A COMPREHENSIVE ANALYSIS OF FERMI GAMMA-RAY BURST DATA. I. SPECTRAL COMPONENTS AND THE POSSIBLE PHYSICAL ORIGINS OF LAT/GBM GRBs

As shown in Figure 2, GRB 080916C is a long GRB with a duration of ∼66 s. The entire light curve can be divided into six segments. The smallest time bins during the brightest epochs (the first two) are 3.7 s and 5.4 s, respectively. This corresponds to a rest-frame time interval ⩽1 s (given a redshift of 4.35; Greiner et al. 2009). In all time intervals, we find that the Bandfunction gives excellent fits to the data, consistent with Abdo et al. (2009a). Initially, there is a spectral evolution where the spectra "widen" with time (α hardening and β softening), but later the spectral parameters essentially do not evolve any more. We note that the steep β in the first time bin is mostly due to non-detection in the LAT band. The tight upper limit above 100 MeV constrains the range of β so it is not too hard. On the other hand, with GBM data alone, the data from the first time bin can still be fit as a Band function, with β ∼ −2.12^+0.158_−0.107, similar of the values at later epochs. This suggests an alternative interpretation of the data: the high-energy spectral index may be similar throughout the burst. The delayed onset of LAT-band emission may result because, initially, there is a spectral cutoff around 100 MeV that later moves to much higher energies (e.g., above 13.2 GeV in the second time bin).

It is interesting to note that the time-integrated spectrum of GRB 080916C throughout the burst is also fit well with a Band function, where the spectral indices do not vary with time resolution. As an example, we present in Figure 18 the νF_ν spectra of GRB 080916C for three time bins with varying time resolutions. Remarkably, the parameters do not vary significantly: α ∼ −1.12, β ∼ −2.25 for 3.5–8 s; α ∼ −1.0, β ∼ −2.29 for 2–10 s; α ∼ −1.0, β ∼ −2.27 for 0–20 s. This is in stark contrast to GRB 090902B, discussed below.

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The short GRB 090510 was triggered with a precursor 0.5 s prior to the main burst. Two LAT photons were detected before the main burst. During the first time slice (0.45–0.5 s), no LAT-band emission is detected, and the GBM spectrum can be fit well with a CPL. In the subsequent time slices, an additional PL component shows up, and the time-resolved spectra are best fit by the CPL + PL model. If one uses a Band + PL model to fit the data, the high-energy spectral index β of the Band component cannot be constrained. If one fixes β to a particular value, it must be steeper than −3.5 to be consistent with the data. The CPL invoked in these fits has a low-energy photon index, Γ_CPL ∼ −(0.6–0.8), which is very different from the case of a BB (where Γ_CPL ∼ +1). On the other hand, the high-energy regime (exponential cutoff) is very similar to the behavior of a BB.

Since this is a short GRB, we do not have enough photons to perform very detailed time-resolved spectral analysis. However, to investigate spectral evolution and the interplay between the MeV component and the extra PL component, we nonetheless make four time bins (see also Ackermann et al. 2010). As a result, the reduced χ² of each segment is outside the range of 0.75 ⩽ χ²/dof ⩽ 1.5, as is required for other GRBs. Our reduction results are generally consistent with those of the Fermi team (Abdo et al. 2009b; Ackermann et al. 2010).

The spectrum of GRB 090902B is peculiar. Abdo et al. (2009c) reported that both the time-integrated and time-resolved spectra of this GRB can be fit with the Band + PL model. Ryde et al. (2010) found that the time-resolved spectra can be fit with a PL + multi-color BB model. This raises the interesting possibility that a BB-like emission component is a fundamental emission unit shaping the observed GRB spectra (Ryde 2004, 2005).

In order to test this possibility, we carried out a series of time-resolved spectral analyses on the data (Figure 18). We first fit the time-integrated data within the time interval 0–20 s and found that they can be fit with a model invoking a Band function and a power law, but with a poor χ²/dof ∼ 3.52. Compared with the Band component of other GRBs, this Band component is very narrow, with α ∼ −0.58, β ∼ −3.32. A CPL + PL model can give a comparable fit, with Γ_CPL ∼ −0.59. Next, we zoom into the time interval 8.5–11.5 s and perform spectral fits. The Band + PL and CPL + PL models can now both give acceptable fits, with parameters suggesting a narrower spectrum. For the Band + PL model, one has α ∼ −0.07, β ∼ −3.69, and χ²/dof = 1.26. For the CPL + PL model, one has Γ_CPL ∼ −0.08 with χ²/dof = 1.30. Finally, we zoom into the smallest time bin (9.5–10 s), in which the photon counts are just enough to perform adequate spectral fits. We find that the Band + PL model can no longer constrain β. The spectrum becomes even narrower, with α ∼ 0.07 and β < −5. The CPL + PL model can fit the data with a range of allowed Γ_CPL. In particular, if one fixes Γ_CPL ∼ +1 (the Rayleigh–Jeans slope of a BB), one gets a reasonable fit, with χ²/dof = 0.92. This encourages us to suspect that a BB + PL model can also fit the data. We test it and find that the model can fit the data, with χ²/dof = 1.11. These different models require different Γ_PL for the extra PL component, but given the low photon count rate at high energies, all these models are statistically allowed. Since the BB + PL model has fewer parameters than the CPL + PL and Band + PL models, we take this model as the simplest model for the smallest time interval.

Next, we try to divide the light curve of GRB 090902B into as many time bins as possible so that the photon numbers in each time bin are large enough for statistically meaningful fits to be performed. Thanks to its high flux, we managed to divide the whole data set (0–30 s) into 62 time bins. We find that the data in each time bin can be fit well by a BB + PL model and that the BB temperature evolves with time. The fitting results are presented in Table 2 and Figure 10. The time-integrated spectrum, however, cannot be fit with such a model (χ²/dof = 14732/276). A Band + PL model gives a much-improved fit, although the fit is still not statistically acceptable (χ²/dof = 2024/275). The best fitting parameters are α = −0.83, β = −3.68, E_p = 847 keV, and Γ = −1.85. Note that the high-energy photon index of the time-integrated Band spectrum is much steeper/softer than that observed in typical GRBs (Figure 19).

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In Figure 20, we display the light curves of both the thermal and power-law components. We find that the two components, in general, track each other. This suggests that the physical origins of the two components are related to each other (see Section 5 for further discussion).

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An important inference from the analysis of GRB 090902B is that a Band-like spectrum can be a result of temporal superposition of many BB-like components. This raises the interesting possibility of whether all "Band"-function spectra are superposed thermal spectra. From the comparison between GRB 090902B and GRB 080916C (Figure 18), we find that such speculation is far-fetched. As discussed above, GRB 080916C shows no evidence of "narrowing" as the time bin becomes small (∼1 s in the rest frame). In the case of GRB 090902B, a clear "narrowing" feature is seen. For the time-integrated spectrum, GRB 080916C has a wide Band function (with α ∼ −1.0, β ∼ −2.27), while GRB 090902B (0–20 s) has a narrow Band function (with α = −0.58, β = −3.32), with worse reduced χ². Another difference between GRB 090902B and GRB 080916C is that the former has a PL component, which leverages the BB spectrum on both the low-energy and high-energy ends to make a BB spectrum look more similar to a (narrow) Band function. GRB 080916C does not have such a component, and the Band component covers the entire Fermi energy range (GBM and LAT). We therefore conclude that GRB 090902B is a special case whose spectrum may have a different origin from GRB 080916C (and probably most other LAT GRBs as well; see Section 3.5 below).

This is another bright, long GRB with a duration of ∼20 s. In our analysis, the light curve is divided into nine segments. The Band function gives an acceptable fit to all the time bins (Figure 11). We notice, however, a flattening of β ∼11 s after the trigger. Also, the Band-function fit gives a worse reduced χ² (although still acceptable) after this epoch. Since our data analysis strategy is to go for the simplest models, we do not explore more complicated models that invoke Band + PL or Band + CPL (as is done by the Fermi team; Ackermann et al. 2011). In any case, our analysis does not discount the possibility that a new spectral component emerges ∼11 s after the trigger (Ackermann et al. 2011).

The time-resolved spectra of the other 13 GRBs are all adequately described by the Band function, similar to GRB 080916C. The Band-function spectral parameters are generally similar to GRB 080916C. It is likely that these GRBs join GRB 080916C, forming a "Band-only"-type GRB. In the current sample of 17 GRBs, only GRB 090510, GRB 090902B, and probably GRB 090926A do not belong to this category and have an extra PL component extending to high energies. One caveat is that some GRBs in the sample are not very bright, so we only managed to divide the light curves into a small number of time bins (e.g., three bins for GRB 080825C, one bin for GRB 081024B, three bins for GRB 090328, three bins for GRB 091031, two bins for GRB 100225A, and one bin for GRB 100325A). So, one cannot disfavor the possibility that the observed spectra are superpositions of narrower components (similar to GRB 090902B). However, at a comparable time resolution, GRB 090902B already shows features that are different from these GRBs: (1) the Band component is "narrower" and (2) there is an extra PL component. These two features are not present in other GRBs. We therefore suggest that most LAT/GBM GRBs are similar to GRB 080916C.

Since the time-resolved spectra of most GRBs in our sample can be adequately described as a Band function, we present the distributions of the Band-function parameters in this section. Since their MeV component may be of a different origin, GRB 090510 and GRB 090902B are not included in the analysis.

The distributions of the spectral parameters α, β, and E_p are presented in Figure 19, with a comparison to those of the bright BATSE GRB sample (Preece et al. 2000). It is found that the distributions peak at α = −0.9, β = −2.6, and E_p ∼ 781 keV, respectively. The α and β distributions are roughly consistent with those found in the bright BATSE GRB sample (Preece et al. 2000). The E_p distribution of the current sample has a slightly higher peak than the bright BATSE sample (Preece et al. 2000). This is likely due to a selection effect, namely, a higher E_p would favor GeV detections.

For time-integrated spectra, it was found that E_p is positively correlated with isotropic gamma-ray energy and isotropic peak gamma-ray luminosity (Amati et al. 2002; Wei & Gao 2003; Yonetoku et al. 2004). For time-resolved spectra, E_p was also found to be generally correlated with flux (and therefore luminosity; Liang et al. 2004), although in individual pulses, both a decreasing E_p pattern and an E_p-tracking-flux pattern have been identified (Ford et al. 1995; Liang & Kargatis 1996; Kaneko et al. 2006; Lu et al. 2010).

In Figure 21, we present the E_p-luminosity relations. Figure 21(a) is for the global $E_p-L_{\gamma,\rm iso}^p$ correlation. Seven GRBs in our sample that have redshift information (and, hence, peak luminosity) are plotted against previous GRBs (a sample presented in Zhang et al. 2009). Since the correlation has a large scatter, all the GBM/LAT GRBs follow the same correlation trend. In particular, GRB 090902B, whose E_p is defined by the BB component, also follows a similar trend. This suggests that even if there may be two different physical mechanisms to define a GRB's E_p, both mechanisms seem to lead to a broad $E_p-L_{\gamma,\rm iso}^p$ relation. It is interesting to note that the short GRB 090510 (the top yellow point), even though it is located at the upper boundary of the correlation, is still not an outlier. This is consistent with the finding (Zhang et al. 2009; Ghirlanda et al. 2009) that long/short GRBs are not clearly distinguished in the $L_{\gamma,\rm iso}^p - E_p$ domain.

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In Figure 21(b), we present the internal $E_p-L_{\gamma,\rm iso}$ correlation. It is interesting to note that with scatter, the general positive correlation between E_p and $L_{\gamma,\rm iso}$ as discovered by Liang et al. (2004) clearly stands. More interestingly, the BB-defined E_p (in GRB 090902B) follows a similar trend as the Band-defined E_p (e.g., in GRB 080916C and GRB 090926A), although different bursts occupy a different space region in the $E_p-L_{\gamma,\rm iso}$ plane.

In Figure 22, we present various pairs of spectral parameters in an effort to search for possible new correlations. The GRBs with redshift measurements are marked in colors, while those without redshifts are marked in gray with an assumed redshift of z = 1. In order to show the trend of evolution, points for the same burst are connected, with the beginning of evolution marked as a circle.

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No clear correlation pattern is seen in the E_p − α and E_p − β plots. Interestingly, a preliminary trend of correlation is found in the following two domains.

• 1.  
  An α–β anti-correlation: Figure 22(a) shows a rough anti-correlation between α and β in individual GRBs. This suggests that a harder α corresponds to a softer β, suggesting a narrower Band function. In the time domain, there is evidence in some GRBs (e.g., GRB 080916C, GRB 090926A, and GRB 100414A; see Figures 2, 11, and 17) that the Band function "opens up" as time goes by, but the opposite trend is also seen in some GRBs (e.g., GRB 091031; Figure 13). The linear Pearson correlation coefficients for individual bursts are shown in the inset of Figure 22(a).
• 2.  
  A flux–α correlation: Figure 22(b) shows a rough correlation between flux and α. Within the same burst, there is a rough trend that as the flux increases, α becomes harder. The linear Pearson correlation coefficients for individual bursts are presented in the inset of Figure 22(b). One possible observational bias is that when flux is higher, one tends to get a smaller time slice based on the minimum spectral analysis criterion. If the time-smearing effect can broaden the spectrum, then a smaller time slice tends to give a narrower spectrum, and hence a harder α. This would be relevant to bursts similar to GRB 090902B, but not bursts similar to GRB 080916C (which does not show spectral evolution as the time resolution becomes finer). More detailed analyses of bright GRBs can confirm whether such a correlation is intrinsic or due to the time resolution effect discussed above.

Several caveats should be noted for these preliminary correlations: first, some bursts do not obey these correlations, so the correlations, if any, are not universal; second, the currently chosen time bins are based on a requirement for adequate spectral analyses, so the time resolution varies in different bursts. For some bright bursts, a burst pulse can be divided into several time bins, while in some faint others, a time bin corresponds to the entire pulse. Third, the current sample is still too small. A time-resolved spectral analysis of more bright GBM GRBs may confirm or dispute these correlations.

The goal of our time-resolved spectral analysis is to look for "elemental" emission units that shape the observed GRB prompt gamma-ray emission. In the past, it was known that time-integrated GRB spectra are mostly fit by the Band function (Band et al. 1993). However, whether this function is an elemental unit in time-resolved spectra is not known. One speculation is that this function is the superposition of many simpler emission units. If such a superposition relies on adding the emission from many time slices, then these more elemental units should show up as the time bins become small enough.

One interesting finding of our time-resolved spectral analyses is that the "Band"-like spectral component seen in GRB 090902B is different from that seen in GRB 080916C and some other Band-only GRBs. While the Band spectral indices of GRB 080916C essentially do not change as the time bins become progressively smaller, those of GRB 090902B indeed show the trend of "narrowing" as the time bin becomes progressively smaller. With the finest spectral resolution, GRB 090902B spectra can be fit by the superposition of a PL component and a CPL function, including a Planck function. Even for the time-integrated spectrum, the "Band"-like component in GRB 090902B appears "narrower" than that of GRB 080916C. All these suggest that the "Band"-like component of GRB 090902B is fundamentally different from that detected in GRB 080916C, and probably other Band-only GRBs.⁹ Similarly, the time-resolved spectra of the short GRB 090510 can be fit well by the superposition of a PL component and a CPL spectrum (although not a Planck function). The PL component extends to high energies, with a positive slope in νF_ν. The CPL component may be modeled as a multi-color BB spectrum. We therefore speculate that the MeV component of GRB 090510 is analogous to that of GRB 090902B.

Phenomenologically, the power-law component detected in GRB 090902B and GRB 090510 is an extra component to the Band-like component. Such a component may have also been detected in the BATSE–EGRET burst GRB 941017 (González et al. 2003), and may also exist in GRB 090926A at later epochs.

We therefore speculate that, phenomenologically, there might be three elemental spectral components that shape the prompt gamma-ray spectrum. These include: (I) a Band-function component ("Band" in abbreviation) that covers a wide energy range (e.g., six to seven orders of magnitude in GRB 080916C) and persists as the time bins become progressively smaller. It shows up in GRB 080916C and 13 other LAT GRBs. (II) A quasi-thermal component ("BB" in abbreviation¹⁰) that becomes progressively narrower as the time bin becomes smaller, and eventually can be represented as a blackbody (or multi-color blackbody) component, as seen in GRB 090902B. (III) A power-law component ("PL" in abbreviation) that extends to high energies, as seen in GRBs 090902B and 090510, has a positive slope in the νF_ν spectrum, and should have an extra peak energy (E_p) at an even higher energy that is not well constrained by the data.

Figure 23 is a cartoon picture of the νF_ν spectrum that includes all three phenomenologically identified elemental spectral components. The time-resolved spectra of the current sample can be understood as being composed of one or more of these components. For example, GRB 080916C and the other 13 GRBs have Component I (Band), GRB 090902B and probably GRB 090510 have Components II (BB) and III (PL), and GRB 090926A has Component I initially and may have components I and III at later times.

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4.2.1. Band Component

4.2.2. Quasi-thermal (BB) Component

4.2.3. Power-law (PL) Component

Using the combined GBM and LAT data, we have phenomenologically identified three elemental spectral components during the prompt GRB phase (Figure 23). Physically, they may have different origins (see above). One may speculate that all the GRB prompt emission spectra may be decomposed into one or more of these spectral components. It is therefore interesting to investigate how many combinations are in principle possible, how many have been discovered, how many should not exist and why, and how many should exist and remain to be discovered. We discuss the following possibilities in turn below (see Figure 24 for illustrations).

• 1.  
  Component I (Band) only:This is the most common situation, which is observed in 14/17 GRBs in our sample and exemplified by GRB 080916C. Either the BB and PL components do not exist, or they are too faint to be detected above the Band component. If the BB component is suppressed, these bursts may signify non-thermal emission from a Poynting-flux-dominated flow.
• 2.  
  Component II (BB) only:No such case exists in the current sample. GRB 090902B and probably GRB 090510 have a BB component, but it is accompanied by a PL component in both GRBs. It remains to be seen whether in the future a BB-only GRB will be detected, or whether a BB component is always accompanied by a PL component. Since the case of GRB 090902B is rare, we suspect that BB-only GRBs are even rarer, if they exist at all.
• 3.  
  Component III (PL) only:Our PL component stands for the high-energy spectral component seen in GRB 090902B and GRB 090510, which likely has a high E_p near or above the boundary of the LAT band. Observationally, there is no solid evidence for such PL-only GRBs.¹¹ In our current sample, which covers the widest energy band, the PL component only exists in 2 out of 17 GRBs and is found to be associated with the BB component. The luminosity of the PL component is found to roughly track that of the thermal component (Figure 20). If the PL component is the Comptonization of a low-energy photon source (e.g., the BB component), then PL-only GRBs may not exist in nature.
• 4.  
  I + II:Such a case is not found in our sample. If the Band component is the emission from internal shocks and the BB component is the emission from the photosphere, then such a combination should exist and be common for fireball scenarios. An identification of such a case would confirm the non-thermal nature of the Band component (since the thermal component is manifested as the BB component). Observationally, an X-ray excess has been observed in 12 out of 86 (∼14%) bright BATSE GRBs (Preece et al. 1996). This could be due to the contamination of a BB component in the X-ray regime. With the excellent spectral coverage of Fermi, we expect that such a spectral combination may be identified in some GRBs, even if technically it may be difficult because there are too many spectral parameters to constrain.
• 5.  
  I + III:Such a combination has not been firmly identified in our sample. Nonetheless, the spectral hardening of GRB 090926A after 11 s may be understood as the emergence of the PL component on top of the Band component seen before 11 s. Physically, it may be related to two non-thermal spectral components or non-thermal emission from two different regions.
• 6.  
  II + III:Such a case is definitely identified in GRB 090902B, and likely in GRB 090510 as well. From the current sample, it seems that such a combination is not as common as the Band-only type, but nonetheless forms a new type of spectrum that deserves serious theoretical investigations. Physically, the high-energy PL component is likely the Compton up-scattered emission of the BB component, although other non-thermal processes (e.g., synchrotron and SSC) could also contribute to the observed emission (Pe'er et al. 2010).
• 7.  
  I + II + III:The full combination of all three spectral components (e.g., Figure 23) is not seen in the current sample. In any case, in view of the above various combinations (including speculative ones), one may assume that the full combination of the three spectral components is in principle possible. Physically, this may correspond to one photosphere emission component and two non-thermal components (either two spectral components or non-thermal emission from two different regions). Nonetheless, technically, there are too many parameters to constrain, so identifying such a combination is difficult.

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The Fermi team reported the delayed onset of LAT emission in several GRBs (080825C, 080916C, 090510, 090902B; Abdo et al. 2009a, 2009b, 2009c, 2009d). Our analysis confirms these results. In Table 1, we mark all the GRBs in our sample that show the delayed-onset feature.

There have been several interpretations of the delayed onset of GeV emission discussed in the literature. Toma et al. (2009) suggested that GeV emission is the upscattered cocoon emission from internal shock electrons. Razzaque et al. (2010) interpreted the GeV emission as the synchrotron emission of protons. Since it takes a longer time for protons to be accelerated and cooled to emit GeV photons, the high-energy emission is delayed. Li (2010b) interpreted GeV emission as the upscattered prompt-emission photons from residual internal shocks.

Although it is difficult to test these models using the available data, our results give some observational constraints to these models. First, except GRBs 090510 and 090902B, whose GeV emission is a distinct spectral component, other GRBs with delayed onset still have a simple Band-function spectrum after the delayed onset. This suggests that for those models that invoke two different emission components to interpret the MeV and GeV components, one needs to interpret the coincidence that the GeV emission appears to be the natural extension of the MeV emission to the high-energy regime.

For such delayed onsets whose GeV and MeV emissions form the same Band component, one may speculate about two simpler explanations. One is that there might be a change in particle acceleration conditions (e.g., magnetic configuration in the particle-acceleration region). As shown in Section 3.1, the early spectrum during the first time bin (before onset of LAT emission) of GRB 080916C may be simply a consequence of changing the electron spectral index. One may speculate that, early on, the particle acceleration process may not be efficient, so the electron energy spectral index is steep. After a while (the observed delay), the particle acceleration mechanism becomes more efficient, so the particle spectral index reaches a regular value. The second possibility is that there might be a change in opacity. The GBM data during the first time bin give a similar β as later epochs. It is possible that there might be a spectral cutoff early on that is slightly above the GBM band. A speculated physical picture would be that the particle acceleration conditions are similar throughout the burst duration, but early on the pair production opacity may be large (probably due to a lower Lorentz factor or a smaller emission radius), so LAT-band emission is attenuated. The opacity later drops (probably due to the increase of the Lorentz factor or the emission radius), so LAT-band emission can escape from the GRB. Within such a scenario, one would expect to see a gradual increase of maximum photon energy as a function of time. Figure 25 shows the LAT photon arrival-time distribution of GRB 080916C. Indeed, one can see a rough trend of a gradual increase in maximum energy with time.

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One last possibility is that LAT-band emission is dominated by the emission from the external shock, which is delayed with respect to GBM-band prompt emission. This possibility is discussed in more detail in Section 5.3.

Inspecting the multi-band light curves (Figures 1–17, left panels) for bright GRBs (e.g., 080916C, 090217, 090323, 090902B), LAT-emission peaks seem to roughly track some peaks of GBM emission (aside from the delayed onset of some of them). For example, the peak of the LAT light curve of GRB 080916C coincides with the second GBM peak. This is consistent with the spectral analysis showing that most time-resolved joint spectra consistently have the same (Band-function) spectral component. Even for GRB 090902B, whose LAT-band emission is from a different emission component from the MeV BB component, the emissions in the two bands also roughly track each other (Figure 20). This suggests that the two physical mechanisms that power the two spectral components are related to each other.

The rough tracking behavior is evidence against the proposal that the entire GeV emission results from the external forward shock (see Section 5.3 for further discussion). Within the forward shock model, the fluctuation in energy output from the central engine should be greatly smeared, since the observed flux change amplitude is related to ΔE/E ≪ 1 (where E is the total energy already in the blastwave and ΔE is the newly injected energy from the central engine) rather than ΔE itself within the internal models.

To study long-term light curve behavior, we extract the GBM-band and LAT-band light curves in the logarithmic scale and present them in the bottom right panel of Figures 1–17. We unevenly bin the LAT light curves with bin sizes defined by the requirement that the S/N must be >5. For a close comparison, we correspondingly rebin the GBM light curves using the same bin sizes. Some GRBs (e.g., 080916C, 090510, 090902B, and 090926A) have enough photons to make a well-sampled LAT light curve.

In several GRBs, LAT emission lasts longer than GBM emission and decays as a single power law (Ghisellini et al. 2010). The decay indices of LAT emission are marked in the last panel of Figures 1–17 and can also be found in Table 3. Due to low photon numbers, it is impossible to carry out a time-resolved spectral analysis. In any case, the LAT-band photon indices of long-term LAT emission are estimated and also presented in Table 3. In Table 1, we mark those GRBs with and without detected LAT emission longer than GBM emission. The most prominent ones with long-lasting LAT afterglow are GRBs 080916C, 090510, 090902B, and 090926A. Spectral analyses suggest that the LAT emission in GRBs 090510 and 090902B is a different spectral component from the MeV emission. The GBM light curves of these GRBs indeed follow a different trend by turning sharply compared to the extended PL decay in the LAT band. GRB 090926A, on the other hand, shows a similar decay trend in both GBM and LAT bands. GRB 080916C is special. Although the spectral analysis shows a single Band-function component, the GBM light curve turns over sharply around 70–80 s, while the LAT emission keeps decaying with a single power law.

Table 3. Temporal Decay Slopes and the Time-integrated Photon Indices of the Long-term LAT Count Rate Light Curves

Name	αLAT	${\bar{\Gamma }_{\rm LAT}}$
080825C	−0.47 ± 0.74	−1.71
080916C	−1.33 ± 0.08	−1.77
081024B	−1.37 ± 0.41	−1.98
081215A	...	...
090217	−0.81 ± 0.23	−1.97
090323	−0.52 ± 0.67	−1.75
090328	−0.96 ± 0.44	−1.82
090510	−1.70 ± 0.08	−1.94
090626	...	−1.53
090902B	−1.40 ± 0.06	−1.76
090926A	−2.05 ± 0.14	−2.03
091003	<−0.93	−1.74
091031	−0.57 ± 0.28	−1.73
100116A	...	−1.68
100225A	...	−1.77
100325A	<−1.04	−1.53
100414A	−1.64 ± 0.89	−1.85

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One caveat of long-term LAT light curves is that they depend on the level of background and time-bin selection. Due to the low count rate at late times, the background uncertainty can enormously change the flux level, and a different way of binning the data may considerably change the shape of the light curve. In our analysis, the background model is extracted from the time interval prior to the GBM trigger in the same sky region that contains the GRB. The bin-size is chosen to meet the 5σ statistics to reduce the uncertainty caused by arbitrary binning.

Our data analysis suggests a controversial picture regarding the origin of this GeV afterglow. Spectroscopically, LAT-band emission is usually an extension of GBM-band emission and forms a single Band-function component, suggesting a common physical origin with GBM-band emission. If one focuses on the prompt emission light curves, the LAT-band activities seem to track the GBM-band activities. Even for GRB 090902B, which shows a clear second spectral component, the PL component variability tracks that of the BB component well (Figure 20), suggesting a physical connection between the two spectral components. These facts tentatively suggest that, at least during the prompt emission phase, LAT-band emission is likely connected to GBM-band emission and may be of an "internal" origin similar to that of GBM-band emission.

It has been suggested that the entire GeV emission originates from an external shock (e.g., Kumar & Barniol Duran 2009, 2010; Ghisellini et al. 2010; Corsi et al. 2010). This idea is based on the PL temporal decay law that follows prompt emission. Such a GeV afterglow scenario is not straightforwardly expected for the following reasons. First, before Fermi, afterglow modeling suggested that for typical afterglow parameters, the GeV afterglow is initially dominated by the SSC component (Mészáros & Rees 1994; Dermer et al. 2000; Zhang & Mészáros 2001; Wei & Fan 2007; Gou & Mészáros 2007; Galli & Piro 2007; Yu et al. 2007; Fan et al. 2008), or by other inverse Compton processes invoking both forward and reverse shock electrons (Wang et al. 2001). For very energetic GRBs such as GRB 080319B, one may expect a synchrotron-dominated afterglow all the way to an energy ∼10 GeV (Zou et al. 2009; Fan et al. 2008). Second, the required parameters for the external shock are abnormal to interpret the data. For example, the magnetic field strength at the forward shock needs to be much smaller than equipartition, consistent with simply compressing the interstellar medium (ISM) magnetic field without shock amplification (Kumar & Barniol Duran 2010). This, in turn, causes a problem in accelerating electrons to an energy high enough to enable emission of GeV photons (Li 2010a; Piran & Nakar 2010). Moreover, the circumburst number density of these long GRBs must be much lower than that of a typical ISM (e.g., Kumar & Barniol Duran 2010), which challenges the collapsar model. Finally, the observed GeV decay slope is typically steeper than the predictions, invoking a standard adiabatic forward shock (e.g., Figures 2, 8, 10, 11, 17; see also Ghisellini et al. 2010). One needs to invoke a radiative blastwave (Ghisellini et al. 2010) or a Klein–Nishina cooling-dominated forward shock (Wang et al. 2010) to account for the steepness of the decay slope.

The external shock model's ability to interpret the entire GeV emission is challenged by the following two arguments. First, the GeV light curve peak coincides with the second peak of the GBM light curve for GRB 080916C. This requires a fine-tuned bulk Lorentz factor of the fireball to make the deceleration time coincide with the epoch of the second central-engine activity. This is highly contrived. Second, the external shock component should not decay steeply while the prompt emission is still ongoing. To examine this last point, we apply the shell-blastwave code developed by Maxham & Zhang (2009) to model the blastwave evolution of GRB 080916C, using the observed data and assuming that the outflow kinetic energy traces the observed gamma-ray light curve (assuming a constant radiation efficiency). The resulting LAT-band light curve always displays a shallow decay phase caused by refreshing the forward shock by materials ejected after the GeV light curve peak time, even for a radiative blastwave, in stark contrast to the data. This casts doubts on the external shock origin of GeV emission during the prompt phase (Maxham et al. 2011). We note that detailed modeling of GRB 090510 (He et al. 2010) and GRB 090902B (Liu & Wang 2011) with the external shock model suggests that the GeV prompt emission cannot be interpreted as the emission from the external forward shock.

Collecting the observational evidence and the theoretical arguments presented above, we suggest that, at least during the prompt emission phase (when GBM-band emission is still ongoing), LAT-band emission does not originate from an external forward shock.

After GBM-band prompt emission is over, LAT-band emission usually decays as a power law. We note that the long-term GeV light curve can be interpreted in more than one way. (1) If one accepts that prompt GeV emission is of internal origin, one may argue that the external shock component sets in before the end of the prompt emission and thereafter dominates during the decay phase (Maxham et al. 2011). This requires arguing for the coincidence of the same decaying index for the early internal and late external shock emissions. Considering a possible superposition effect (i.e., the observed flux during the transition epoch includes the contributions from both the internal and external shocks), this model is no more contrived than the model that interprets GeV prompt emission as coming from external shocks, which requires the coincidence of the internal emission spectrum and the external shock emission spectrum to mimic the same Band spectrum in all time bins (Kumar & Barniol Duran 2009). (2) An alternative possibility is to consider an internal origin of the entire long-lasting GeV afterglow, which reflects the gradual "die off" of the central engine activity. The difficulty of such a suggestion is that it must account for the different decaying behaviors of GBM-band emission and LAT-band emission in some (but not all) GRBs (e.g., GRB 080916C). To differentiate between these possibilities, one needs a bright GRB cotriggered by the Fermi LAT/GBM and Swift BAT, so an early Swift XRT light curve is available along with the early GeV light curve. The external-shock-origin GeV afterglow should be accompanied by a PL early-decay X-ray light curve (Liang et al. 2009) instead of the canonical steep-shallow-normal decaying pattern observed in most Swift GRBs (Zhang et al. 2006; Nousek et al. 2006; O'Brien et al. 2006). A violation of such a prediction would suggest an internal origin of the GeV afterglow.