Multiple Components in the Broadband γ-Ray Emission of the Short GRB 160709A

Gamma-ray bursts (GRBs) are the most energetic explosions in the universe. The GRBs are classified into two types based on their duration (T₉₀): long GRBs (T₉₀ > 2 s) from the collapse of massive stars (e.g., Woosley 1993; MacFadyen & Woosley 1999; Woosley & Bloom 2006) and short GRBs (T₉₀ ≲ 2 s) from the merger of two compact objects such as two neutron stars or a neutron star with a black hole (e.g., Paczynski 1986, 1991; Rosswog et al. 1999; Abbott et al. 2017a). Both long and short GRBs show similar spectral features. The observed keV–MeV prompt emission spectra of GRBs have been traditionally fitted with an empirical model, the Band function (Band et al. 1993), which is two smoothly connected power laws (PLs) with low- (α) and high- (β) energy photon indices. Despite the empirical nature of the Band function, its low- and high-energy photon index values have been used to test the emission mechanisms as well as the underlying particle distributions. According to the standard internal shock model, accelerated electrons in relativistic collisionless shocks radiate via synchrotron radiation (Rees & Mészáros 1994). The energy spectrum of the synchrotron radiation resulted from the PL electron distribution has an upper limit on its spectral steepness, $\alpha \leqslant -2/3$ (Katz 1994). The observation of some hard spectra challenges any model invoking the synchrotron process as the main emission mechanism of the observed prompt emission spectrum (Preece et al. 1998, 2000; Gruber et al. 2014). For such hard spectra, modified internal shock models as well as alternative models have been introduced: a decaying magnetic field behind the shock front (Pe'er & Zhang 2006; Derishev 2007), globally decreasing magnetic fields (Uhm & Zhang 2014), slow heating (Asano et al. 2009), synchrotron self-Compton scattering (SSC) (Panaitescu & Mészáros 2000), and the Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) model (Zhang & Yan 2011). In addition to exploring alternative emission mechansims, the observation of several GRBs suggests modification of the Band function itself. For several GRBs, the Band function was attenuated by a spectral cutoff at high energy in the sub-GeV band (e.g., Ackermann et al. 2013; Tang et al. 2015). Furthermore, spectral cutoffs were reported at high energy in the ≲MeV band (Vianello et al. 2017) and at low energy in the X-ray energy band (Oganesyan et al. 2017).

Alternate spectral models to the Band function have been explored. For instance, a possible signature of thermal emission was explored to fit the data collected with the Burst And Transient Source Experiment (BATSE) on board the Compton γ-ray Observatory (CGRO) either by a single blackbody (Ghirlanda et al. 2003) or a blackbody with an additional PL (Ryde 2004). A sub-dominant thermal component in addition to a nonthermal one in the prompt emission were discovered from the long GRB 100724B (Guiriec et al. 2011) and short GRB 120323A (Guiriec et al. 2013) detected with the Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) on board the Fermi Gamma Ray Space Telescope (hereafter, Fermi). Similar results were reported in many short and long GRBs detected with Fermi (Axelsson et al. 2012; Guiriec et al. 2015a, 2015b), CGRO/BATSE (Guiriec et al. 2016a), Swift and Suzaku (Guiriec et al. 2016b), and Wind/Konus (Guiriec et al. 2017). These thermal components have been interpreted as emission from a photosphere. Mészáros & Rees (2000) investigated the roles and possible observational features of the photosphere. The idea of photospheric thermal emission has been extended with the consideration of various dissipative mechanisms (Daigne & Mochkovitch 2002; Rees & Mészáros 2005; Beloborodov 2010; Vurm et al. 2011).

Using CGRO/BATSE, González et al. (2003) reported another deviation at high energy from the Band function adequately fitted by an additional PL. This result was confirmed using data collected with the Large Area Telescope (LAT; Atwood et al. 2009) on board Fermi for both long and short GRBs. The additional component generally crosses the whole gamma-ray spectrum and extends up to a few GeV (e.g., Abdo et al. 2009b; Ackermann et al. 2010, 2011; Yassine et al. 2017). One possible explanation for this high-energy component is that it may originate from the external forward shock (e.g., De Pasquale et al. 2010; Ghirlanda et al. 2010). The temporal and spectral properties of the external blast wave are well understood (Sari et al. 1998; Zhang et al. 2006; Uhm et al. 2012). According to the external forward shock model, the spectra and light curves of GRBs are characterized by a series of broken power laws (Sari et al. 1998), and the temporal and spectral indices are related by the "closure relation," which is determined by the surrounding environment (Rees & Mészáros 1994; Mészáros & Rees 1997; Dai & Lu 1998; Sari et al. 1998; Chevalier & Li 2000; Dai & Cheng 2001). The LAT high-energy extended emission typically decreases as a function of time (Ghisellini et al. 2010; Ackermann et al. 2013), which supports the external forward shock model. Furthermore, the detailed spectral and temporal properties are consistent with those predicted by the external shock model (Kumar & Barniol Duran 2009, 2010; De Pasquale et al. 2010; Ghisellini et al. 2010; Panaitescu 2017), although bright and spiky temporal structures observed in the prompt phase of LAT light curves challenge this interpretation (Maxham et al. 2011; Zhang et al. 2011). Recently, Gompertz et al. (2018) applied the closure relation to a large sample of LAT-detected long GRBs and identified their surrounding environment conditions. Alternatively, the GeV emission has been interpreted as due to a magnetically dominated jet model based on the combined effects of dissipation from magnetic reconnection and nuclear collision (Mészáros & Rees 2011). Synchrotron self-Compton (Mészáros & Rees 1993; Corsi et al. 2010) and hadronic emission (Asano et al. 2009; Razzaque 2010) have also been proposed.

Recently, Guiriec et al. (2015a) reported the simultaneous existence of three components in GRBs detected with both Fermi/GBM and Fermi/LAT: (i) a thermal-like component interpreted as photospheric emission from the jet photosphere; (ii) a nonthermal component interpreted as the synchrotron emission from charged particles accelerated within the jet or as a strongly reprocessed photospheric emission; and (iii) a second nonthermal component whose physical process is unknown. Guiriec et al. (2016a) confirmed this result in a sample of GRBs detected with CGRO/BATSE and Guiriec et al. (2016b) showed that this three-component model is a good fit to the whole broadband prompt emission spectrum of GRB 110205A from optical to γ-rays using Swift and Suzaku data.

In this paper, we present the analysis of the bright short GRB 160709A detected with both GBM and LAT. Even though the LAT has detected more than 120 GRBs, only 10% of them are short GRBs (Ackermann et al. 2013). Due to the scarcity of short GRBs detected with LAT, the nature of their high-energy emission is not well established yet, and the bright short GRB 160709A will improve our understanding of the emission mechanisms powering short GRBs. The observation of GRB 160709A is presented in Section 2. Section 3 reports GBM and LAT spectral analyses. The interpretations of the analysis results are discussed in Section 4. Finally, Section 5 summarizes and concludes the article.

At 19:49:03.50 UT on 2016 July 09 (hereafter T₀), GRB 160709A triggered GBM with a significance of 5.6σ (GCN report, Jenke 2016). The ground analysis of Swift/Burst Alert Telescope (BAT) reported a 9σ excess consistent with GRB 160709A at (R.A., decl.) = (235996, −28188) within a 004 error radius (GRB Coordinates Network report, Sakamoto et al. 2016). GRB 160709A was also detected by LAT at ∼17σ with the clean event type of the data beyond 100 MeV (GCN report, Guiriec et al. 2016c), as well as at 10σ using LAT Low Energy (hereafter, LLE) data beyond 10 MeV. The prompt emission of GRB 160709A was also detected by Wind/Konus (GCN report, Frederiks et al. 2016), the CALorimetric Electron Telescope (CALET) (GCN report, Asaoka et al. 2016), and AstroSat (GCN report, Bhalerao et al. 2016).

Figure 1 shows the light curves of GRB 160709A in various GBM and LAT energy bands. The GBM was triggered by a low-intensity pulse compared to the main emission episode observed about 0.3 s later. The main emission episode is followed by a ∼4 s—long tail. The T₉₀ and T₅₀ durations of GRB 160709A computed between 50 and 300 keV (Kouveliotou et al. 1993) using GBM data are 5.63 ± 1.29 s and 0.58 ± 0.20 s, respectively. This GRB is considered to belong to the short GRB category because its T₅₀ value is a characteristic of a short GRB (T₅₀ ≲ 1), although the T₉₀ value places GRB 160709A in the overlapped region of the T₉₀ distribution of long and short GRBs (Bhat et al. 2016). This apparent inconsistency between T₉₀ and T₅₀ is explained by the fact that the former is more sensitive to the low-energy tail that follows the main emission episode. A similar result was also reported for the very bright short GRB 090510 detected with GBM (Ackermann et al. 2010). The LAT detected more than 20 events above 100 MeV within ∼30 s. The highest energy photon is 991 MeV, detected at T₀ + 1.47 s.

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3.1. Analysis Methods

3.2. Time-integrated Spectral Analysis for Each Episode

We divide the time interval corresponding to T₉₀ into three episodes (Figure 1). Both visual inspection of the composite light curve and the Bayesian-Block algorithm (Scargle et al. 2013) in different energy bands reach the same conclusion and result in the following cuts. The first episode is the time interval [T₀ − 0.064 s, T₀ + 0.320 s] where the emission is noticeable only in the low-energy region. The second time interval [T₀ + 0.320 s, T₀ + 0.768 s] corresponds to the main episode and consists of the bulk of the prompt emission in both the GBM and LLE energy ranges. The third episode [T₀ + 0.768 s, T₀ + 5.536 s] corresponds to the decaying phase of the keV–MeV emission tail with high-energy photons detected above 100 MeV. The burst peak is detected almost simultaneously in the GBM (10 keV–5 MeV) and LLE (20 MeV–100 MeV) energy ranges; however, it is delayed by ∼0.3 s in the LAT range (>100 MeV). We perform spectral analyses in each episode. Table 1 reports the fit results of various models listed in the previous section (see Appendix A for the agreement between data and the best-fit spectral model).

Table 1.  Spectral Fitting to GBM + LLE + LAT Data (8 keV–10 GeV) for Various Time Intervals

		Band Model			Power Law with break		Blackbody
T–T0	Model	α	β	Epeak	Γ	Ebreak	kT	PGstats/dof	${\rm{\Delta }}{PGstats}$
(s)				(keV)		(MeV)	(keV)
Time-integrated analysis for each episode
−0.064 + 0.320	PL				$-{1.93}_{-0.06}^{+0.05}$			710/709
(Episode 1)	CPL	$-{0.95}_{-0.31}^{+0.38}$	${163}_{-40}^{+82}$					683/708	−29
+0.320 + 0.768	CPL	$-{0.40}_{-0.05}^{+0.05}$	${2329}_{-139}^{+149}$					882/708
(Episode 2)	Band	$-{0.34}_{-0.06}^{+0.06}$	$-{3.17}_{-0.12}^{+0.11}$	${2011}_{-127}^{+141}$				753/707	−129
	CPL + PL	$-{0.19}_{-0.07}^{+0.08}$		${2097}_{-114}^{+120}$	$-{1.73}_{-0.04}^{+0.04}$			735/706	−147
	CPL + PLbreak	$-{0.18}_{-0.08}^{+0.08}$		${2081}_{-114}^{+120}$	$-{1.61}_{-0.06}^{+0.07}$	${58.6}_{-20.0}^{+46.0}$		726/705	−156
	CPL + BB	$-{1.46}_{-0.06}^{+0.06}$		${14690}_{-2619}^{+3608}$			${351}_{-16}^{+17}$	832/706	−50
	3CMa	$-{0.44}_{-0.17}^{+0.18}$		${2407}_{-258}^{+336}$	$-{1.71}_{-0.05}^{+0.06}$		${358}_{-62}^{+60}$	733/704	−149
	Fixed 3CMb	−0.70fixed		${2785}_{-234}^{+233}$	−1.50fixed		${376}_{-33}^{+36}$	738/706	−144
+0.768 + 5.568	PL				$-{1.72}_{-0.02}^{+0.02}$			857/709
(Episode 3)	PLbreak				$-{1.66}_{-0.03}^{+0.03}$	${219}_{-67}^{+134}$		845/708	−12
	PLbreak+low rolloffc				$-{1.75}_{-0.05}^{+0.05}$	${230}_{-82}^{+203}$		838/707	−19
	PL8 keV–200 keVd				$-{1.22}_{-0.15}^{+0.16}$			321/230
	PL200 keV–100 MeVe				$-{1.77}_{-0.07}^{+0.08}$			509/467
	PL100 MeV–10 GeVf				$-{2.22}_{-0.24}^{+0.24}$
	PL200 keV–10 GeVg	$-{1.83}_{-0.04}^{+0.05}$						521/477
	Broken PL200 keV–10 GeV	−1.77fixed	−2.18fixed			${166}_{-95}^{+207}$		517/477	−4
Time-resolved analysis for the second episodeh
+0.448 + 0.512	BB + PL				$-{1.68}_{-0.06}^{+0.05}$		${341}_{-23}^{+25}$	667/707
	CPL + PL	${0.91}_{-0.32}^{+0.38}$		${1423}_{-129}^{+148}$	$-{1.67}_{-0.06}^{+0.06}$			665/706	−2
+0.512 + 0.576	BB + PL				$-{1.85}_{-0.09}^{+0.07}$		${334}_{-28}^{+30}$	735/707
	CPL + PL	${0.72}_{-0.35}^{+0.42}$		${1422}_{-156}^{+200}$	$-{1.85}_{-0.09}^{+0.08}$			734/706	−1
+0.448 + 0.576	BB + PL				$-{1.75}_{-0.04}^{+0.04}$		${338}_{-18}^{+19}$	751/707
	CPL + PL	${0.85}_{-0.24}^{+0.28}$		${1419}_{-101}^{+115}$	$-{1.74}_{-0.05}^{+0.04}$			748/706	−3
	Fixed 3CMi	−0.70fixed		${3558}_{-1390}^{+1883}$	−1.73fixed		${338}_{-21}^{+23}$	746/706	−5

Notes.

^aThree-component model (CPL + PL + BB). ^bThree-component model with fixed parameters suggested by Guiriec et al. (2015a) (with α of CPL = −0.7, Γ of PL = −1.5, and BB). ^cPL_break with low-energy exponential rolloff, E_rolloff = ${25}_{-11}^{+16}$ keV. ^dGBM only. ^eGBM + LLE. ^fLAT only. ^gGBM + LLE + LAT. ^hOnly selected time intervals are presented here. The other time intervals are fitted best with either a CPL or a CPL+PL model. ⁱΓ in PL is fixed to Γ = −1.73 based on the time-integrated result.

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3.2.1. The First Episode

The best-fit model for the first episode [T₀ − 0.064 s, T₀ + 0.320 s] is CPL (see Figures 2 and 8). This model show a significant improvement in the PG-stat compared to the PL with ΔPG-stat ∼ 29, which corresponds to 5.2σ. The index of CPL is $-{0.95}_{-0.31}^{+0.38}$, in agreement with the typical low-energy index of GRBs, with E_peak = ${163}_{-40}^{+82}$ keV. Even though the best-fit model is CPL, it is possible that we underestimate its complexity due to the low fluence of this episode.

3.2.2. The Second Episode (Main Peak)

We find some interesting features in this time interval [T₀ + 0.320 s, T₀ + 0.768 s]. The Band function, the standard GRB model, is not sufficient for describing the prompt emission spectral shape of GRB 160709A. Instead, the CPL + PL model ($\alpha =-{0.19}_{-0.07}^{+0.08};{E}_{\mathrm{peak}}={2097}_{-114}^{+120}$ keV; ${\rm{\Gamma }}=-{1.73}_{-0.04}^{+0.04}$) is a better description of data than the Band function alone (ΔPG-stat ∼ 18, ∼4.2σ; see Figures 2 and 8). We try to fit the data with the Band + PL model, but then β becomes very soft ($\leqslant -10$) and the Band function and CPL are indistinguishable.

We add a break in the PL component of the CPL + PL model (CPL + PL_break). The spectral fit yields a break energy at E_break = ${59}_{-20}^{+46}$ MeV with a decrease of the PG-stat value by 9. The improvement of PG-stat, however, is not enough to confirm the existence of the break in the PL component.

To check the existence of a blackbody component (BB), we test CPL + BB to the data. The value of PG-stat obtained with this model increases by ∼50 with respect to CPL alone, therefore the CPL + BB model is less preferred than the CPL + PL model with the same number of dof. We also test a model consisting of three components: CPL + PL + BB. This model fits the data like the CPL + PL model does, with only ΔPG-stat ∼2 for two dof. As suggested by Guiriec et al. (2015a), we fit the data with the three-component model by fixing the two spectral parameters, α of CPL and Γ of PL, to −0.7 and −1.5, respectively. Both this model and the CPL + PL model give similar PG-stat values (ΔPG-stat ∼3) with the same dof, although the three-component model returns much bigger errors with respect to the CPL + PL model.

We perform simulation studies with Xspec–Fakeit for all alternative models (CPL + PL, CPL + PL_break, CPL + PL + BB and CPL + PL + BB with fixed parameters). As a result, we find that all models resemble each other under the observed brightness of GRB 160709A, and one can reproduce others' results within 1σ. Under the circumstances, we conclude that the CPL + PL is enough to explain the observed data and choose the model as the best-fit model for this episode.

3.2.3. The Third Episode (Weak Tail of the Prompt Emission)

A weak tail of the prompt emission is observed during the third episode. In this time interval, the PL_break model is the best-fit model (see Figures 2 and 8). The fit result shows a break at ${219}_{-67}^{+134}$ MeV with ΔPG-stat = 12 (∼3.5σ) with respect to a simple PL model. On the other hand, we reanalyze this episode with the GBM and LLE data (GBM + LLE, 8 keV–10 GeV) and find the hint of a break at E_break = ${314}_{-115}^{+285}$ MeV (ΔPG-stat = 7). This confirms that the break does not originate from systematic effects such as different effective areas between LLE and LAT. We also test a model, PL_break, with an exponential rolloff at low energy.¹⁵ This model yields the lowest PG-stat, but the ΔPG-stat compared to PL_break is not enough to compensate for one dof (ΔPG-stat = 7). Neither the Band function + low-energy rolloff nor a broken PL + low-energy rolloff show any improvement compared to the PL_break + low-energy rolloff.

We also perform energy-resolved spectral analyses for this episode with the PL model in the energy bands; 8 keV–200 keV, 200 keV–100 MeV, and 100 MeV–10 GeV (Table 1). For the 100 MeV–10 GeV analysis, we use the Fermi Science Tool rather than Xspec, as the former provides a better background estimation for LAT data. The three energy bands are well-fitted with PL, with clearly different photon indices, −1.22 (8 keV–200 keV), −1.77 (200 keV–100 MeV), and −2.22 (100 MeV–10 GeV) (Table 1). We double-check the LAT result with Xspec which shows similar results within 1σ. The data in the large energy range (200 keV–10 GeV) are fitted also with a broken PL model. The low and high spectral indices of this model are fixed to the values obtained from the PL fits in (200 keV–100 MeV) and (100 MeV–10 GeV) ranges, −1.77 and −2.22, respectively. The break energy of the broken PL is consistent with E_break of PL_break, which is the best-fit model of the third time interval in the energy band from 8 keV to 10 GeV.

3.3. Detailed Temporal and Spectral Analyses

3.3.1. Time-resolved Spectral Analysis of the Main Emission

We perform a time-resolved analysis in the main episode with 64 ms time-binned intervals with the GBM + LLE + LAT data. Since the CPL + PL model is the best-fit model in the time-integrated interval, we test the model in each time interval. When it is difficult to constrain PL due to a low fluence in the high-energy regime, we use CPL alone (see Figure 9).

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Figure 3 shows the time evolution of PL and CPL parameters. The PL index (Γ) is almost constant at ∼−1.7 for all time intervals (red in Figure 3). This value is consistent with the time-integrated result, Γ ∼ −1.73 (Table 1). The PL flux reaches its maximum during the third time interval and then decreases with time (pink in Figure 3).

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The CPL parameters (blue and cyan in Figure 3) show significant evolution with time. Particularly, in the third and fourth time intervals, [T₀ + 0.448 s, T₀ + 0.512 s] and [T₀ + 0.512 s, T₀ + 0.576 s], the slope of CPL (α) reaches ∼+0.9 and ∼+0.8, respectively. Such values are similar to a typical BB spectral index. We test the BB + PL model in these two time intervals. The model successfully fits the data with ΔPG-stat ≲2, with one more dof with respect to the CPL + PL model (Table 1). The temperatures of BB in the two sequential time intervals are ${341}_{-23}^{+25}$ keV and ${334}_{-28}^{+30}$ keV, respectively. The evolution of the temperature seems to be natural. Considering the evolution of α and the fit result with the BB + PL model in these sequential time intervals, there is a thermal dominant phase lasting ∼0.12 s, [T₀ + 0.448 s, T₀ + 0.576 s]. In other time intervals, α is almost constant around -0.3, which is harder than the expected index of the synchrotron emission process as reported in many observations (e.g., Katz 1994; Preece et al. 1998, 2000; Gruber et al. 2014).

The parameter E_peak of CPL fluctuates during the main episode (bottom panel in Figure 3). Particularly, in the time intervals where α is very hard (∼0.9), the values of E_peak tend to be lower than those of the other time intervals. This implies that the E_peak fluctuation may be related to the BB component existing in the thermal dominant phase, [T₀ + 0.448 s, T₀ + 0.576 s]. The spectral analysis in the thermal dominant phase is performed with the three-component model (CPL + PL + BB), as shown in Figure 4. The peak energy of CPL and the temperature of BB are E_peak  ∼ 3600 keV and kT ∼ 340 keV, respectively (Table 1). If BB with kT = 340 keV is fitted with CPL, the temperature of BB is equivalent to E_peak  ∼ 1300 keV, E_peak ∼ 3.9 kT. This E_peak of the BB component is consistent with the E_peak of CPL (∼1400 keV) in the the third and fourth time intervals, [T₀ + 0.448 s, T₀ + 0.512 s] and [T₀ + 0.512 s, T₀ + 0.576 s]. The fluxes of the CPL and BB components in the energy range from 10 keV to 10 MeV are (0.6 ± 0.4) × 10⁻⁵ erg cm⁻² s⁻¹ and (2.1 ± 0.3) × 10⁻⁵ erg cm⁻² s⁻¹, respectively. Depending on the relative dominance of the two components, the E_peak of CPL in the CPL + PL model is constrained to one of the two peaks; i.e., as the thermal (nonthermal) component dominates the nonthermal (thermal) component, E_peak is constrained to the peak energy of thermal (nonthermal) component. The E_peak fluctuation is therefore self-consistent with the existence of the BB component in the second episode.

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3.3.2. Spectral and Temporal Analyses of the Extended Emission

In the third episode, a spectral break at ∼200 MeV is observed (Section 3.2.3). To track the temporal evolution of the energy spectrum below and above E_break independently, we perform spectral and temporal analyses in two different energy bands, GBM + LLE (200 keV to 100 MeV) and LAT (100 MeV to 10 GeV), with Xspec and Fermi Science Tool, respectively. We ignore energy bands below 200 keV due to a steep break in the lower-energy band at ∼150 keV, i.e., NaI low-energy channels, 1–71, are ignored. For the GBM + LLE analysis, the time interval [T₀ + 0.448 s, T₀ + 5.568 s] is considered. This time interval contains part of the second episode and the third episode, assuming that the additional PL component observed in the second episode and the PL_break component in the third episode originate from the same source. As for the LAT analysis, we use the time interval [T₀ + 0.464 s, T₀ + 31 s], where they are the time of the first and last LAT events associated with GRB 160709A (with probability >90%).

Figure 5 (top panel) shows the evolution of the PL fluxes in the two energy bands. Both GBM + LLE and LAT show time-decaying features except for the first point in the GBM + LLE energy range. We perform the maximum likelihood fit with the following PL equation:

$$\begin{eqnarray}&&F(t)={F}_{0}{\left(\displaystyle \frac{t}{1{\rm{s}}}\right)}^{-\hat{\alpha }}.\end{eqnarray} \tag{ 1 }$$

The flux in the two energy ranges decreases as a function of time, with marginally different exponents for the temporal decays: the temporal indices $\hat{\alpha }$ of the GBM + LLE and LAT analyses are 1.09 ± 0.21 and 1.32 ± 0.16, respectively. During the time-decaying phase, the photon indices in the GBM + LLE and LAT energy bands are also different: 1.77 ± 0.08 and 2.22 ± 0.24, respectively (bottom panel in Figure 5).

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The photon index of GBM + LLE in the third episode is similar to that of the additional PL component observed in the second episode. Also, the flux of GBM + LLE decreases with time (Figure 5), similar to the evolution of the flux of the additional PL component (Figure 3). These analogous features suggest that an emission process producing a PL spectrum is continuous from the main episode to the tail end of the emission (at least in the energy band from 200 keV to 100 MeV).

4.1. Thermal Emission Component

Given the steepness of the spectrum in the time-resolved analysis of the main episode, we interpret the spectrum as being dominated by thermal emission during ∼0.12 s. Photospheric emission is naturally expected from the standard fireball model (e.g., Piran 1999), and the photospheric model is suggested to explain the very hard low-energy spectral index (thermal emission) (Mészáros & Rees 2000; Mészáros et al. 2002; Rees & Mészáros 2005; Pe'er et al. 2006; Asano & Mészáros 2013). Since we observe a very hard spectral index in GRB 160709A in the time interval [T₀ + 0.448 s, T₀ + 0.576 s], we test the photospheric model. This model constrains several important physical parameters such as the size of the central engine R₀, the photospheric radius R_ph, and the Lorentz factor Γ (Daigne & Mochkovitch 2002; Pe'er et al. 2007; Hascoët et al. 2013). They are expressed as

$$\begin{eqnarray}&&{R}_{0}\simeq \left[\displaystyle \frac{{D}_{L}{ \mathcal R }}{2{\left(1+z\right)}^{2}}{\left(\displaystyle \frac{{F}_{\mathrm{Th}}}{{F}_{N\mathrm{th}}}\right)}^{3/2}\right]\times {\left[\displaystyle \frac{{f}_{N\mathrm{th}}}{{\epsilon }_{T}}\right]}^{3/2},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{R}_{\mathrm{ph}}\simeq {\left[\displaystyle \frac{{\sigma }_{T}}{16{m}_{p}{c}^{3}}\displaystyle \frac{{D}_{L}^{5}{{ \mathcal R }}^{3}{F}_{N\mathrm{th}}}{{\left(1+z\right)}^{6}}\right]}^{1/4}\times {\left[(1+{\sigma }_{m}){f}_{N\mathrm{th}}\right]}^{-1/4},\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&{\rm{\Gamma }}\simeq {\left[\displaystyle \frac{{\sigma }_{T}}{{m}_{p}{c}^{3}}\displaystyle \frac{{\left(1+z\right)}^{2}{D}_{L}{F}_{N\mathrm{th}}}{{ \mathcal R }}\right]}^{1/4}\times {\left[(1+{\sigma }_{m}){f}_{N\mathrm{th}}\right]}^{-1/4},\end{eqnarray} \tag{ 4 }$$

where z and D_L are redshift and luminosity distance. The luminosity distance D_L is calculated as

$$\begin{eqnarray}&&{D}_{L}=(1+z)\displaystyle \frac{c}{{H}_{0}}{\int }_{0}^{z}\displaystyle \frac{{dz}^{\prime} }{\sqrt{{{\rm{\Omega }}}_{m}{\left(1+z^{\prime} \right)}^{3}+{{\rm{\Omega }}}_{{\rm{\Lambda }}}}}\end{eqnarray} \tag{ 5 }$$

with cosmological parameters from Planck Collaboration et al. (2016). F_Th and F_Nth are the measured fluxes from the thermal component (BB) and nonthermal components (CPL and PL), respectively. The fluxes of the thermal and nonthermal components are (2.1 ± 0.3) × 10⁻⁵ erg cm⁻² s⁻¹ and (0.9 ± 0.5) × 10⁻⁵ erg cm⁻² s⁻¹, respectively, which are computed in the energy band from 8 keV to 250 MeV. _T is the fraction of the initial energy released by the source in thermal form, and σ_m is the magnetization of the relativistic outflow at the end of the acceleration process. f_NTh is the efficiency of the nonthermal emission mechanism observed in the spectrum. ${ \mathcal R }$ represents the ratio between the measured BB flux and the expected BB flux by the Stefan–Boltzmann law;

$$\begin{eqnarray}&&{ \mathcal R }={\left(\displaystyle \frac{{F}_{\mathrm{BB}}}{\sigma {T}_{\mathrm{BB}}^{4}}\right)}^{1/2}.\end{eqnarray} \tag{ 6 }$$

As the redshift of GRB 160709A is unknown, we estimate R₀, R_ph, and Lorentz factor (Γ) as a function of redshift (Figure 6). The parameter R₀ ranges from 10⁷ to 10⁹ cm, R_ph from 10⁸ to 10¹¹ cm, and Γ from 10² to a few 10³, assuming that the ratio f_Nth/_T and the product (1 + σ_m)f_Nth are of order unity, each, for 0.01 ≲ z ≲ 10. This assumption is possible when f_Nth and _T have the same order. The f_Nth term should be f_Nth ≲ 0.1 for an internal shock model (Daigne & Mochkovitch 1998) and can be higher than this limit for other models, such as the magnetic reconnection model (see, e.g., Spruit et al. 2001; Lyutikov & Blandford 2003; Zhang & Yan 2011). In terms of the fraction of the thermal energy of the source, the standard GRB scenario suggests _T ≲ 0.1 (Daigne & Mochkovitch 2002; Zhang & Pe'er 2009; Guiriec et al. 2011; Hascoët et al. 2013). The magnetization factor σ_m in Equations (3) and (4) varies widely from σ_m ≲ 1 to σ_m ≫ 1 depending on the theoretical models; however, its impact on R_ph and Γ is negligible. A variation of σ_m of order 10⁴ results in negligible changes of R_ph and Γ, of order 10.

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Since GRB 160709A is a short GRB, the expected size of R₀ is 10–100 times larger than the Schwarzschild radius of the central engine (∼10⁶ cm) (Ryde & Pe'er 2009; Pe'er et al. 2015). On the other hand, the size of photosphere R_ph is known to be 10¹¹–10¹³ cm. The typical redshift of short GRBs is z ∼ 1 (Racusin et al. 2011), and with a redshift of this order (or above) the values of R₀ and R_ph become plausible, R₀ ∼ 3.8 × 10⁸ cm and R_ph ∼ 7.4 × 10¹⁰ cm. We note that they are still small, but can be explained by the unexpectedly high temperature of the BB component (kT ∼ 340 keV). The Lorentz factor for z ≳ 1 extends from a few 10² to a few 10³ in harmony with a bulk Lorentz factor constrained from γγ opacity in other GRBs (Fenimore et al. 1993; Baring & Harding 1997; Lithwick & Sari 2001; Abdo et al. 2009a, 2009c; Racusin et al. 2011; Zhao et al. 2011). Testing the photosphere model for the observed thermal emission, we suggest that the redshift of GRB 160709A is z ≳ 1 to be consistent with the theoretical expectations and other observations.

4.2. Additional PL Component and High-energy Extended Emission

The additional spectral component emerges 0.448 s after T₀ during the main emission episode and persists up to the GeV domain until the end of the extended emission (Section 3.3.1). The flux in two energy bands, GBM + LLE (200 keV–100 MeV) and LAT (100 MeV–10GeV), decreases with time as a PL function with two different temporal exponents (see Figure 5). This PL decaying feature is well explained by the standard external forward shock model (e.g., Kumar & Barniol Duran 2009, 2010; De Pasquale et al. 2010; Ghisellini et al. 2010; Panaitescu 2017). Sari et al. (1998) calculated the expected broadband spectrum of synchrotron emission and its corresponding light curve using a PL distribution of electrons in an expanding relativistic shock. The evolution of the spectrum and light curve of a GRB depends on its surrounding environment, its jet geometry, the electron distribution in the jet, and the cooling condition of the accelerated electrons (Rees & Mészáros 1994; Mészáros & Rees 1997; Dai & Lu 1998; Sari et al. 1998; Chevalier & Li 2000; Dai & Cheng 2001; Gao et al. 2013). The two representative surrounding medium profiles for GRBs, which are described as a function of radius, are the interstellar medium (ISM, n(r) = constant) and the wind (n(r) ∝ r⁻²) profiles. The synchrotron cooling regime is determined by the two physical parameters ν_m and ν_c (Sari et al. 1998). The parameter ν_m corresponds to the minimum Lorentz factor of the electrons accelerated in the shocks, and ν_c is the frequency of electrons after cooling down in shocks. If ν_m is larger than ν_c, all accelerated electrons cool down rapidly (fast cooling). The opposite case is called the slow cooling case, and the accelerated electrons with ν > ν_c can cool down. For electrons with a PL distribution of index p and a spectral flux F_ν = F_ν,0 ${t}^{-\hat{\alpha }}$ ${\nu }^{-\hat{\beta }}$, the spectral index $\hat{\beta }$ where $\hat{\beta }$ = −(Γ+1), and the temporal index $\hat{\alpha }$ can be expressed as a function of p depending on the surrounding environment and cooling conditions. In the ISM environment, the index α is either −1/4 (ν_c < ν < ν_m) or (2–3 × p)/4 (ν > ν_m, ν_c) for the fast cooling case, and either 3 × (p–1)/4 (ν_m < ν < ν_c) or (2–3 × p)/4 (ν > ν_m, ν_c) for the slow cooling case. Likewise, the index $\hat{\beta }$ is either 1/2 (ν_c < ν < ν_m) or p/2 (ν > ν_m, ν_c) for the fast cooling case, and either (p–1)/2 (ν_m < ν < ν_c) or p/2 (ν > ν_m, ν_c) for the slow cooling case. The dependence of $\hat{\beta }$ and $\hat{\alpha }$ with the electron spectral index p therefore shows that the two parameters are related by a closure relation.

We test the forward shock model with a set of closure relations derived in an adiabatic hydrodynamic evolution (for the complete set of closure relations, see Gao et al. 2013). Figure 7 shows the closure relations of different surrounding environment and cooling regime conditions. The two sets of spectral and temporal indices from the GBM + LLE and LAT analyses seem to be related with different closure relations. The set obtained from GBM + LLE analysis is positioned at a closure relation of the slow cooling condition (ν_m < ν < ν_c) and ISM environment (red line in Figure 7). On the other hand, the set from the LAT analysis is at a closure relation corresponding to the fast cooling condition (ν > ν_m and ν_c) with an undetermined surrounding environment condition (blue line in Figure 7).

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From the two $\hat{\beta }$ and $\hat{\alpha }$ sets and corresponding closure relations, we compute the value of the electron spectral index p of GRB 160709A (Table 2). The p values from the two different closure relations are consistent with each other. A weighed average of p_β is 2.49 ± 0.12, which is consistent with other observational studies (e.g., Shen et al. 2006; Starling et al. 2008; Curran et al. 2009, 2010).

Table 2.  Closure Relation Test

	Energy Range	$\hat{\alpha }$	$\hat{\beta }$	${p}_{\hat{\alpha }}$	${p}_{\hat{\beta }}$	Weighted Average p
GBM + LLE	200 keV–100 MeV	1.09 ± 0.21	0.77 ± 0.08	2.46 ± 0.29	2.55 ± 0.16	2.49 ± 0.12
LAT	100 MeV–10 GeV	1.32 ± 0.16	1.22 ± 0.24	2.43 ± 0.21	2.44 ± 0.49

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The closure relation from the GBM + LLE implies that the surrounding medium of GRB 160709A is the ISM environment rather than the wind environment. This accords with the theoretical expectation for the surrounding medium of short GRBs (Paczynski 1986, 1991; Rosswog et al. 1999; Abbott et al. 2017b).

The closure relation of the GBM + LLE energy band implies ${\nu }_{\mathrm{GBM}+\mathrm{LLE}}$ < ν_c, while that of the LAT energy band suggests ν_LAT > ν_c. The two results indicate that ν_c is located in between the GBM + LLE energy band and the LAT energy band. The spectral break detected with 3.5σ in the third episode (E_break ∼ 166 MeV) supports the hypothesis of the existence of ν_c between the two energy bands. We explore the plausibility of the high ν_c with a simple assumption. Assuming that the GRB isotropic energy E_iso = 10⁵² erg and surrounding medium density n = 10⁻³ cm⁻³ (Bernardini et al. 2007; Caito et al. 2009), the electron cooling frequency ν_c in the ISM environment can be expressed as (Sari et al. 1998)

$$\begin{eqnarray}\begin{array}{rcl}{\nu }_{c} & \simeq & 7.9\times {10}^{14}{\epsilon }_{B}^{-3/2}{\left(\displaystyle \frac{{E}_{\mathrm{iso}}}{{10}^{52}\mathrm{erg}}\right)}^{-1/2}\\ & & \times {\left(\displaystyle \frac{n}{{10}^{-3}{\mathrm{cm}}^{-3}}\right)}^{-1}{\left(\displaystyle \frac{t}{1{\rm{s}}}\right)}^{-1/2}\ \mathrm{Hz}.\end{array}\end{eqnarray} \tag{ 7 }$$

If ν_c is 166 MeV at 3 s, the middle of the third episode, the above equation gives the fraction of the total energy contained in the magnetic field, _B ≃ 5.1 × 10⁻⁴. This fraction is consistent with other observations (e.g., Kumar & Barniol Duran 2009, 2010; Santana et al. 2014). Santana et al. (2014) made a distribution of _B with Swift observations and found that _B has a range from 10⁻⁸ to 10⁻³.

GRB 160709A is an unusual short burst detected by both GBM and LAT, which allows us to analyze the burst in broad energy ranges. GRB 160709A triggered GBM with a weak soft emission. This emission is followed by the main emission lasting ∼1 s. A weak tail of the prompt emission continues about 3 s after the main episode, which increases GBM T₉₀. The GRB spectrum consists of several components including the thermal component; CPL, PL, and BB. The multi-component spectrum implies that GRB 160709A is produced not by a single emission process but with multiple emission processes including both thermal and nonthermal emissions. In summary, our observational analyses of the prompt emission of GRB 160709A show the following features:

• 1.  
  We determined that the keV–GeV spectrum of GRB 160709A is well described by a combination of CPL and PL. The weak soft emission triggering GBM is described by CPL with α ∼ −1 and E_peak ∼ 163 keV. For the main emission, the best-fit model is the CPL + PL model, although many other models well-fitted the data including the three-component model (CPL + BB + PL). After the main emission episode, a simple PL is observed continuously up to the end of the LAT extended emission.
• 2.  
  In time-resolved analyses of the main emission episode, we found very steep spectra in the sequential time intervals and regarded them as a thermal dominated phase lasting ∼0.12 s. In this phase, a CPL component was observed with very hard spectral index ∼+0.9, therefore, it can be completely replaced by a BB component. The temperature of BB is about 340 keV, which is unexpectedly high compared to other sub-dominant thermal emission reports. The time-resolved analysis suggests that the best description of GRB 160709A spectrum in the main episode is the combination of the three components (CPL + PL + BB).
• 3.  
  The observation of high-energy events (LAT) is delayed compared to the lower-energy events (GBM). The delayed emission seems to be related to the onset of the additional PL component, which starts to appear during the main emission and remains until the end of the prompt phase. The best-fit model of this time interval is PL_break with 3.5σ significance. The flux of this component decreases as a function of time (PL), and the spectral index of this component does not significantly change in time. The two energy bands (GBM + LLE and LAT) show different spectral and temporal indices.
• 4.  
  Guiriec et al. (2010) reported a detailed analysis of three of the brightest short GRBs detected with Fermi/GBM. The sub-dominant thermal component observed in GRB 160709A was reported for the first time in 2011 in a long GRB (Guiriec et al. 2011) and in 2013 in a short GRB (Guiriec et al. 2013), thus after the publication of Guiriec et al. (2010). It is not excluded that such a photospheric emission is also present in the three short GRBs of Guiriec et al. (2010), as suggested in a new analysis not yet published. Therefore, GRB 160709A may not be that different from the bursts published in Guiriec et al. (2010). Guiriec et al. (2013) reported the existence of an intense thermal component (kT ∼ 10–13 keV) in one of the brightest short GRBs detected with Fermi/GBM; in this article and conversely to GRB 160709A, there was no clear indication of the existence of an extra PL in addition to the other two components.

The interpretations of these observational features lead to several conclusions.

• 1.  
  A thermal component in the time-resolved analyses can be interpreted as the photosphere emission of GRB 160709A. This burst clearly shows the thermal emission (BB) with very high temperature overwhelming nonthermal emission (CPL) in the 100–1000 keV energy band during the time interval [T₀ + 0.448 s, T₀ + 0.576 s]. Assuming the redshift of GRB 1060709A ≳1, we derived the central engine radius R₀ ≃ 10⁸ cm and the photospheric radius 10¹¹ cm, which is surprisingly small compared to other previous reports.
• 2.  
  The origin of the extended emission is regarded as the external forward shock. The spectral and temporal indices of the GBM + LLE (200 keV–100 MeV) and the LAT (100 MeV–10 GeV) analyses separately have different closure relations, although the implications from the two closure relations do not conflict. We inferred that ν_c seems to be located between GBM + LLE and LAT energy bands. The surrounding environment is preferred to be the ISM environment rather than the wind environment. This analysis revealed the electron spectral index p = 2.49 ± 0.12 for GRB 160709A. This is the first trial of testing GRB closure relations in the two distinct high-energy bands, and the observational properties are well interpreted by the external forward shock model.

The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat á l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden.

Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France. This work performed in part under DOE Contract DE-AC02-76SF00515.

Software: RMfit (4.3.2), XSPEC (v12.9.1; Arnaud 1996), Fermi Science Tools (v11r5p3).

We perform the time-integrated spectral fit in the three episode (Section 3.2). Figure 8 shows the best-fit model for each episode and its residual.

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We perform the time-resolved spectral analysis in the second episode (Section 3.3.1). Figure 9 shows the best-fit model for each time interval and its residual.

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