INTRODUCTION

The recent and brightest gamma-ray burst, GRB 221009A, has been detected by many space X-ray–\(\gamma \)-ray observatories, including Fermi [1, 2], Swift (for more detailed analysis see [3]), SRG/ART-XC [4], Konus–Wind [5] and others. The burst and its afterglow were also registered by LHAASO on Earth in the range of hundreds GeV to several TeV [6]. Carpet-2 on Baksan Neutruno Observatory has detected an atmospheric shower 250 TeV photon from the location of GRB 221009A [7]. On the other hand HAWC collaboration reports no detection of photons from the af-terglow in TeV range beyond 8 h after the trigger [8] and claim the upper limit on the energy flux \(4.16 \times \) 10‒12 TeV cm–2 s–1.

The burst was intrinsically strong and relatively nearby, \(z = 0.151\). The apparent brightness of GRB 221009A is exceptional. In Fermi GBM burst catalog it exceeds the next brightest by factor 15 in energy fluence. However the strongest impact of this event is due to claims of two photons 18 GeV (LHAASO) and 250 TeV (Carpet 2) which cannot come from \(z = 0.15\) because of the absorption on extragalactic background light. New physics has been proposed to explain these photons, see, e.g., [9–12] and [13] (the latter also contains a comprehensive list of references on the subject). Study of GRB 221009A spectra can be used also to put constraints on the strength of the extragalactic magnetic field [14].

Taking advantage of the brightness of GRB 221009A we try to find something new about GRBs themselves in publicly available Fermi data. Namely:

\( \bullet \) Is there anything interesting between the precursor of the burst and its main emission three minutes later.

\( \bullet \) What does the transition from the prompt phase of gamma-ray bursts to afterglow look like?

\( \bullet \) How bright is the afterglow and how long can it be traced in the GeV range.

DATA AND THEIR CALIBRATION

Some raw Fermi data for GRB 221009A are shown in Fig. 1. Large Area Telescope (LAT) and NaI detectors of Gamma Burst Monitor (GBM) were oversaturated while Bismuth Germanate (BGO) scintillation detectors satisfactory reproduce the peak flux in energy channels above \( \sim \)1 MeV. There are no LAT data in the most interesting intervals 220–240 and 260–270 s (photon detections lack not only from the GRB direction but from the whole sky).

Fig. 1.
figure 1

(Color online) Time evolution of GRB 221009A in raw data. Prompt phase and early afterglow. (a) Count rates in various energy ranges on a logarithmic scale, upper curve GBM NaI 295–540 keV, middle curve GBM BGO 22–38 MeV, lower blue curve LAT, 8° circle around the location of GRB 221009A, yellow curve, all LAT photons. Dips at 210 and 260 s result from detector saturation. (b) Individual LAT photons in the 8° circle around the position of GRB 221009A (left logarithmic energy scale) and the angle between the LAT axis and the burst direction (right scale). Note the emission in the 10–200 MeV range 50 s after the precursor.

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The next circumstance that makes the direct interpretation of LAT data problematic is a large angle \(\theta \) between the direction of LAT z-axis and the burst location. The burst has occurred at the very edge of the telescope field of view where the detection efficiency is low. Figure 1b shows time dependence of \(\theta \) on time during the event. The inclination angle varied from 75° to more than 80° at \(t \sim 500\) s when the source leaved the field of view for an hour.

The angular dependence of LAT effective area is   given in [15], see also https://www.slac.stanford.edu/exp/glast/groups/canda/lat_Performanc e.htmFermi LAT Performance. However these data have insufficient resolution for this specific problem, therefore we have performed a detailed calibration of LAT detection efficiency for large incident angles using the brightest GeV source Vela X (both the pulsar and the nebula). The same object was used by Fermi team for calibration of the point spread function [15].

We use photons in 8° circle around Vela X location as the calibration sample. The size of this circle is a result of a trade-off between sufficient containment for ~100 MeV photons \(( > {\kern 1pt} \; 68{\kern 1pt} \% )\) and the contamination of the sample with background photons. The result of our calibration is shown in Fig. 2.

Fig. 2.
figure 2

(Color online) Calibration data for LAT performance at large incident angles using Vela-X gamma-pulsar. The ratio of effective area to on-axis effective area is shown as a function of the angle between the photon source and the z-axis of the LAT. Curves from top to bottom correspond to energy intervals: >1 GeV, 1 GeV–562 MeV, 562–316 MeV, 316–178 MeV, 178–100 MeV.

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The number of photons in our calibration sample is 9.4 × 106 while the number of background photons is 2 × 106 as we have estimated from a neighboring site of Milky Way. So, the background is considerable, but its effect should be moderate because the angular dispersion of background photons contributes the detection efficiency with different signs: the number of photons incident at \(\theta + \Delta \) is comparable with those arrived at \(\theta - \Delta \). Nevertheless wide angular cut in calibration sample mimics some extension of the field of view. We have checked the effect of the wide angular cut with the same calibration cutting the sample at 4°. The difference at \(\theta = 78^\circ \) for photons with \(E \gtrsim 1\) GeV is \(40{\kern 1pt} \% \) and factor 2.5 for 100–178 MeV interval. The latter large value is certainly the effect of widening of point spread function at edge of the field of view. Therefore we prefer to use the calibration with 8° calibration sample as it better reproduces the soft end of the spectrum and an extra background just slightly affects its hard range.

Except angular dependence of detection efficiency one should take into account the energy dependence. We use that described by [15]. Note that for lowest energy bin 100–178 MeV that we use the efficiency is 0.45 of the maximal efficiency. Therefore a 100 MeV photon detected by LAT at 400 s after the trigger represents ~300 photons of the same energy crossing the detector area (see Figs. 1b and 2). In our analysis and calibration we do not distinguish the conversion type and the quality class of photons, using total effective area for the “transient” event class.

MAIN EPISODE AND ONSET OF THE AFTERGLOW

Normalized Fermi data for the first 600 s are shown in Fig. 3. LAT data were normalized using our Vela X calibration results (Fig. 2) and energy dependent effective area from [15]. Total effective area of two BGO detectors was set to 200 cm2 independently on energy and incident angle as such assumption is sufficient for qualitative demonstration. For the energy and angular performance of BGO detectors see [16].

Fig. 3.
figure 3

(Color online) (a) Prompt GRB and early afterglow in different energy ranges. Histogram: energy flux of LAT photons normalized to angular-dependent effective area calibrated with Vela-X source. Pink line: energy flux in 0.93–2.1 MeV range from Gamma-Burst Monitor BGO detectors. Blue circles: the same in 22–38 MeV energy band. (b) Lower left corner of (a) with additional data. Magenta: sum of 5 brightest NaI detectors, in 0.1–0.3 MeV band assuming 400 cm2 effective area. Blue: BGO detectors in 0.38–0.93 MeV band assuming 200 cm2 effective area. Pink: BGO, 0.93–2.1 MeV band. Black: distribution of the energy flux represented by 6 LAT photons from 20 to 230 MeV.

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BGO 22–38 MeV energy flux in 300–600 s interval is very sensitive to the background model. We use three parametric description: constant plus one sinusoidal half period with fitting intervals 300–150 s and 600–1300 s. Resulting \({{\chi }^{2}}\) is good, however the error in energy fluence in BGO is large therefore we do not take BGO data into consideration when reconstructing photon spectra. We see a striking transition in time behavior at \( \sim \)300 s: a sharp decline of main pulse changes to a flat smooth slope. The exception is another soft episode of prompt emission at 400–600 s which we discuss below. It would be reasonable to suggest then the high energy emission after 300 s can be considered as the main afterglow.

Phenomenologically, prompt emission usually undergoes a very fast variation of intensity and spectrum while afterglow has a smooth long decline with a stable wide spectral energy distribution. Prompt emission sometimes consists of multiple pulses of different duration and spectra, this pulses can overlap in time producing in some cases complex structures with a wide temporal Fourier power spectrum [17]. Their time behavior is very diverse. On the contrary, all afterglows have typical time behavior: a power law decline slightly faster than t–1.

Theoretically, there exists a paradigm that the prompt emission arises from internal shocks (or magnetic reconnection or both) in the jet while the afterglow from external shock form collision of the jet with ambient medium (see, e.g., [18]), dominated by the stellar wind of the GRB progenitor [19]. Physically, the prompt emission in many cases can be described as a radiation of an optically thick medium due to multiple Comptonization (e.g., [20]), while afterglow better corresponds to synchrotron/Compton radiation of electrons accelerated in an optically thin environment, see [21] for a review.

In the case of GRB 221009A we can describe as the prompt emission the precursor, a soft pulse at \(t \sim 180{-} 200\) s, two main hard pulses and a soft long structure in 400–600 s interval. Photon flux detected by LAT since 250 s with its spectrum (see Fig. 4) and light curve resembles an afterglow rather than a prompt emission. The structure at 400–600 s is probably an independent prompt emission episode overlapping in time with the early afterglow.

Fig. 4.
figure 4

(Color online) Spectral energy distribution of photons detected by LAT at time intervals 280–500 s and 4000–6000 s reconstructed with calibrated effective area (see Fig. 2).

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Probably the afterglow mechanism (presumably the external shock) has turned on slightly earlier, e.g., at 230 s. Thereafter we use this time as a reference point for a power law decline of the afterglow.

Our estimate of the energy fluence represented by 229 photons detected by LAT in the time interval 220–500 s is \(1.55 \times {{10}^{{ - 3}}}\) erg/cm2. Actual fluence could be several times higher since we do not know how many photons are lost in over-saturation gaps. The low energy fluence preliminary estimated by [2] is 2.9 × 10–2 erg/cm2, the total energy fluence can be much higher, see [22]. The spectral energy distribution in 100 MeV–100 GeV range is shown in Fig. 4. We made a forward-folding fit to the numbers of detected photons in energy bins. We use the maximum likelihood method with Poisson statistics taking into account the energy and angular dependent effective area. We factorize the on-axis effective area (parametrization ve-rsion https://fermi.gsfc.nasa.gov/ssc/data/analysis/documentation/Cicerone/Cicerone_LAT_IRFs/IRF_EA.htmlPR8_TRANSIENT020_V3) with \(\theta \)-dependence shown in Fig. 2. The resulting photon index for LAT photons in background-free 8° field is \( - 1.66 \pm 0.07\) which is harder than estimate of [23].

MAIN AFTERGLOW

After 500 s since the trigger the GRB came out of LAT field. The next time window was open from \( \sim {\kern 1pt} 4100\) to \( \sim {\kern 1pt} 5700\) s. Then the location of GRB221009 periodically appeared in the field of view with duty cycle ~20%.

Figure 5 shows counts of photons detected by LAT versus logarithm of time. Unlike the main episode which is essentially background free, the background during the late afterglow is considerable and is too large in 8° field of view which we accepted for the description of the main episode. For this reason we analyze the afterglow using 1° circle. The background estimated with photons detected from the same direction during 300 000 s prior the trigger is shown in Fig. 5. With this window the afterglow is significant up to two days (see Fig. 5b). Further contraction of the field of view does not improve the significance.

Fig. 5.
figure 5

(Color online) Response-independent demonstration of signal/background ratio. Events in the 1° circle around GRB 221009A detected by LAT. (a) Photons in the time interval 103–3 × 105 s since the trigger (magenta circles) and background photons in the interval of the same length but before trigger (red squares). (b) The same but as a histogram. The estimate of the background has been done with 8° field around the GRB location for 300 000 s before the burst.

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Figure 5a shows LAT photons in log–log scale for 1° field. It looks like the afterglow is getting softer with time, however note a 400 GeV photon at \(\log (t) \sim 4.5\) (33 554 s). The angular deviation of this photon from the GRB location is 0.06°, the probability of chance coincidence with such angular deviation during a day is \( \sim {\kern 1pt} {{10}^{{ - 6}}}\). This photon is missing in the telegram of Fermi team, but was noticed by [24]. The impression of softening can result from the lack of soft photons in the main episode and their excess at \(t \sim {{10}^{5}}\) s. The former can be explained by a stronger suppression of soft photons at large incident angles (see Fig. 2) and the latter by the contribution of a softer background. The statistics is insufficient to reveal an evolution of the afterglow spectrum.

The spectral energy distributions for the beginning of the afterglow and for the second window are shown in Fig. 4. They are consistent with each other and just slightly differ from the “canonical” spectrum with flat SED (photon index \(\alpha = - 2\)). We suggest that it would be reasonable to set the spectral index to –2 when fitting the afterglow energy flux. Figure 6 shows the photon flux of the afterglow versus time. We normalize the flux taking into account the containment of point source photons in 1° field which depends on the photon energy and the spacecraft orientation. Here we rely on Fermi response function taking PSF version for transient class. We add for comparison some data points for high energy fluxes of other bright GRBs: GRB 130427SA [25], GRB 180720B [26], GRB 190114C [27] and GRB 190829 [28]. These data are summarized and discussed by [29]. The afterglow of GRB is slightly brighter than afterglow of GRB 130427A and almost an order of magnitude brighter than GRB 180720B, 190114C and 190829 which were detected by Cherenkov telescopes. This is the first case when the afterglow is still visible in the Fermi range two days after the GRB (the second brightest afterglow of GRB 130427SA is visible in the Fermi LAT data up to half a day). Intriguingly, it was not detected by the HAWC Collaboration [8], see Fig. 6.

Fig. 6.
figure 6

(Color online) Afterglow of several \(\gamma \)-ray bursts. Black: GRB221009A, (squares with error bars) this work, (circle with an upper limit) HAWC Collaboration. Blue: GRB 190114C, (circles) MAGIC (0.3–1 TeV), (stars with error bars) Fermi LAT. Green: GRB 190829A–H.E.S.S. (0.2–4 TeV). Violet: GRB 180720B–H.E.S.S. (100–440 GeV). Red: GRB 130427A–Fermi LAT.

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The afterglow is still \(3\sigma \) significant in 100 000–200 000 s interval: the number of photons is 40 versus expectation of 24.4 photons measured in the “mirror” \( - 100{\kern 1pt} {\kern 1pt} 000{-} 200{\kern 1pt} {\kern 1pt} 000\) s interval. The afterglow light curve in 0.1–10 GeV range can be described as a power law \(F \sim {{t}^{{ - {{\alpha }_{\tau }}}}}\), where \({{\alpha }_{\tau }} = 1.47 \pm 0.05\) or \(1.36 \pm 0.05\) if we remove the first data point, as it could be affected by the uncertainty in the afterglow start time (for which we set 230 s after the trigger). This decay is somewhat slower than that measured by LHAASO [6] in \(20 < t < 1000\) s interval above 0.2 TeV energy range (\({{\alpha }_{\tau }} = 2.21 + 0.30 - 0.83\)). The afterglow energy fluence in 0.1–10 GeV range is 3.6 × 10–4 erg cm–2.

Results of the Fermi collaboration of LAT response for GRB 221009A are still not published. The afterglow flux has been analyzed by other groups using public Fermi data. In particular, work [30] gives a slightly higher flux estimate than ours, although the difference is within one standard deviation. The points of [31] after 3000 s also coincide with our results within errors. Both groups give only upper limits for the flux after 68 000 s while we see \(3{\kern 1pt} \sigma \) signal beyond the first day.

AFTERGLOW OF THE PRECURSOR

Fermi LAT detected 6 photons in the range 20–230 MeV in time interval 7–50 s after the trigger (Fig. 1b) when the angle \(\theta \) varied from 65° to 70° and LAT effective area was several times less than for on-axis photons (see Fig. 2). Note that the prompt precursor emission already has relaxed when LAT has detected first of these photons. We estimate the energy fluence represented by these 6 photons as 1.5 × 10‒6 erg cm–2.

In Fig. 3b we show GBM light curve in 0.1–0.29 MeV channel (NaI detectors), and in 0.38–2.12 MeV band (BGO detectors) together with contribution of 6 LAT-GRB photons presented as a histogram. The precursor itself looks like a typical fast rise in the form of exponential decay pulse (FRED) which usually constitute the prompt emission of GRBs. It decays faster at higher energies which is also a typical feature of FREDs. At several seconds FRED pulse changes to a flat emission tail of a wide spectrum looking like a typical GRB afterglow. We suggest the same phenomenon takes place here: a prompt precursor turns to a precursor afterglow.

How significant is this “preafterglow”? It is highly significant in 0.1–0.29 MeV channel up to 50 s, marginally significant in 0.38–2.12 band up to 40 s. In higher energy channels of GBM we obtain only upper limits above 10–7 erg cm–2 s–1. However the best marker of an afterglow is high energy emission presumably originating from an external shock.

We have counted photons from 8° circle when the orientation of LAT z-axis to the GRB was \(63^\circ < \theta < 71^\circ \) during 30 000 s before the burst. The result is 302 photons for 23 400 s which gives the expectation 0.64 photons for 50 s interval after the precursor. The probability to sample 6 photons by chance is \(0.5 \times {{10}^{{ - 4}}}\) (\(4\sigma \)). Note that there is no “look elsewhere” effect in this case: the photons appear in a proper place with no sample manipulation. Therefore this significance is quite sufficient to claim that Fermi has detected an afterglow of a precursor. This is the first case of such detection. The idea that a GRB precursor could produce its own afterglow was suggested by [32].

The spectral fit to 6 photons is, of course, quite loose, the resulting spectral index is \(\alpha = - 2.5 \pm 0.5\) which is consistent with the spectrum of the main afterglow with \(\alpha \sim - 2\). Moreover, if the emission in 10–50 s interval in sub-MeV range is a part of a single wide spectrum, then the spectral energy distribution is very close to a flat one (i.e., \(\alpha \sim - 2\)).

DISCUSSION AND CONCLUSIONS

Probably the most interesting fact that we see in Fermi data is the afterglow of the precursor. This is the first direct evidence of such phenomenon at least if we treat a precursor as a relatively weak event separated from the main episode by a long time interval.

A weak precursor that occurs long before (up to several minutes) the main GRB is a feature of many GRBs. The estimates of their occurrence varies from 3% GRBs [33] up to 10% [34] or even 20% [35]. A useful review of the phenomenon is given by [36]. In fact, this fraction may be even higher, since the precursor can be easily lost. The precursor of GRB 221009A has a few hundred times lower peak count rate and several thousand times lower energy fluence than the main emission episode. Such relatively weak precursor can be detected only in rare cases of very strong GRBs and one cannot exclude that this phenomenon is common for the majority of GRBs and we observe just strongest precursors.

However this weak precursor has a bright afterglow. The energy fluence of the precursor and its afterglow is: \( \sim {\kern 1pt} 1.7 \times {{10}^{{ - 5}}}\) erg cm–2 (0.1–4.8 MeV, BGO) and \( \sim {\kern 1pt} 1.5 \times {{10}^{{ - 6}}}\) erg cm–2 in 23–230 MeV range correspondingly. Also, the estimate by [37] of the precursor fluence is \((2.38 \pm 0.04) \times {{10}^{{ - 5}}}\) erg cm–2. Therefore, their ratio is ~10–1 while the same ratio for the main event is below 10–2 (or down to 10–3 if one uses the estimate 0.21 erg cm–2 for the main prompt emission episode in 0.02–10 MeV band by [22]). This is a hint that the precursor could differ from the main GRB in its nature. If we follow the paradigm that the prompt emission originates from internal shocks in the jet and the afterglow comes from external shock in the ambient medium (see [18]), then we have to conclude that internal shock is pathologically weak in the case of the precursor. In principle, one cannot exclude that a precursor with its afterglow is an essentially different phenomenon preceding the main emission.

Up to our knowledge this is the first case of the detection of a precursor afterglow. Unfortunately, there is a very small chance to observe such afterglow of a relatively weak precursor directly in the nearest future, nevertheless it probably could be sensed statistically using existing databases. If our interpretation of high energy emission after the precursor as the result of external shock is correct, then one can reject some theoretical models of precursors. Any model based on evolution of a single jet which describes both precursor and main episode (like photospheric [38] or shock breakout precursors) do not satisfy the observation of two independent shocks.

As for the main afterglow, this is the brightest one as well as the GRB 221009 itself. In other respects (relative energy flux, spectrum, decay law) it looks typical. The afterglow due to its brightness is visible in Fermi data during two days and could be visible even longer by Cherenkov telescopes unless bad observational conditions including bright moon.

HAWC collaboration has reported no detections beyond 8 hours after the event and set the upper limit \(4.16 \times {{10}^{{ - 12}}}\) erg cm–2 s–1 [8]. This upper limit is in apparent tension with Fermi data unless one implies a sharp spectral decline between ~10 GeV and TeV energy ranges.

In principle, such spectral cutoff in 0.1–1 TeV range is possible due to \(\gamma {-} \gamma \) absorption in the source. The opacity for high energy photons can arise from side scattered photons of optical range emitted at the prompt stage. An example of a numerically simulated spectrum with a cutoff at ~TeV energy is given in [29]. This issue requires a separate study with extensive numerical simulation as the problem is very complicated. It includes pair loading of external medium [39], its pre-acceleration and shock dynamics [40]. We believe that in a certain parameter range it is possible to reproduce a spectral cutoff which can explain the contradiction between GeV flux and the HAWC upper limit.

However other GRB do not have such decline in their afterglows which is supported by data of Cherenkov telescopes for other GRBs (cf. Fermi and MAGIC data in Fig. 6). Moreover, the 400 GeV photon detected at 9 h is an argument against a spectral cutoff.