistical studies and discuss some theoretical evidence to support the GF origin of GRB 200415A.

To compare with previous GF short GRB candidates and known SGR GF events, we list some detailed properties of the GF short GRBs 200415A, 051103, and 070201, as well as the SGR 1806–20 GF in Table 4. They are all located near (or in) galaxies or massive star clusters with high star formation rates. In terms of isotropic energy and peak luminosity, they are also analogous when we assume the distance of GRB 200415A is 3.5 Mpc. Interestingly, as we show in Figure 10, GRB 200415A at a luminosity distance of 3.5 Mpc seems to belong to the same population as the SGR 1806–20 GF and is closer to it than the GF short GRBs 051103 and 070201.

Table 4.  Comparison among GRB 200415A, the SGR 1806–20 GF, GRB 051103, and GRB 070201

Properties	GRB 200415A	SGR 1806–20 GF	GRB 051103	GRB 070201
Location	NGC 253	Massive star cluster	M81	M31
Distance	3.5 Mpc	8.7 kpc	3.6 Mpc	0.78 Mpc
Initial Pulse
Steep rise, ms	∼2	∼1	≤6	∼20
Decay, ms	∼8	∼200	∼40	∼160
Rapid spectral evolution	✓	✓	✓	✓
CPL photon index Γph	$-{0.28}_{-0.08}^{+0.06}$	$-{0.73}_{-0.47}^{+0.64}$	${0.16}_{-0.15}^{+0.19}$	$-{0.52}_{-0.13}^{+0.15}$
CPL peak energy, keV	${1118.09}_{-75.49}^{+113.39}$	${850}_{-303}^{+1259}$	${2300}_{-150}^{+350}$	${360}_{-38}^{+44}$
BB temperature, keV	${140.45}_{-6.83}^{+8.48}$	175 ± 25, 116	⋯	⋯
Peak flux, erg cm−2 s−1	${1.11}_{-0.11}^{+0.15}\times {10}^{-3}$	∼5.0, ${13.1}_{-4.4}^{+8.0}$	(2.8 ± 0.3) × 10−3	${1.61}_{-0.50}^{+0.29}\times {10}^{-3}$
Peak luminosity, erg s−1	${1.62}_{-0.16}^{+0.21}\times {10}^{48}$	$0.45(1.19)\times {10}^{47}$	(4.34 ± 0.46) × 1048	1.2 × 1047
Tail
Tail duration	∼150 ms	∼380 s	∼130 ms	∼100 ms
Period, s	⋯	7.56	⋯	⋯
QPO	⋯	✓	⋯	⋯
BB temperature, keV	${143.09}_{-5.38}^{+5.27}$	∼30	⋯	⋯
CPL photon index Γph	$-{0.01}_{-0.08}^{+0.09}$	⋯	${0.43}_{-0.40}^{+0.34}$	∼(−1)
CPL peak energy, keV	${826.43}_{-52.00}^{+59.65}$	⋯	530 ± 80	∼125
Fluence, erg cm−2	${5.44}_{-0.52}^{+0.63}\times {10}^{-6}$	8 × 10−3	(2 ± 0.3) × 10−6	∼10−6
Total fluence, erg cm−2	${9.29}_{-0.90}^{+0.92}\times {10}^{-6}$	${0.87}_{-0.24}^{+0.50}$	(4.4 ± 0.5) × 10−5	${2}_{-0.26}^{+0.10}\times {10}^{-5}$
Total energy, erg	${1.36}_{-0.13}^{+0.14}\times {10}^{46}$	${7.88}_{-2.17}^{+4.53}\times {10}^{45}$	(6.82 ± 0.78) × 1046	${1.5}_{-0.19}^{+0.07}\times {10}^{45}$
References		Hurley et al. (2005)	Frederiks et al. (2007b)	Mazets et al. (2008)
		Frederiks et al. (2007a)	Ofek et al. (2006)	Ofek et al. (2008)

Note. The spectral properties of GRB 200415A are given by the best models of time-integrated spectra. The distance of ∼8.7 kpc to the location of SGR 1806–20 is suggested by Bibby et al. (2008).

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To further check if these GF short GRBs are a special group in the whole short GRB sample, we overplot them in various distributions of characteristic parameters of short GRBs from the Fermi/GBM burst catalog (Gruber et al. 2014; von Kienlin et al. 2014, 2020; Narayana Bhat et al. 2016). The GF from SGR 1806–20 is also marked, where applicable. As shown in Figure 11, the four events are clustered together in the distributions, with smaller ${T}_{90}$, significantly larger fluence, relatively typical photon index, and slightly higher E_p in the whole short GRB sample. In addition, the four events are also clustered in the E_p–E_iso diagram (Figure 10). All of the above statistical similarities suggest that GRB 200415A should originate from an SGR GF.

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Theoretically speaking, generating a short GRB–like event is plausible in the context of the GF model. Large-scale shearing and reconnection of an external magnetic field stronger than ∼10¹⁴ G (Duncan & Thompson 1992), which may be induced by internal instabilities, launch an expanding pair fireball (Thompson & Duncan 1995). The internal stored magnetic energy is released rapidly during the crossing time of the Alfvén wave in the neutron star interior. The timescale that is consistent with the duration of the initial spike is ${T}_{\mathrm{spike}}\gtrsim {R}_{\mathrm{NS}}/{V}_{{\rm{A}}}\gtrsim 0.1\,{\rm{s}}$ with ${R}_{\mathrm{NS}}=10\,\mathrm{km}$, where ${V}_{{\rm{A}}}\lesssim {B}_{{\rm{p}}}/{(4\pi \rho )}^{1/2}$ is the Alfvén velocity with a poloidal magnetic field ${B}_{{\rm{p}}}={10}^{15}\,{\rm{G}}$ and density $\rho ={10}^{15}\,{\rm{g}}\,{\mathrm{cm}}^{-3}$ (Feroci et al. 2001). In another case, where the instabilities are driven by an external twisted magnetic field, the large-scale magnetic reconnection event will last $\sim {10}^{2}{R}_{\mathrm{NS}}/c\sim {10}^{-2}$ s (Parfrey et al. 2013). Actually, the "tail emission" of GRB 200415A is hard (see Table 4) and still presents a strong spectral evolution of hard to soft (see Figure 8), like the decaying stages of the initial pulses of other GFs. As the previous observations suggested, the insignificant quasi-thermal spectral evolution was predicted in the soft tail of the GF (Thompson & Duncan 1995). It implies that the main spike and weak emission of GRB 200415A may be combined into the initial pulse of a typical GF. The energy released through the fireball should be $\lesssim {10}^{47}{B}_{15}^{2}{({R}_{\mathrm{NS}}/10\mathrm{km})}^{3}$ erg, which is carried by an internal dipole field with $B={10}^{15}$ G (Thompson & Duncan 2001).

In the context of the GF model, the emissions could be quasi-thermal, as the mBB model fits the spectra of GRB 200415A well. The initial bright pulse is emitted by a sharply expanding pair fireball (Thompson & Duncan 1995). The radius of the neutron star gives a lower limit to the size of the initial fireball ($\gtrsim {R}_{\mathrm{NS}}=10$ km), which emits the maximum luminosity ($1.62\times {10}^{48}$ erg s⁻¹). Then, the minimum time variability of 1.9 ms provides an upper limit to the size of the emission region ($\lesssim {{\rm{\Delta }}}_{{\rm{t}},\min }c=570$ km) with an average luminosity of ∼10⁴⁷ erg s⁻¹. Assuming BB emission, we can derive the temperature range from ${kT}_{max}\sim 600$ to ${{kT}}_{\min }\sim 40\,\mathrm{keV}$ of the expanding fireball, which overlaps into an mBB spectrum. We note that such restrictions on temperature are similar to those of our mBB spectral fitting during the first spike (Table 1). On the other hand, for the peak time-dependent spectrum measured from ${T}_{0}-0.001$ to ${T}_{0}+0.001\,{\rm{s}}$, the BB model can give an acceptable fit with ${kT}={299.57}_{-42.39}^{+0.40}$ keV and flux ${5.49}_{-1.12}^{+0.80}\times {10}^{-4}$ erg cm⁻² s⁻¹. The corresponding radius of the emission source should be ${27.80}_{-2.84}^{+8.12}$ km, which is similar to the radii of the emission regions inferred in previous studies (e.g., Nakar et al. 2005; Ofek et al. 2006, 2008).

Assuming that GRB 200415A is an SGR GF at a distance of 3.5 Mpc, it is the first detection of GeV emission that is coincident with a GF. The first high-energy photon was detected at ∼19 s after the onset of GRB 200415A, whose energy is 480 MeV. The photon number spectrum during 0–1000 s in the 0.1–10 GeV band is $N(E)\sim 1.4\,\times \,{10}^{-5}{E}^{-1.47}$ MeV⁻¹ s⁻¹ cm⁻² with a spectral index of ∼−1.47. The photon number that can annihilate the photons with an energy of ${E}_{\max }$ is ${N}_{\gt {E}_{\max ,\mathrm{an}}}=4\pi {d}_{{\rm{L}}}^{2}T{\int }_{{E}_{\max ,\mathrm{an}}}^{\infty }N(E){dE}$, where ${E}_{\max ,\mathrm{an}}\equiv {({\rm{\Gamma }}{m}_{e}{c}^{2})}^{2}/{E}_{\max }$ and Γ is the Lorentz factor of the emission region. Such a photon number corresponds to the opacity for the ${E}_{\max }$ photons being $\tau \approx 0.1{\sigma }_{T}{N}_{\gt {E}_{\max ,\mathrm{an}}}/(4\pi {R}^{2})$ (Lithwick & Sari 2001). The emission region optically thin to the ${E}_{\max }$ photons requires that its radius should be $R\gtrsim 3.8\times {10}^{11}{({E}_{\max }/480\mathrm{MeV})}^{0.235}{(T/19{\rm{s}})}^{1/2}{{\rm{\Gamma }}}^{-0.47}$ cm. The speed of the GeV emission region is unknown. If it is relativistic, taking ${\rm{\Gamma }}=10$, for example, then $R\sim {{\rm{\Gamma }}}^{2}{cT}\approx 6\times {10}^{13}$ cm. This suggests that the delayed GeV emission region is much larger than the GF emission region, implying that there is an additional mechanism that is responsible for such GeV photons after the GF. A natural source is the afterglow-like emission from the outflow launched from the GF. For a relativistic outflow, the synchrotron or synchrotron self-Compton radiation from electrons generated from the forward shock can produce such detectable sub-GeV or GeV afterglow emission (Fan et al. 2005).

The energy of the GF was used to constrain the magnetic field of the magnetar (Hurley et al. 2005). In our scenario, we estimate an upper limit on ${B}_{\mathrm{NS}}$ using the main flare energy ($\sim {10}^{46}$ erg). The magnetic field, B, within a radius ${\rm{\Delta }}R\sim 10$ km, which is above the stellar radius ${R}_{\mathrm{NS}}$, is $B{({R}_{\mathrm{NS}}+{\rm{\Delta }}R)\lesssim (8\pi {E}_{\gamma ,\mathrm{iso}}/3{\rm{\Delta }}{R}^{3})}^{1/2}$ (Thompson & Duncan 1995). At a radius r, the magnetic field, approximated as a dipole field, is $B{(r)={B}_{\mathrm{NS}}(r/{R}_{\mathrm{NS}})}^{-3}$. Then, we constrain ${B}_{\mathrm{NS}}\lesssim 2\times {10}^{15}$ G.