THE ULTRALUMINOUS GRB 110918A

GRB 110918A was detected by four IPN experiments—INTEGRAL SPI-ACS (Rau et al. 2005), in a highly elliptical orbit; Konus-WIND (Aptekar et al. 1995), in orbit around the Lagrangian point L1; MESSENGER GRNS (Gold et al. 2001), in orbit around Mercury; and Mars Odyssey HEND (Hurley et al. 2006), in orbit around Mars—at 0.46, 5.0, 645.9, and 943.0 lt-s from Earth, respectively. The light curve of the event (Figure 1) starts with an extremely bright, hard, and short pulse followed by three weaker, softer, and partly overlapping pulses in the next 25 s.

Zoom In Zoom Out Reset image size

An initial 62 arcmin² IPN error box was derived using Konus-WIND, MESSENGER, and Odyssey, and was announced in a GCN Circular (Hurley et al. 2011). A Swift target-of-opportunity observation was requested; when the XRT position was announced (Mangano et al. 2011a), it was evident that the error box was significantly displaced from the counterpart. After lengthy investigation, it was found that both the MESSENGER and Odyssey times were inaccurate due to the use of outdated spacecraft clock files. With the updated files, and with INTEGRAL added, the burst was triangulated again; an error ellipse was derived using the method described in Hurley et al. (2000). The 3σ ellipse has a 316 major axis, 12 minor axis, and an area of 2.6 arcmin²; the ellipse is centered at R.A.(J2000) = $02^{\rm h}10^{\rm m}07\buildrel{\mathrm{s}}\over{.}9$, decl..(J2000) = −27°06'544, with χ² = 0.06 for one degree of freedom (dof; three annuli minus two fitted coordinates). The optical counterpart found by Tanvir et al. (2011) lies inside the ellipse, 066 from its center (Figure 2).

Zoom In Zoom Out Reset image size

GRB 110918A triggered the Konus-WIND γ-ray spectrometer (KW) at T₀(KW) = 77222.856 s UT (21:27:02.856) on 2011 September 18, hereafter T₀. It was detected by the S1 detector, which observes the Southern ecliptic hemisphere; the incident angle was 531. The propagation delay from Earth to WIND is 3.928 s for this GRB; correcting for this factor, the KW trigger time corresponds to the Earth-crossing time 77218.928 s UT (21:26:58.928).

2.2.1. Time History

In the instrument's "triggered mode," count rates are recorded in three energy bands: G1(22–90 keV), G2(90–375 keV), and G3(375–1450 keV). The record starts at T₀ − 0.512 s and continues to T₀ + 229.376 s with an accumulation time varying from 2 to 256 ms. The "background mode" count rate data are available up to T₀ + 250 s in the same energy bands with a coarse resolution of 2.944 s.

The prompt-emission light curve (Figure 3) can be divided into two groups of overlapping pulses, which are separated by a minimum around ∼T₀ + 11.5 s when the observed rate in the harder G2 and G3 bands is comparable to the background level. The first group, hereafter referred as Phase I, is characterized by two pronounced pulses: the huge P₁, which peaks at ∼T₀ + 0.368 s, and P₂ (∼T₀ + 4.032 s); the second group (Phase II) comprises considerably overlapping pulses P₃ (∼T₀ + 14.6 s) and P₄ (∼T₀ + 17.7 s). Shown in the same figure, the temporal evolution of the G2/G1 and G3/G2 hardness ratios indicates an apparent hardness–intensity correlation of the emission against a general tendency of spectral softening in the course of the burst.

Zoom In Zoom Out Reset image size

The bright, pulsed emission decays up to ∼T₀ + 30 s. However, a stable excess in the count rate over the background level was detected, mostly in the softer G1 and G2 energy bands, until T₀ + 250 s when the KW measurements stopped due to the limited capacity of the WIND spacecraft telemetry. The detailed analysis of the extended γ-ray emission is given in Section 2.3.

The burst starts with a sharp rise of the bright, hard, short pulse P₁, which culminates after a ∼350 ms two-step onset (Figure 4). In this phase, a spectrum with high and evolving peak energy is suggested by the hardness ratio behavior: the G3/G2 ratio rapidly decays from a maximum at the onset of the initial pulse, while G2/G1 remains at a high, but stable, level until ∼T₀ + 0.370 s, when a peak of the emission is reached. The observed count rate of ∼2 × 10⁵ s⁻¹ in the cumulative G1+G2+G3 (22–1450 keV) energy band is unprecedented in almost 19 yr of KW observations of long GRBs. Although the photon flux is very high, a standard KW dead-time correction procedure (i.e., a simple non-paralyzable dead-time correction in each of the measurement bands, taking into account a softer gate blocking by harder ones) is still applicable to the burst; no additional modeling, which was used, e.g., in an analysis of the KW detection of the 1998 August 27 giant flare from SGR 1900+14, is required (details of these simulations and the KW dead-time correction procedures can be found in Mazets et al. 1999).

Zoom In Zoom Out Reset image size

The trailing edge of the initial pulse is more gently sloping; the emission intensity decreases until T₀ + 2.5 s and gives way, with a small "bump" at ∼T₀ + 2.95 s, to the rise of the second, relatively weaker, and softer pulse, P₂. The G1+G2+G3 count rate in this pulse reaches a 64 ms peak value of ∼3 × 10⁴ s⁻¹ (or ∼0.15 of that in P₁) at T₀ + 4.032 s and then gradually decays to a minimum around ∼T₀ + 11.5 s, which separates Phase I and Phase II.

A new rise begins at ∼T₀ + 11.5 s. The third (P₃) and fourth (P₄) pulses form an overlapping structure (Phase II) in the time interval from T₀ + 11.5 s to ∼T₀ + 25 s. The peak 64 ms count rate reached in these two pulses is ∼1.9 × 10⁴ s⁻¹ and ∼3.8 × 10⁴ s⁻¹, respectively. While these rates are on par with that in the second pulse, P₂, the hardness ratios indicate a considerably softer emission spectrum. Despite the huge count rate in the initial pulse, the count fluence recorded by KW in the 22–1450 keV band during the first ∼25 s of the burst is nearly equally divided between Phase I and Phase II.

In the G2+G3 energy band (90–1450 keV)—standard for calculations of the KW GRB light-curve characteristics—the total duration of the burst, determined at the 5σ level, is T₁₀₀ = 95.154 s (from T₀ − 0.178 s to T₀ + 94.976 s). The corresponding T₉₀ value is 19.6 ± 0.1 s and T₅₀ = 14.3 ± 0.1 s. The G2+G3 count rate reached a maximum of (1.46 ± 0.02) × 10⁵ s⁻¹ in the 64 ms bin starting 0.368 s after the trigger, and the total number of counts during the T₁₀₀ interval is 1.34 × 10⁵.

2.2.2. Spectral Lags

The observed evolution of the hardness ratios suggests that soft photons are delayed with respect to the higher energy ones, a common property of long GRBs. We examined the spectral lag, τ_lag, using the cross-correlation function (CCF) between the light curves in two energy bands (Norris et al. 2000; Band 1997). After calculating the CCF as a function of τ_lag, we obtained the peak value of τ_lag by fitting it with a fourth-degree polynomial.

The resulting values of τ_lag between the 16 ms G1, G2, and G3 light curves at different phases of the burst are listed in Table 1. Statistically significant lags in the 40–360 ms range are derived for the initial pulse (P₁), Phase I, Phase II, and in the entire prompt phase of the emission. The positive τ_lag are indicative of hard-to-soft spectral evolution.

Table 1. Spectral Lags between Konus-WIND Light Curves

Time Interval	Light Curves	$\tau _{\mathrm{lag}}^{\rm a}$
from T0(s)		(s)
−0.032–26.368	G3–G1	0.092 ± 0.003b
	G2–G1	0.047 ± 0.002
	G3–G2	0.047 ± 0.002
−0.032–2.000	G3–G1	0.091 ± 0.003
(Initial pulse)	G2–G1	0.043 ± 0.002
	G3–G2	0.047 ± 0.002
−0.032–8.000	G3–G1	0.092 ± 0.003
(Phase I)	G2–G1	0.044 ± 0.002
	G3–G2	0.047 ± 0.002
12.096–26.368	G3–G1	0.36 ± 0.13
(Phase II)	G2–G1	0.19 ± 0.01
	G3–G2	0.09 ± 0.05

Note. ^aPositive spectral lag τ_lag means that the spectrum has hard to soft evolution. ^b1σ uncertainties throughout this table.

Download table as:  ASCIITypeset image

Predictably, the lags for the entire burst and Phase I are almost identical to the lags found for the huge initial pulse alone. However, for the soft Phase II, the values of τ_lag are two to four times longer than for the hard initial phase of the event.

2.2.3. Light-curve Decomposition

The prompt emission of long GRBs shows a wide range of structures in its light curve. Attempts have been made to fit the light curves with Fast Rise Exponential Decay models described by combinations of PL functions (Kocevski & Liang 2003; Kocevski et al. 2003), exponential functions (Norris et al. 1996, 2005; Lee et al. 2000a, 2000b), and lognormal functions (Bhat et al. 2012).

The light curve of the initial pulse (Figure 4) shows a clear two-step onset, which suggests at least two overlapping episodes of emission. We performed the analysis of this pulse with the background-subtracted G1, G2, and G3 light curves using the four-parameter exponential model from Norris et al. (2005):

$$\begin{equation} A(t)=A_m\lambda \exp \lbrace -\tau _{1}/(t-t_0)-(t-t_0)/\tau _{2}\rbrace \end{equation} \tag{ 1 }$$

for t > t₀, where λ = exp (2μ); μ = (τ₁/τ₂)^1/2; A_m is the pulse amplitude; t₀ is the pulse start time; τ₁ and τ₂ are time constants characterizing the rise and decay parts of the pulse. This pulse peaks at t_m = t₀ + (τ₁τ₂)^1/2 and has a width measured between two 1/e points, w = τ₂(1 + 4μ)^1/2.

The 16 ms light curves in the T₀ − T₀ + 1.3 s interval have been fitted, using a χ² statistic, with models comprising a single pulse, and two or more overlapping components. The single-component model yields very high $\chi ^2_r$. Introducing the second component improved the fit dramatically: χ² changed from 1123/78 dof to 132/74 dof for the G2 light curve. A similar improvement is found for the G1 and G3 light curves. Further addition of components to the model results in ambiguous, poorly constrained fits and does not improve the statistic. Thus, we conclude that the KW light curves of the initial pulse are best described by the double-component model.

Figure 5 shows the decomposition and Table 2 lists the model parameters and the derived quantities. The narrow component, C₂, which dominates at the peak of the emission in the harder bands, is delayed with respect to a wider component, C₁, which describes the onset of the initial pulse before ∼T₀ + 0.2 s and its decay after ∼T₀ + 0.8 s. The delays between the components, calculated as the difference between their peak times, t_m, are ∼0 ms, ∼62 ms, and ∼136 ms in the G1, G2, and G3 bands, respectively. In the same way, we calculated lags between the G1, G2, and G3 bands for each component. The G3–G1, G2–G1, and G3–G2 lags for the leading sub-pulse C₁ (160 ± 10 ms, 72 ± 8 ms, and 87 ± 8 ms, respectively) are ∼7 times longer than the corresponding lags for C₂ (24 ± 7 ms, 10 ± 5 ms, and 14 ± 6 ms, respectively). The relatively longer lags obtained for the leading component are in agreement with the strong evolution of the G3/G2 hardness ratio present in the first ∼300 ms of the burst.

Zoom In Zoom Out Reset image size

Table 2. Initial Pulse Decomposition

Light	Am	t0	τ1	τ2	tm	w
Curve	(103 counts s−1)	(s)	(s)	(s)	(s)	(s)
Component C1
G1	28.7 ± 0.3	−0.144 ± 0.002	0.631 ± 0.009	0.491 ± 0.005	0.412 ± 0.007	1.154 ± 0.012
G2	53.7 ± 0.4	−0.157 ± 0.001	0.801 ± 0.007	0.307 ± 0.002	0.339 ± 0.005	0.839 ± 0.005
G3	15.5 ± 0.2	−0.150 ± 0.003	0.648 ± 0.011	0.250 ± 0.003	0.262 ± 0.007	0.682 ± 0.007
Component C2
G1	27.1 ± 0.7	0.177 ± 0.003	0.706 ± 0.021	0.079 ± 0.002	0.413 ± 0.004	0.283 ± 0.006
G2	56.7 ± 1.1	0.137 ± 0.002	1.221 ± 0.020	0.057 ± 0.001	0.402 ± 0.003	0.253 ± 0.003
G3	24.1 ± 0.6	−0.179 ± 0.002	12.418 ± 0.107	0.026 ± 0.001	0.388 ± 0.005	0.244 ± 0.002

Download table as:  ASCIITypeset image

Since a rapid variability in GRB light curves could be linked directly to the activity of the central engine (Sari & Piran 1997; Kobayashi et al. 1997; Ryde 2004), the shortest variability timescale for a GRB is clearly of interest. In particular, assuming that the shortest timescale in GRB prompt emission is the shortest pulse width, the length scale of the GRB central engine can be estimated (see, e.g., Bhat et al. 2012 and references therein). For GRB 110918A, we find a width of δT ≡ w = 0.25 s, obtained for the sub-pulse C₂ in the energy bands G2 and G3.

2.2.4. Time-resolved Spectral Analysis

In the triggered mode, Konus-WIND measures 64 energy spectra in 128 channels of two overlapping energy bands: PHA1 (22–1450 keV) and PHA2 (375 keV–18 MeV). The first four spectra have a fixed accumulation time of 64 ms; after that, the accumulation time varies over 0.256–8.192 s, depending on the current intensity of the burst. During the bright prompt phase of GRB 110918A, 35 energy spectra were measured. Seventeen of them covered the first hard pair of pulses (T₀ − T₀ + 5.632 s) and spectrum 18 was recorded during the temporary decrease in the burst intensity (T₀ + 5.632–T₀ + 13.312 s). The remaining 17 spectra (T₀ + 13.312–T₀ + 28.416 s) covered the second soft group of pulses and the transition to the extended emission tail.

The spectral analysis was performed with XSPEC version 12.5 (Arnaud 1996) with the Band GRB function (Band et al. 1993): f(E)∝E^αexp (− (2 + α)E/E_peak) for E < E_peak(α − β)/(2 + α), and f(E)∝E^β for E ⩾ E_peak(α − β)/(2 + α), where α is the PL photon index, E_peak is the peak energy in the νF_ν spectrum, and β is the photon index at higher energies. The spectral model was normalized to the energy flux in the 20 keV–10 MeV range, a standard band for the KW GRB spectral analysis.

Typically, the raw count rate spectra were rebinned to have at least 20 counts per energy bin to ensure Gaussian-distributed errors and the correctness of the χ² statistic. Spectra 3, 4, and 5 have good count statistics in the MeV band, which allowed us to study the hard emission with a minimal channel binning. For these spectra, the cstat and pgstat options of XSPEC were also used. We found the fit results to be consistent with those obtained by the first method. At the very high count rate observed in the GRB 110918A initial pulse, the differential nonlinearity (DNL) of the instrument's analog-to-digital converters must be taken into account as a source of systematic errors in the count spectra. To account for the known level of uncertainty in the DNL, we added up to 25% systematics to statistical errors for 256 ms spectra covering the initial pulse. Also, channels below 50 keV were excluded from fits for spectrum 5 since the influence of a pulse-pileup effect on the low-energy part of this spectrum is not negligible. The same precautions were taken for time-averaged spectra, which include the initial pulse.

Results of the KW time-resolved spectral analysis are listed in Table 3. A good quality of fit is achieved for the majority of the spectra, which enables us to construct the temporal behavior of the model parameters (α, β, E_peak) and to trace in detail the evolution of the spectral composition of radiation over the course of the burst (Figure 6).

Zoom In Zoom Out Reset image size

Table 3. Konus-WIND Time-resolved Spectral Fits with the Band Function

Spectrum	Accumulation	α	β	Epeak	Fluxa	χ2/dof
	Interval (s from T0)			(keV)	(10−6 erg cm−2 s−1)
1	0–0.064	$-0.75_{-0.09}^{+0.10}$	−2.35b	$4050_{-2770}^{+1610}$	$290_{-19}^{+20}$	22.7/25
2	0.064–0.128	$-0.67_{-0.09}^{+0.10}$	−2.35b	$1630_{-270}^{+330}$	$348_{-20}^{+21}$	33.3/33
3	0.128–0.192	$-0.68_{-0.11}^{+0.12}$	$-2.49_{-0.40}^{+0.29}$	$1230_{-260}^{+300}$	$370_{-30}^{+32}$	65.3/75c
4	0.192–0.256	$-0.54_{-0.13}^{+0.18}$	$-2.23_{-0.26}^{+0.23}$	$1160_{-300}^{+330}$	$487_{-37}^{+40}$	76.7/77c
5	0.256–0.512	$-0.47_{-0.08}^{+0.09}$	$-2.39_{-0.14}^{+0.11}$	$1120_{-150}^{+160}$	$775_{-26}^{+27}$	92.4/86c
6	0.512–0.768	$-0.44_{-0.10}^{+0.11}$	$-2.45_{-0.10}^{+0.09}$	$443_{-41}^{+45}$	$289_{-12}^{+12}$	77.2/57
7	0.768–1.024	$-0.48_{-0.15}^{+0.17}$	$-2.48_{-0.16}^{+0.15}$	$290_{-32}^{+40}$	$125_{-6.8}^{+6.8}$	30.3/50
8	1.024–1.280	$-0.88_{-0.14}^{+0.18}$	$-2.39_{-0.27}^{+0.23}$	$270_{-45}^{+62}$	$51.5_{-4.4}^{+4.5}$	31.2/44
9	1.280–1.536	$-1.26_{-0.14}^{+0.14}$	$-2.37_{-2.60}^{+0.22}$	$294_{-62}^{+118}$	$24.6_{-4.4}^{+3.7}$	54.2/74
10	1.536–2.304	$-1.34_{-0.11}^{+0.15}$	$-2.33_{-0.56}^{+0.16}$	$260_{-51}^{+74}$	$13.1_{-1.7}^{+2.0}$	52.7/50
11	2.304–3.328	$-1.25_{-0.09}^{+0.10}$	$-2.58_{-0.53}^{+0.24}$	$261_{-35}^{+43}$	$10.9_{-1.1}^{+1.2}$	51.1/51
12	3.328–3.840	$-0.98_{-0.11}^{+0.12}$	$-2.89_{-1.85}^{+0.32}$	$301_{-40}^{+51}$	$24.8_{-2.2}^{+2.1}$	65.5/48
13	3.840–4.096	$-0.97_{-0.10}^{+0.11}$	$-2.75_{-0.62}^{+0.28}$	$378_{-53}^{+58}$	$48.7_{-4.2}^{+4.3}$	68.5/44
14	4.096–4.352	$-1.00_{-0.11}^{+0.14}$	$-2.78_{-0.61}^{+0.31}$	$300_{-48}^{+45}$	$41.1_{-3.4}^{+3.7}$	46.6/43
15	4.352–4.608	$-0.86_{-0.18}^{+0.30}$	$-2.49_{-0.29}^{+0.19}$	$205_{-44}^{+45}$	$33.7_{-3.0}^{+3.3}$	36.6/41
16	4.608–4.864	$-0.69_{-0.24}^{+0.28}$	$-2.29_{-0.15}^{+0.11}$	$155_{-23}^{+31}$	$29.2_{-2.8}^{+3.0}$	40.7/39
17	4.864–5.632	$-1.28_{-0.13}^{+0.16}$	$-2.44_{-0.28}^{+0.16}$	$150_{-22}^{+26}$	$12.1_{-1.2}^{+1.2}$	38.9/47
18	5.632–13.312	$-1.33_{-0.14}^{+0.18}$	$-2.60_{-0.27}^{+0.17}$	$90_{-9}^{+9}$	$1.94_{-0.16}^{+0.18}$	63.8/82
19	13.312–14.080	$-0.79_{-0.20}^{+0.25}$	$-2.68_{-0.20}^{+0.15}$	$99_{-9}^{+9}$	$9.69_{-0.66}^{+0.73}$	29.5/44
20	14.080–14.336	$-0.60_{-0.28}^{+0.36}$	$-2.68_{-0.31}^{+0.20}$	$116_{-15}^{+16}$	$16.2_{-1.5}^{+1.7}$	28.0/34
21	14.336–14.592	$-0.64_{-0.21}^{+0.26}$	$-2.99_{-0.43}^{+0.26}$	$119_{-11}^{+11}$	$17.5_{-1.3}^{+1.5}$	28.8/33
22	14.592–14.848	$-0.87_{-0.22}^{+0.24}$	$-3.28_{-2.30}^{+0.38}$	$111_{-10}^{+12}$	$15.8_{-1.2}^{+1.3}$	29.1/33
23	14.848–15.360	$-0.96_{-0.15}^{+0.18}$	$-3.58_{-0.83}^{+0.39}$	$85_{-5}^{+5}$	$12.9_{-0.58}^{+0.63}$	26.0/38
24	15.360–16.128	$-1.12_{-0.21}^{+0.26}$	$-3.11_{-0.29}^{+0.19}$	$59_{-3}^{+3}$	$9.99_{-0.42}^{+0.45}$	37.0/39
25	16.128–17.664	$-1.39_{-0.10}^{+0.10}$	<−3.39	$68_{-4}^{+3}$	$9.63_{-0.33}^{+0.32}$	37.8/51
26	17.664–17.920	$-0.73_{-0.22}^{+0.28}$	$-3.68_{-1.35}^{+0.46}$	$95_{-6}^{+6}$	$26.3_{-1.4}^{+1.5}$	37.7/33
27	17.920–18.176	$-0.64_{-0.18}^{+0.25}$	<−3.70	$87_{-5}^{+4}$	$23.2_{-0.95}^{+1.0}$	33.9/31
28	18.176–18.432	$-0.73_{-0.20}^{+0.28}$	$-3.78_{-0.83}^{+0.43}$	$81_{-5}^{+5}$	$23.9_{-1.00}^{+1.0}$	42.6/30
29	18.432–18.688	$-0.66_{-0.22}^{+0.24}$	$-3.65_{-0.73}^{+0.34}$	$82_{-4}^{+5}$	$22.9_{-1.0}^{+1.0}$	32.9/29
30	18.688–18.944	$-0.81_{-0.22}^{+0.23}$	<−3.75	$81_{-5}^{+5}$	$20.9_{-0.91}^{+0.92}$	16.6/27
31	18.944–19.200	$-0.67_{-0.21}^{+0.21}$	<−4.01	$75_{-3}^{+4}$	$19.4_{-0.82}^{+0.78}$	33.9/29
32	19.200–19.456	$-0.62_{-0.29}^{+0.32}$	$-3.82_{-2.04}^{+0.40}$	$71_{-4}^{+4}$	$19.1_{-0.82}^{+0.84}$	21.3/29
33	19.456–19.712	$-0.75_{-0.28}^{+0.34}$	$-3.67_{-0.73}^{+0.38}$	$67_{-4}^{+4}$	$18.1_{-0.87}^{+0.92}$	22.7/27
34	19.712–20.224	$-0.98_{-0.22}^{+0.33}$	$-3.63_{-0.59}^{+0.34}$	$52_{-3}^{+3}$	$13.0_{-0.47}^{+0.50}$	34.6/35
35	20.224–28.416	$-1.50_{-0.31}^{+0.38}$	$-3.11_{-0.25}^{+0.18}$	$34_{-10}^{+8}$	$1.46_{-0.076}^{+0.075}$	80.1/94

Notes. ^aIn the 20 keV–10 Mev energy band. ^bSpectra 1 and 2 were fitted with index β fixed to that of the time-averaged spectrum 1+2, for which: $\alpha =-0.68_{-0.08}^{+0.10}$, $\beta =-2.35_{-0.79}^{+0.32}$, and $E_{\mathrm{peak}}=2290_{-540}^{+610}$ (χ² = 61.6/57 dof). ^cPG-statistic/dof.

Download table as:  ASCIITypeset image

Spectra 1–4 were measured at the onset of the extremely intense initial pulse (Figure 4). The emission at this moment is very hard; E_peak reaches the highest value for the burst (∼4 MeV) in the first 64 ms interval after the trigger. As the intensity surges up, E_peak starts to decrease gradually, but the flattening low-energy photon index, α, indicates a spectrum enriched by higher-energy photons. Spectrum 5 describes the culmination of the pulse (T₀ + 0.256–T₀ + 0.512 s). At this time, E_peak remains above 1 MeV and the energy flux, averaged over 256 ms, reaches a huge value of ∼7.8 × 10⁻⁴ erg cm⁻² s⁻¹. The falling edge of the initial pulse (spectra 6–10, T₀ + 0.512–T₀ + 2.304 s) is described by the further decrease in E_peak down to ∼260 keV and by a slightly time-delayed steepening of α to ∼ − 1.3.

At the peak rate, no obvious high-energy cutoff was observed up to the instrument's upper energy threshold (Figure 7). For the initial 64 ms spectra 1 and 2 taken individually, the high-energy photon index, β, is poorly constrained. However, after applying a minimal time-averaging, the fit to the average spectrum 1+2 yields $\beta =-2.35_{-0.79}^{+0.32}$, consistent with the indices obtained for the subsequent spectra 3, 4, 5, and 6. Thus, no significant spectral variation is observed above several MeV during the onset and the culmination of the initial pulse. This result is illustrated by plot 7 in Figure 8, where photon light curves for different energy ranges are shown as constructed from the unfolded spectra. From this figure, one can see that the MeV emission decays dramatically with the decay of the initial pulse and has almost ceased after ∼T₀ + 5 s.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

As already mentioned when discussing the KW light curves and their hardness ratio behavior, a correlation between the radiation intensity and its hardness is notable for the whole history of the burst. Onsets of all four major emission pulses are characterized by an apparent rise in E_peak and by a pronounced flattening of the low-energy part of the spectrum, with an opposite pattern in the decaying emission phases. At the same time, there is a clear trend of spectral softening from pulse to pulse: the top value of E_peak reached during each of the four major emission pulses steadily declines in time from ≈4 Mev for the initial pulse to ≈380 keV, ≈130 keV, and ≈105 keV for pulses P₂, P₃, and P₄, respectively. The general trend of the peak energy evolution in the prompt emission phase can be roughly described by a PL slope: E_peak(t)∝t^−0.6 (Figure 9).

Zoom In Zoom Out Reset image size

The behavior of the high-energy photon index, β, is consistent with the general tendency of the emission softening: β steepens, displaying weak variations, from ≈ − 2.3 at the onset of the burst to β ⩽ −3 soon after the onset of Phase II and later.

2.2.5. Time-averaged Spectra and Energetics in the Prompt Emission

We analyzed the time-averaged spectrum of the entire prompt phase of the emission and its separate parts in the same way as described in the previous section. Among the tested models, the Band function is the only model that adequately describes the shape of the spectrum. The results of the fits are summarized in Table 4.

Table 4. Konus-WIND Time-averaged Spectral Fits with the Band Function

Interval	α	β	Epeak	χ2/dof	Fluencea
from T0(s)			(keV)		(10−4 erg cm−2)
0.000–28.416	−1.64$_{-0.05}^{+0.06}$	−2.25$_{-0.09}^{+0.09}$	340$_{-60}^{+70}$	77.5/81	7.78$_{-0.45}^{+0.46}$
0.000–2.304	−0.95$_{-0.05}^{+0.05}$	−2.41$_{-0.12}^{+0.10}$	990$_{-90}^{+100}$	103/80	4.03$_{-0.11}^{+0.11}$
(Initial pulse)
0.000–13.312	−1.12$_{-0.08}^{+0.08}$	−2.28$_{-0.10}^{+0.08}$	630$_{-100}^{+160}$	54.4/81	6.09$_{-0.38}^{+0.34}$
(Phase I)
13.312–28.416	−1.2$_{-0.1}^{+0.2}$	−3.3$_{-0.2}^{+0.2}$	78$_{-3}^{+3}$	86.2/83	1.57$_{-0.27}^{+0.33}$
(Phase II)

Note. ^aIn the 20 keV–10 MeV energy band.

Download table as:  ASCIITypeset image

It should be emphasized that, having E_peak ≈ 340 keV, α ≈ −1.6, and β ≈ −2.3, the overall time-integrated spectrum (T₀ to T₀ + 28.416 s) is, indeed, the "average" one and does not reflect the spectral composition of the emission at any particular phase of the burst. As expected from the time-resolved spectral analysis, the average spectra of the first (T₀ − T₀ + 13.312 s, Phase I) and the second (T₀ + 13.312 − T₀ + 28.416 s, Phase II) pairs of overlapping pulses are essentially different. With only the low-energy photon index being close, α ≃ −1.2, the peak energy differs between these phases of the burst almost by an order of magnitude (E_peak ≈630 keV and ≈78 keV, respectively). Also, the high-energy photon index of the time-averaged spectrum is substantially softer in Phase II than in Phase I (β ≈ −3.3 and β ≈ −2.3, respectively). The average spectrum of the initial pulse (T₀ − T₀ + 2.304 s) is very hard: E_peak ≈1 MeV, α ≈ −1, and β ≈ −2.4.

Based on the results of the spectral and temporal analysis, we calculated the time-integrated and peak energy flux of the prompt γ-ray emission of GRB 110918A. In the 20 keV–10 MeV band, which is standard for Konus-WIND, the total energy fluence, S, from T₀ to T₀ + 28.416 s, is (7.8 ± 0.5) × 10⁻⁴ erg cm⁻². More than half of this energy (∼55%) is released in the initial pulse, ∼80% during the hard Phase I, and only ∼1/5 of the total fluence comes from the much softer Phase II.

The 64 ms peak energy flux, F_max = (9.2 ± 0.4) × 10⁻⁴ erg cm⁻² s⁻¹, is reached in the interval starting 0.384 s after the trigger, at the culmination of the initial pulse (see Figure 4). As for the exceptionally high count rate, the F_max is the highest among >2000 GRBs detected by Konus-WIND so far. The 64 ms peak flux for Phase II is found to be ∼20 times lower, (4.5 ± 0.5) × 10⁻⁵ erg cm⁻² s⁻¹, in the interval starting at T₀ + 17.536 s, at the peak of the last, softest pulse in the light curve.

It can be seen from the entire time history recorded by Konus-WIND (Figure 10) that the extremely bright pulsed phase of GRB 110918A ends ∼30 s after the trigger. However, a stable excess in the count rate over the background level was detected by the instrument until the end of the measurements at T₀ + 250 s.

Zoom In Zoom Out Reset image size

At this final phase of the γ-ray emission, the light curve shows a smooth temporal decay with a photon flux several orders of magnitude fainter and a substantially changed spectrum shape, as compared to the prompt phase. The "transitional" spectrum 35 (from T₀ + 20.224 s to T₀ + 28.416 s) is the last one which requires a "curved" spectral model in the fits. The subsequent time-resolved spectra were measured by KW out to T₀ + 102.144 s. Since the emission is weak, the individual spectra have poor signal-to-noise ratios (S/N), but may be adequately described by a simple PL: f(E)∝E^−Γ, with a photon index, Γ, of 1.7–2.3. The average spectrum from T₀ + 28.416 s to T₀ + 102.144 s (interval 1 in Figure 10) extends to ∼9 MeV and is best fit by a simple PL with Γ = 2.00 ± 0.12 (1σ errors hereafter in this section) and χ2 = 106/99 dof. The final portion of the KW data for GRB 110918A is available from the background mode light curves, which are measured out to T₀ + 250 s (interval 2 in the same figure). The time histories recorded in the G1, G2, and G3 energy bands are, in effect, a continuous three-channel spectrum covering the 22–1450 keV energy range. The PL fit to the average three-channel spectrum from T₀ + 100 s to T₀ + 250 s yields Γ = 2.18 ± 0.24 (χ² = 0.40/1 dof), suggesting that there is no spectral evolution from the preceding interval 1, for which the same method gives Γ = 1.96 ± 0.13 (χ² = 0.96/1 dof); this is consistent with the index obtained for the multi-channel spectrum.

In the INTEGRAL SPI-ACS data (∼80 keV–10 MeV energy band), the γ-ray emission of GRB 110918A can be traced to ∼T₀ + 700 s, after which the source flux becomes indistinguishable from the unstable background. Although the energy responses of the KW and SPI-ACS detectors are quite different, the stable PL shape of the spectrum allowed us to extend the late-time γ-ray light curve beyond the end of the KW observation (open symbols in Figure 10). To ensure the correctness of the extrapolation, we normalized the count rate between the two instruments using counts accumulated in the interval from T₀ + 50 to T₀ + 250 s, well beyond the cessation of the prompt emission. For this interval the KW three-channel spectral fit yields Γ = 2.00 ± 0.16 (χ² = 0.51/1 dof); in the following analysis we assume this slope and the corresponding spectral index, β_γ ≡ Γ − 1 = 1.00 ± 0.16, for the extended γ-ray emission.

A temporal PL fit to the combined light curve, N(t)∝t^−α, yields, in the T₀ + 30 s–T₀ + 700 s time interval, the decay index α_γ = 0.84 ± 0.05 (χ² = 19.1/15 dof). A count rate excess over this slope is found around T₀ + 165 s. Since the "bump" is present at the ∼2σ level in both KW and SPI-ACS data, it is unlikely to be a simple count rate fluctuation. Excluding the corresponding KW and SPI-ACS data points from the fit results in a better χ² = 10.8/13 dof, while the temporal index changes only marginally to α_γ = 0.88 ± 0.05 (the solid line in Figure 10).

Traced back in time, this slope lies just below the count rate observed at the KW light curve minimum around T₀ + 11 s, which may suggest that the PL component emerges before the rise of Phase II of the prompt emission. A PL fit to a three-channel spectrum constructed for the narrow time interval from T₀ + 9.728 s to T₀ + 11.776 s yields Γ = 2.01 ± 0.03 (χ² = 0.27/1 dof), thus favoring this hypothesis.

Assuming a PL spectrum with Γ = 2, we estimate the 22–1450 keV energy fluence of the GRB 110918A extended emission from T₀ + 28.416 s to T₀ + 700 s to be (2.6 ± 0.5) × 10⁻⁵ erg cm⁻², or ≈0.3% of the energy in the prompt phase of the burst.

2.4.1. Swift/XRT Observations

2.4.2. XRT Light Curve

The Swift/XRT count rate light curve in the 0.3–10 keV band has been built according to the light curve creation procedure described in Evans et al. (2007), requiring a minimum of 70 counts per bin and dynamic binning. In the 2012 observations, the source was not detected and only a 3σ upper limit of 1.28 × 10⁻³ counts s⁻¹ has been calculated using the Bayesian method of Kraft et al. (1991). The best-fit model is a single PL with decay slope α_X = −1.63 ± 0.02 and χ² = 46.4/45 dof. The count rate light curve, together with the best-fit model and residuals, is shown in Figure 11.

Zoom In Zoom Out Reset image size

We tested the XRT afterglow light curve for the presence of a temporal break by fitting the data with a broken power law (BPL) function:

$$\begin{equation} N(t)\propto \left\lbrace \begin{array}{@{}l@{\quad }l@{}}t^{-\alpha _1}, & (t<t_{b}) \\ t_{b}^{(\alpha _2-\alpha _1)}\,t^{-\alpha _2}, & (t>t_{b}), \\ \end{array}\right. \end{equation} \tag{ 2 }$$

where t_b is the time of break in the light curve; α₁ and α₂ are the temporal indices before and after the break, respectively. An F-test shows that there is little evidence of an improvement in the fit if a break is added (F = 4.62, giving a null-hypothesis probability of 0.015). This result has been checked using different binning criteria. We generally find an F-test probability of >10⁻², suggesting that a BPL model is not needed, with a high significance, to fit the light curve. We also tested a smooth BPL model (Granot & Sari 2002); it results in an ambiguous fit and does not limit the break.

2.4.3. XRT Spectra

We extracted average spectra of the source and the background after merging all the 2011 observations (sequences from 00020186002 to 00020187051 in Table 5, covering times from ∼107.3 ks to ∼4.325 Ms after the trigger). For the source extraction region, we used the 15-pixel-radius circular region needed to remain within the XRT FOV in sequence 00020186002.

To perform time-resolved spectral analysis, we also extracted a set of nine source and background spectra with comparable statistics. The observations were grouped as shown in Table 5. The small source extraction region with 15 pixel radius was used for spectrum 1 (coming from the highly offset initial observation) and for spectrum 9, corresponding to the faintest state of the source. The other spectra have been extracted from a circular 30-pixel-radius region. All background spectra were extracted from the same region used for the average background spectrum.

The spectra were all fit with an absorbed PL model with two absorption components: Galactic absorption in the direction of the source fixed at the value of 0.168 × 10²¹ cm⁻² (Kalberla et al. 2005) and intrinsic absorption at the measured redshift of z = 0.984. A solar metallicity is assumed for both absorption components.

The XRT average spectrum is best fit by an intrinsic absorption $N_{\mathrm{H,i}}=2.33_{-0.53}^{+0.58}\times$ 10²¹ cm⁻², a photon index Γ = 1.85$_{-0.07}^{+0.07}$, and $\chi ^2_r$ = 1.02 (134 dof). The average (observed) unabsorbed flux in the 0.3–10 keV band is 6.2 (5.3)× 10⁻¹³ erg cm⁻² s⁻¹. In Figure 12, we show the data and best-fit model. From this fit, we derived a count rate to the observed and unabsorbed 0.3–10 keV flux conversion factors of 4.58 × 10¹¹ and 5.15 × 10¹¹ erg cm², respectively.

Zoom In Zoom Out Reset image size

The time-resolved spectra are all best fit with the same absorbed PL model. Fits performed with a free N_{H, i} parameter always lead to best-fit parameter values consistent within errors with those previously obtained for the average spectrum. We then fixed N_{H, i} to 2.33 × 10²¹ cm⁻². Final results for the photon index, average observed flux, and $\chi ^2_r$ for the time-resolved spectra are listed in Table 6; the index is shown in the lower panel of Figure 11, where we see no evidence of spectral evolution.

Table 6. Absorbed PL Fits to the Time-resolved Swift/XRT Spectra

Mean Epoch	Photon Index	Observed Flux	χ2/dof
(ks from T0)	Γ	(10−13 erg cm−2 s−1)
111	1.85$^{+0.17}_{-0.17}$	$90.1^{+15.9}_{-12.4}$	7.64/9
162	1.79$^{+0.09}_{-0.09}$	$60.5^{+5.0}_{-4.3}$	36.7/41
223	1.85$^{+0.10}_{-0.10}$	$40.8^{+3.7}_{-2.9}$	33.5/34
310	1.86$^{+0.19}_{-0.18}$	$20.0^{+2.7}_{-2.4}$	21.6/17
408	1.89$^{+0.20}_{-0.19}$	$14.5^{+2.6}_{-1.9}$	7.37/11
491	1.96$^{+0.21}_{-0.22}$	$10.3^{+2.1}_{-1.5}$	8.56/8
613	1.78$^{+0.21}_{-0.21}$	$7.9^{+1.6}_{-1.2}$	11.9/12
802	1.78$^{+0.27}_{-0.28}$	$4.8^{+1.2}_{-0.89}$	12.7/10
2643	1.83$^{+0.18}_{-0.19}$	$0.78^{+0.13}_{-0.10}$	16.7/18

Notes. The flux is given in the (0.3–10) keV range. Galactic and intrinsic N_H at redshift z = 0.984 have been fixed to 0.168 × 10²¹ cm⁻² and 2.33 × 10²¹ cm⁻², respectively.

Download table as:  ASCIITypeset image

2.4.4. Swift-UVOT Observation and Analysis

Swift's UVOT (Roming et al. 2000, 2004, 2005) began observing the burst approximately 153 ks after the KW trigger. Data were initially taken in UVOT's white filter, but late-time data (200–500 ks after the trigger) were also taken in UVOT's four ultraviolet filters (u, uvw1, uvm2, and uvw2) until Swift ceased observations.

Photometry was measured with UVOTSOURCE using the calibrations of Poole et al. (2008), Breeveld et al. (2010), and Breeveld et al. (2011). A combined light curve from all detections, normalized to the count rate in the white filter, suggests a late-time flattening of the light curve. In order to exclude contamination from nearby sources or the possible host galaxy, we requested additional observations with Swift/UVOT. Since the best coverage of the afterglow was in the white and u filters, we requested 10 ks of observations for each of these two filters. We examined these data for the presence of a host galaxy and, within the source aperture, we found a candidate object. Analysis of this object provided a 5.3σ detection in white with a magnitude of 22.63 ± 0.21 and a 2.6σ detection in the u band at a magnitude of 22.49 ± 0.42 (1σ errors). These findings are in agreement with E13, where results of detailed studies of the host can be found.

Using the late-time UVOT observations, we subtracted the underlying flux from the white- and u-band data. Figure 13 and Table 7 show the combined light curve from these two bands, normalized to the u filter and co-added. The host-subtracted light curve shows a PL decay with a slope of α_opt = −1.52 ± 0.09 (χ² = 9.35/11 dof) out to 3.4 Ms after the trigger. Introducing a temporal break does not improve the fit: the best BPL fit yields χ² = 9.27/9 dof and a very high (96%) probability of chance improvement over the simple PL. The pre- and post-break indices, α₁ = 1.46 ± 0.19 and α₂ = 1.55 ± 0.16, are indistinguishable within 1σ errors, and the break time, t_b = 258 ± 415 ks, cannot be determined. A search for an achromatic break in the UV/optical and X-ray afterglow was performed by fitting the UVOT and XRT data with the BPL model simultaneously. We put minimal restrictions on the procedure and tied only the key model parameter, t_b, between the optical and the X-ray light curves. Nevertheless, no limits on the break were found in the fits and an F-test probability of ≈0.09 suggests that the BPL model is not needed.

Zoom In Zoom Out Reset image size

Table 7. UVOT Combined Normalized Photometry

Tmid	Half-exposure	Count Rate	u
(ks from T0)	(ks)	(s−1)	(mag)
168.1	14.8	0.2895 ± 0.0099a	19.69$^{+0.04}_{-0.04}$
208.5	20.7	0.1961 ± 0.0098	20.11$^{+0.06}_{-0.05}$
257.5	23.7	0.1788 ± 0.0160	20.21$^{+0.10}_{-0.09}$
326.8	29.6	0.1090 ± 0.0122	20.75$^{+0.13}_{-0.11}$
496.7	48.5	0.0574 ± 0.0061	21.44$^{+0.12}_{-0.11}$
618.2	61.8	0.0340 ± 0.0052	22.01$^{+0.18}_{-0.16}$
755.0	74.9	0.0263 ± 0.0043	22.29$^{+0.20}_{-0.17}$
933.8	92.8	0.0235 ± 0.0068	22.41$^{+0.37}_{-0.28}$
1108.7	61.2	0.0189 ± 0.0056	22.65$^{+0.38}_{-0.28}$
1525.1	38.5	0.0228 ± 0.0102	22.45$^{+0.64}_{-0.40}$
2054.1	197.7	0.0107 ± 0.0051	23.27$^{+0.70}_{-0.42}$
2741.1	197.1	0.0045 ± 0.0064	24.20$^{+nan}_{-0.98}$
3591.8	358.7	0.0056 ± 0.0046	23.96$^{+1.81}_{-0.65}$
4143.1	182.7	<0.0022	>24.98
33366.3	410.9	<0.0034	>24.51

Note. ^a1σ errors in this table.

Download table as:  ASCIITypeset image

2.4.5. Broadband SED

In a companion paper (E13), a broadband spectral energy distribution (SED) of the GRB 110918A afterglow was studied, as constructed from the optical/near-IR GROND photometry at a midtime of 194 ks, and the XRT data between 140 ks and 250 ks. From the best simple PL fit (χ² = 85/73 dof), the authors derived a line-of-sight extinction of A_V = 0.16 ± 0.06¹⁵ mag, an intrinsic column density of $N_{\mathrm{H,i}}=1.56_{-0.46}^{+0.52}$ × 10²¹ cm⁻², and a broadband spectral slope of β_OX = 0.70 ± 0.02; they also found that a BPL modeling of the SED does not improve the fit (χ² = 83/71 dof).

Using the GROND host-subtracted photometry from E13, we analyzed a broadband SED—built following the method of Schady et al. (2010)—from the GROND data in the g'r'i'z'JHK_S bands, the XRT data, and the host-subtracted UVOT photometry in the u and white filters. The SED was constructed for an epoch centered at 300 ks utilizing the observations from 107 ks to 450 ks after the trigger. Fits were made in XSPEC with the absorbed PL model and three dust extinction curves from Pei (1992): the Milky Way with R_V = 3.08, the Large Magellanic Cloud with R_V = 3.16, and the Small Magellanic Cloud (SMC) with R_V = 2.93. The Galactic reddening is fixed to 0.02 mag (Schlegel et al. 1998) and the Galactic column density is set to 0.168 × 10²¹ cm⁻². The best fit with a simple PL (χ² = 155.3/111 dof) is achieved for the SMC dust profile and closely reproduces the results of E13 at 194 ks: A_V = 0.22 ± 0.02 mag, $N_{\mathrm{H,i}}=1.65_{-0.38}^{+0.42}$ × 10²¹ cm⁻², and β_OX = 0.69 ± 0.01. This slope and the implied column density are in poor agreement with the ranges obtained in our analysis of both time-resolved and time-averaged XRT spectra; this suggests that a single PL does not describe the broadband SED adequately. As distinct from E13, a BPL model significantly improves our fit, with χ² = 128.4/109 dof and a chance improvement probability over the simple PL of 3.1 × 10⁻⁵. The best BPL fit (Figure 14) is found for the same SMC dust profile; it yields A_V = 0.35 ± 0.09 mag, $N_{\mathrm{H,i}}=2.94_{-0.66}^{+0.73}$ × 10²¹ cm⁻², the break energy $E_b=0.022_{-0.013}^{+0.046}$ keV, β_opt = 0.42 ± 0.18, and $\beta _{\rm X}=0.89_{-0.07}^{+0.08}$. This result is in agreement with the XRT spectral analysis and a spectral slope change of β_X − β_opt ≈ 0.47 suggests a cooling break between the UVOT and XRT spectral bands; the derived range of E_b favors this hypothesis.

Zoom In Zoom Out Reset image size

The XRT+UVOT+GROND SED centered at 194 ks (the E13 epoch) was also tested and we found that both simple and broken PL fits result in a 1σ agreement with those for the SED at 300 ks. Thus, the significant improvement found for the BPL fits in this work may result from a combination of at least two factors. First, with the UVOT observations added, the shape of the optical part of the SEDs at both epochs is better understood. Second, the overall S/N in the SED at 300 ks is considerably higher, since it was built from the ∼3.5-times longer time span of observations.

We note that A_V ∼ 0.35 derived from the BPL fit is higher than the line-of-sight extinction resulting from a simple PL, but still much smaller than the average A_V of the host galaxy's starlight (∼0.90 mag) reported by E13. This inconsistency has been discussed in E13. The authors consider two explanations: (1) a clumpy geometry of dust within the host and (2) the progenitor had enough time to destroy local dust with its UV emission. Bearing in mind the huge brightness of GRB 110918A, the latter option can be naturally extended by the possibility that the GRB itself partially destroyed dust grains along the line of sight (see, e.g., Waxman & Draine 2000; Fruchter et al. 2001).

Konus-WIND started operation in 1994 November, and, in almost 19 yr, has detected more than 2000 GRBs, with virtually no bright GRBs having been missed. Among these bursts, GRB 110918A is, without a doubt, an outstandingly bright event (Figure 15). Its fluence, both in energy and count spaces, is among the half-dozen highest observed. The burst's 64 ms peak count rate is unprecedented. Its peak energy flux is surpassed only on the short 2 ms timescale by the two ultra-bright, short, hard bursts GRB 051103 and GRB 070201, the candidate giant flares from soft γ-ray repeaters in the nearby galaxies M81/82 and M31 (Frederiks et al. 2008; Mazets et al. 2008; Hurley et al. 2010).

Zoom In Zoom Out Reset image size

The huge energy flux measured by KW suggests an enormous energy released in the cosmological rest frame. Assuming a redshift of z = 0.984 and a standard cosmology model with H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, and Ω_Λ = 0.73, the luminosity distance D_L is 2.0 × 10²⁸ cm. Derived from the total energy fluence and the peak energy flux (Section 2.2.5), the isotropic-equivalent energy release in γ-rays,E_iso, is (2.1 ± 0.1) × 10⁵⁴ erg, and the peak isotropic luminosity, L_iso, is (4.7 ± 0.2) × 10⁵⁴ erg s⁻¹ (both quantities are in the rest-frame 1–10000 keV band).

These estimates make GRB 110918A one of the most energetic GRBs and the most luminous GRB ever observed since the beginning of the cosmological era in 1997. Figure 16 shows E_iso and L_iso for GRB 110918A along with almost one hundred KW GRBs with known redshifts; this sample is discussed in detail by A. E. Tsvetkova et al. (in preparation, hereafter T13). One can see that GRB 110918A lies at the upper edge of the E_iso distribution and is nearly an order of magnitude more luminous than any burst at z ∼ 1.

Zoom In Zoom Out Reset image size

In Figure 16, the KW detection horizon for a GRB 110918A-like event is also indicated. The limit of z ∼ 7.5 is estimated by applying the KW triggering algorithm to simulated light curves at different redshifts. The simulations, which account for both time dilation and spectral reddening, show that at z ⩾ 5, only the initial pulse remains detectable in the KW band; at high redshifts, the burst is seen as a short (T₉₀ ∼ 2–3 s) GRB with moderate E_peak ∼ 300 keV and a relatively long spectral lag of ∼200 ms. Assuming a Swift/Burst Alert Telescope (BAT) sensitivity of 10⁻⁸ erg cm⁻² s⁻¹ in the 15–150 keV band (Barthelmy et al. 2005), its detection threshold is reached at z ∼ 12.

The key rest-frame parameters of GRB 110918A—the intrinsic peak energy, E_{p, i} ≡ E_peak(1 + z) = 670 ± 140 keV, and the rest-frame duration, T₉₀/(1 + z) = 9.9 ± 0.05 s—are nearly at the center of the distributions for the KW sample and may be considered typical. Consequently the huge energetics of GRB 110918A cannot be easily explained by an extremely hard spectrum or by long-lasting prompt emission. Since more than half of the burst's energy is released in the hard initial pulse (Section 2.2.5), the intrinsic peak energy of the pulse's time-averaged spectrum (2000 ± 200 keV) is also an important characteristic of the event. It is in the top 10% of the KW E_{p, i} distribution, but it cannot be the sole reason for the GRB 110918A record energy. Therefore, the most likely explanation for both the observed and isotropic-equivalent rest-frame energetics is a huge photon flux, which suggests a highly collimated emission.

We tested the GRB 110918A rest-frame characteristics against E_{p, i}–E_iso and E_{p, i}–L_iso relations—known as the "Amati" and "Yonetoku" correlations (Amati et al. 2002; Yonetoku et al. 2004, respectively; we used their recent updates from Ghirlanda et al. 2012). One can see from Figure 17 that the burst is close to being a luminous outlier with respect to both relations, suggesting that the spectral hardness of GRB 110918A is likely a minor ingredient of the burst's isotropic energy as compared to the population. On the other hand, the spread in the spectral-energy correlations is known to diminish when the jet effect is taken into account (Ghirlanda et al. 2004, 2007); this supports the hypothesis that the GRB 110918A collimation is relatively tighter when compared to an average GRB. It should be noted, finally, that the initial pulse taken alone follows the E_{p, i}–E_iso relation to within 1σ and the E_{p, i}–L_iso relation to within ∼1.5σ. This is particularly important since, as mentioned above, the initial pulse is the only phase of the burst which could be seen from high redshifts and emphasizes the role of observational bias in these studies.

Zoom In Zoom Out Reset image size

Several methods have been proposed to estimate the bulk Lorentz factor of the GRB ejecta (Γ₀): the pair-opacity constraint from the "compactness" problem (Lithwick & Sari 2001), the optical afterglow onset method (e.g., Sari & Piran 1999), and the very early external shock emission method, which considers the quiescent periods between the prompt emission pulses (Zou & Piran 2010). Since no early observations are available for the GRB 110918A afterglow and the prompt emission pulses overlap considerably, only the first method mentioned is applicable.

We calculated the lower limit on Γ₀ using inequalities from Lithwick & Sari (2001). The first (Limit A) is

$$\begin{equation} \Gamma _{\mathrm{0,A}} > \hat{\tau }^{1/(2\beta +2)}(E_{\max }/m_e c^2)^{(\beta -1)/(2\beta +2)}(1+z)^{{\beta -1}/{\beta +1}}; \end{equation} \tag{ 3 }$$

and the second (Limit B) is

$$\begin{equation} \Gamma _{\mathrm{0,B}} > \hat{\tau }^{1/(\beta +3)}(1+z)^{{\beta -1}/{\beta +3}}, \end{equation} \tag{ 4 }$$

where β is the photon PL index at MeV energies (in the N(E)∝E^−β notation), E_max is the highest energy at which photons were observed, and

$$\begin{equation} \hat{\tau } \simeq 4.3\times 10^{10} \frac{f_1}{\beta -1}\, D_{L,28}^2 \, 0.511^{1-\beta }\, (\delta T/0.1)^{-1}, \end{equation} \tag{ 5 }$$

where δT is the minimum variability timescale of the prompt emission, and f₁ is the photon flux at 1 MeV.

From the KW analysis, we assume the following parameters for GRB 110918A: δT = 0.25 s, β = 2.39, E_max > 18 MeV, and f₁ = 160 cm⁻² s⁻¹ MeV⁻¹, all taken at the peak of the initial pulse (see Sections 2.2.3 and 2.2.4). This yields Γ_{0, A} > 240 and Γ_{0, B} > 360; by applying the tighter limit, we conclude Γ₀ > 360.

Typically, when photons are observed at high energies (E_max ∼ GeV), Limit A yields a stricter constraint than Limit B. Unfortunately, GRB 110918A was not observed by high-energy missions and we proceeded from a very conservative Konus-WIND limit, E_max > 18 MeV. However, the value of Γ_{0, B} allows us to set the lower limit on the high-energy cutoff of the GRB 110918A emission spectrum to E_max ⩾ 100 MeV (assuming that the spectrum measured by Konus-WIND in the MeV band extends unchanged to those energies).

Liang et al. (2010) discovered a tight correlation between Γ₀ and E_iso. This correlation was confirmed and refined on a broader GRB sample by Lü et al. (2012), who obtained $\Gamma _0\simeq 91E^{0.29}_{\mathrm{iso,52}}$. In the latter work, another tight correlation between Γ₀ and L_iso was found in the form of $\Gamma _0\simeq 249L^{0.30}_{\mathrm{iso,52}}$. Applied to GRB 110918A these relations yield Γ₀ values of 430 and 1580, respectively. Close values (Γ₀(E_iso) ∼ 450 and Γ₀(L_iso) ∼ 1450) are evaluated based on slightly different slopes from Ghirlanda et al. (2012). It should be noted, however, that the GRB samples used by Lü et al. (2012) and Ghirlanda et al. (2012) do not contain any burst with Γ₀ > 1000 or L_iso > 10⁵⁴ erg s⁻¹, which is the case for this burst. Thus, the Γ₀ value of ∼450 obtained from the Γ₀–E_iso relation, which is tested by both authors up to E_iso ∼ 10⁵⁴ erg, may be considered more feasible than Γ₀ ∼ 1500 derived from L_iso. The Γ₀ estimate of a few hundred is supported by another correlation studied by Ghirlanda et al. (2012), the Γ₀ − E_{p, i} relation. From E_{p, i} = 670 keV, this relation yields Γ₀ = 150 and, from E_{p, i} = 2000 keV for the initial pulse, Γ₀ = 400.

In Section 2.3, it was shown that at ∼30 s after the KW trigger, the prompt phase of GRB 110918A rapidly developed into a steadily decaying "tail" of the extended γ-ray emission. The decay follows a PL with the temporal index α_γ ≈ 0.88 out to ∼T₀ + 700 s. At the same time, the emission spectrum is well described by a PL with spectral index β_γ ≈ 1. The combination of the spectral and temporal behavior is in fairly good agreement with that expected at the "plateau" (II) and "normal" (III) phases of the canonical X-ray afterglow (Nousek et al. 2006; Zhang et al. 2006). This supports a scenario in which the extended γ-ray emission of GRB 110918A is generated by the synchrotron forward-shock mechanism with a possible late-time energy injection (EI).

Swift observations of the GRB 110918A afterglow started ∼107 ks after the burst and showed no clear signature of a possible jet break in the X-ray and UV/optical light curves up to the time the observations ceased ∼48 days later. The XRT temporal slope, α_X ≈ 1.63, cannot be unambiguously attributed to the "normal" (III) or "jet" (IV) segment of the canonical X-ray afterglow; α_X is at the steep end of the segment III indices and at the shallow end of the segment IV indices for a sample of XRT afterglows with "prominent" jet breaks (Racusin et al. 2009). The slope of 1.5, which is widely suggested as critical to distinguish the pre-break and post-break segments of both X-ray and optical afterglows (see, e.g., Panaitescu 2007; Liang et al. 2008), is also too close to α_X and α_opt ≈ 1.52 to draw any firm conclusion. Thus the question of the jet break location with respect to the time span of the Swift observations cannot be easily answered when discussing the afterglow temporal slopes alone.

The standard fireball model for GRB afterglows suggests that their temporal α, and spectral β, indices follow closure relations (CRs), which are linear relationships between α and β, both being linear functions of a PL index of the underlying electron spectrum, p. We tested the GRB 110918A observations against an extensive set of CRs collected in Table 1 of Racusin et al. (2009), which, in turn, are taken from Zhang & Mészáros (2004), Dai & Cheng (2001), Zhang et al. (2006), Panaitescu (2005), and Panaitescu et al. (2006). Following Zhang et al. (2006), we expect the typical synchrotron frequency, ν_m, to lie below the observational bands and, for the XRT and UVOT observations, which started ∼107 ks after the burst, we assume the slow-cooling regime (ν_m < ν_c), where ν_c is the synchrotron-cooling frequency.

In Table 8, the values of p(β_obs) and the deviations f_cr ≡ α_cr(β_obs) − α_obs are listed, where α_cr is the temporal slope predicted by the CR and the indices α_obs, β_obs, are obtained from our observations. Figure 18 shows the α(β) diagram for the CRs and the data.

Zoom In Zoom Out Reset image size

X-ray afterglow. In the ν_c < ν_X regime, the electron index p = 2β_X = 1.7 ± 0.14. From (α_X, β_X) and CRs for this spectral regime (Figure 18, right) a pre-break geometry of ejecta, which mimics an isotropic, spherical expansion (SE), is rejected at >20σ. The best-fitting CR (2.5σ) is for the non-spreading jet (JETns) and ISM-like CBM. Another option, the ν_X < ν_c spectral regime, which is considered unlikely for late-time X-ray afterglows (see, e.g., Zhang et al. 2006; Nysewander et al. 2009), yields a steep electron spectrum, p = 2β_X + 1 = 2.7 ± 0.14. In this case, all the jet CRs are >6σ from the X-ray observations; the best fitting CR suggests the pre-break (SE) geometry and a stellar-wind-like CBM (2.3σ).

UV/optical afterglow. The UVOT temporal slope α_opt = 1.52 ± 0.09 is shallower but consistent with α_X. For the spectral slope in the optical band, we accept β_opt = 0.42 ± 0.11 (1σ) obtained from the broadband XRT+UVOT+GROND SED in Section 2.4.5. The ν_c < ν_opt regime implies an ultra-hard electron index of p = 2β_opt = 0.84 ± 0.22, which is at odds with both values of p suggested from the X-ray spectrum. Alternatively, in the ν_opt < ν_c regime, p = 2β_opt + 1 = 1.84 ± 0.22, which is in good agreement with the electron index found for ν_c < ν_X. In this case, a cooling break of Δβ = 1/2 is expected between the UVOT and XRT bands, which is consistent with β_X − β_opt = 0.43 ± 0.12. From (α_opt, β_opt), all pre-break CRs are >3σ from the data, and the JETns+ISM combination is again the best fitting CR (0.5σ).

Extended γ-ray emission. Given β_γ = 1.00 ± 0.16 and α_γ = 0.88 ± 0.05, the fast-cooling regime ν_c < ν_γ < ν_m, which requires β = 1/2 for the ISM and α = 0 for the wind-like CBM, is ruled out at >3σ. The same is true for the slow-cooling regime and ν_γ < ν_c (see Figure 18, left panel). In the max(ν_m, ν_c) < ν_γ regime, the electron index is p = 2β_γ = 2.0 ± 0.3, which is consistent with p ∼ 1.7, implied for ν_c < ν_X. The SE CR fits the observations within 1σ (same figure, right panel), with α_γ being slightly shallower than the value of unity predicted by the CR. This shallow slope could be explained by a continuous EI, caused, e.g., by prolonged activity of a central engine (Zhang & Mészáros 2001; Zhang et al. 2006). The EI can be characterized by a parameter q < 1 such that the continuous luminosity injection is L(t)∝t^−q; q = 1 means no additional EI. The CR for EI in the max(ν_m, ν_c) < ν regime is α = (q − 2)/2 + β(2 + q)/2 (Zhang et al. 2006). This yields q = 0.88 ± 0.15 and suggests a mild late-time EI.

Thus, the CR analysis results in a consistent scenario for the extended γ-ray emission, X-ray, and UV/optical afterglows. The scenario is characterized by a hard electron spectrum, with p in the 1.7–2.0 range, and implies the ν_opt < ν_c < (ν_X, ν_γ) spectral regime for the observations. In this scenario, the X-ray and UV/optical afterglows are observed after the jet break and, assuming a forward-shock origin, the extended γ-ray emission is generated at the pre-break phase of the fireball expansion. These choices are indicated by dashed circles in Figure 18. The temporal slope change, α_X − α_γ = 0.75 ± 0.05, is in reasonably good agreement (<2σ) with the jet break, Δα = 2/3, expected for the combination of p ⩽ 2, JETns, and ISM-like environment; when accounting for the late-time EI, the agreement is even better. The shallow post-break temporal slope can be explained, in this model, by a "flat" electron spectrum and by a limited lateral spreading of the jet.

We note that these conclusions are drawn under the assumption of non-transitional regimes for the cooling and the geometry; this approach is justified by the results of our temporal and spectral analysis of the extended emission and the afterglow.

Assuming that the PL energy spectrum measured by Konus-WIND at >T₀ + 30 s extends unchanged to lower energies, the extrapolated X-ray flux light curve can be calculated from the extended γ-ray emission. The correctness of this approach has been tested, e.g., with the KW data on the "naked-eye" GRB 080319B and the recent nearby GRB 130427A, for which statistically significant tails of an extended emission in the 20–1200 keV band have been observed, both having PL spectra with Γ ∼ 2. For both GRBs, we found the extrapolated unabsorbed 0.3–10 keV flux to be consistent, within 2σ–3σ (or ⩽20%), with simultaneous Swift-XRT observations extracted from the XRT light-curve repository (Evans et al. 2007, 2009).

Using the KW counts-to-flux conversion factor and the spectral index from the T₀ + 50–T₀ + 200 s interval, we found the extrapolated unabsorbed 0.3–10 keV flux to be in the (10⁻⁸ − 10⁻⁷) erg cm⁻² s⁻¹ range, which has been previously reported at early phases of bright X-ray afterglows (e.g., GRB 061007, Schady et al. 2007; GRB 080319B, Racusin et al. 2008; GRB 130427A, Evans et al. 2013; Perley et al. 2013). In Figure 19, a hypothetical light curve, which combines the extrapolated late-time γ-ray observations of GRB 110918A and the XRT afterglow, is shown. Assuming that the accuracy of the extrapolation procedure is comparable to that found for GRB 080319B and GRB 130427A, we added 20% systematics to the statistical-only errors for the extrapolated points. A transition from the initial, flat slope to the final, steeper one occurs in the T₀ + 10³–T₀ + 10⁵ s region, which is not covered by the observations. A simple estimate from the BPL fit to this combined light curve yields, at $\chi ^2_r=0.97$, the 1σ break region of t_b = (1.74 ± 1.15) × 10⁴ s with pre- and post-break slopes of α₁ = 0.90 ± 0.09 and α₂ = 1.64 ± 0.02, respectively.

Zoom In Zoom Out Reset image size

In the post-break scenario for the X-ray afterglow, t_b ∼ 1.7 × 10⁴ s (or ∼0.2 days) may be considered as a lower limit for t_jet, since the extended γ-ray emission cannot be attributed unambiguously to a "plateau" (II) or "normal" (III) phase. In the former case, introducing an additional, "injection" break to the light curve (the break from segment II to segment III) will shift the jet break toward the start of the XRT observations at ∼107 ks (1.24 d) after the burst. The 0.2–1.24 days range for t_jet is consistent with the value suggested from the multi-parameter E_iso–E_{p, i}–t_jet correlation (Liang & Zhang 2005; Ghirlanda et al. 2007), which predicts, for GRB 110918A, the jet break at 0.3 ± 0.13 days using the slopes provided in the latter work.

The isotropic-equivalent K-corrected X-ray luminosity in the rest-frame energy band E₁ − E₂ can be calculated from the unabsorbed 0.3–10 keV flux $F_{\mathrm{X}}\propto E^{-\beta _{\mathrm{X}}}$:

$$\begin{equation} L_{\mathrm{X}}(t)=4\pi D_L^2 \frac{F_{\mathrm{X}}[t(1+z)]}{(1+z)^{1-\beta _{\mathrm{X}}}} \frac{\left(E_2^{1-\beta _{\mathrm{X}}}-E_1^{1-\beta _{\mathrm{X}}}\right)}{(10^{1-\beta _{\mathrm{X}}}-0.3^{1-\beta _{\mathrm{X}}})}, \end{equation} \tag{ 6 }$$

where E₁ and E₂ are measured in keV. The GRB 110918A afterglow luminosities at 5 minutes, 1 hr, 11 hr, and 1 day after the trigger in the rest-frame were estimated from the combined extrapolated light curve and are listed in Table 9. We tested the 2–10 keV L_X and the rest-frame prompt emission parameters against L_X–E_iso, L_X–L_iso, and L_X–E_{p, i} correlations reported by D'Avanzo et al. (2012) from a sample of 56 bright Swift GRBs with well-measured X-ray afterglows. GRB 110918A was found to fit these relations within 3σ scatter at all four time marks. The best fit (⩽1σ) is for the L_X–E_{p, i} relation; the data are consistently ∼2.5σ–3σ from the L_X–L_iso relation, in general agreement with other correlations for which the extreme L_iso of this GRB is considered.

In the case of an ISM-like CBM with constant number density n, the jet opening angle is given by Sari et al. (1999):

$$\begin{equation} \theta _{\mathrm{jet}}=\frac{1}{6}\left(\frac{t_{\mathrm{jet}}}{1+z}\right)^{3/8}\left(\frac{n\eta _{\gamma }}{E_{\mathrm{iso,52}}}\right)^{1/8}, \end{equation} \tag{ 7 }$$

where η_γ is the radiative efficiency and t_jet is measured in days.

For calculations, we adopted canonical values η_γ = 0.2 and n = 1 cm⁻³ (Frail et al. 2001). In Table 10, values of θ_jet, the collimation factor (1 − cos (θ_jet)), the collimation-corrected energy release in γ-rays E_γ = E_iso(1 − cos (θ_jet)), and the collimation-corrected peak luminosity L_γ = L_iso(1 − cos (θ_jet)) are listed for the key points of the GRB 110918A observations timeline: t_jet = 1.2 days (start of the Swift observations), t_jet = 48 days (end of the Swift observations), and t_jet = 0.2 days (a lower limit for the jet break suggested in the previous section).

Figure 20 shows our estimates of the GRB 110918A collimation-corrected energy. For the jet-break time favored from our previous analysis, between 0.2 and 1.24 days (points (a) and (b) in the figure), the implied collimation angle is small, 17–34, and the inferred values of E_γ and L_γ are in the ranges determined by T13 for the KW GRBs with known collimation factors; also, the E_γ range is effectively the $_{-1.5}^{+2.5}\sigma$ scatter of the E_{p, i}–E_γ relation (Ghirlanda et al. 2007) calculated at E_{p, i} = 670 keV. It should be noted, however, that among such tightly collimated bursts, the fraction of which we estimate to be <25% of KW GRBs with known collimation factors, both E_γ and L_γ for GRB 110918A are at the upper edges of their distributions; this implies that the burst's intrinsic brightness is still remarkable. In the case of a "hidden" break in the afterglow light curve, between points (b) and (c) in Figure 20, the inferred radiated energy still does not move far beyond the observed range of E_γ ⩽ 3.4 × 10⁵² erg s⁻¹. However, the collimated peak luminosity shifts toward an unprecedented L_γ ∼ 10⁵³ erg s⁻¹, an order of magnitude higher than the current record.

Zoom In Zoom Out Reset image size

For a stellar-wind-like environment with n(r) = 5 × 10¹¹A_*r⁻², the jet opening angle depends on t_jet through (Chevalier & Li 2000)

$$\begin{equation} \theta _{\mathrm{jet}}=0.202\left(\frac{t_{\mathrm{jet}}}{1+z}\right)^{1/4}\left(\frac{A_*\eta _{\gamma }}{E_{\mathrm{iso,52}}}\right)^{1/4}, \end{equation} \tag{ 8 }$$

where $A_*=(\dot{M}_W/4\pi V_W)/5\times 10^{11}$ g cm⁻¹ is the wind parameter, $\dot{M}_W$ is the mass-loss rate due to the wind, and V_W is the wind velocity; A_* ∼ 1 is typical for a Wolf–Rayet star. Although the wind-like CBM is not preferred from our analysis, the θ_jet estimate for A_* = 1 also results in a tight collimation angle of ∼45 and reasonable estimates for E_γ ∼ 6.5 × 10⁵¹ erg and L_γ ∼ 1.5 × 10⁵² erg s⁻¹ even at t_jet =48 days.

To date, seven GRBs with L_iso > 10⁵⁴ erg s⁻¹ have been observed; Table 11 lists estimates of their rest-frame prompt emission characteristics derived from the Konus-WIND observations. While the scope of this paper does not involve an analysis of this sample, one can see that the GRB 110918A parameters do not differ much from those of other ultraluminous events: almost all of them are hard-spectrum GRBs with a moderately short rest-frame duration.

Notably, none of these bursts (with the exception of GRB 000131; Andersen et al. 2000) demonstrate a "canonical" steep late-time decay of an afterglow light curve (Grupe et al. 2006; Greiner et al. 2009; Prochaska et al. 2009; Starling et al. 2009). When the late-time temporal and spectral PL indices of X-ray afterglows are considered, the second and third most luminous GRBs (GRB 130505A¹⁶ and GRB 050603; Grupe et al. 2006) resemble GRB 110918A most closely, suggesting a similar interpretation. Particularly, a flat electron energy spectrum with p ∼ 1.4 is implied for GRB 050603 by Grupe et al. (2006), as well as a jet scenario for its afterglow observed by Swift from 11 hr after the trigger onward. For this burst, the authors estimate a θ_jet of 1°–2°; a similar collimation angle of ∼16 can be roughly estimated for GRB 130505A from the latest break in its XRT light curve at ∼29 ks, as suggested by the automated analysis.