GRB 080916C AND GRB 090510: THE HIGH-ENERGY EMISSION AND THE AFTERGLOW

Gamma-ray bursts (GRBs) are the most luminous explosions in the universe. They feature extremely relativistic outflows with bulk Lorentz factors ∼10^2–3 and isotropic energies of 10^48–55 erg. Though their cosmological origin as well as the relativistic movement has been firmly established, the radiation mechanism and the outflow composition are still uncertain (Piran 1999; Zhang & Mészáros 2004). It is widely believed that the high-energy emission of GRBs can shed light on these two fundamental issues (see Fan & Piran 2008 for a review). For example, a distinct GeV–TeV spectrum excess can be taken as an indication evidence of a baryonic outflow and a radiation process in addition to synchrotron (e.g., inverse Compton scattering) will be needed, while the absence of such a component in most spectra may favor the magnetic outflow model. Recently, the Fermi collaboration has released their observation data of GRBs 080916C and 090510 (Abdo et al. 2009a, 2009b). In this work, we examine the origins of these prompt and afterglow GeV emission. The work is structured as follows. In Section 2, we discuss the origin of the prompt GeV emission and the corresponding constraint on the physical composition. In Section 3, we employ the standard external forward shock model to interpret the X-ray and optical afterglow data. In Section 4, we investigate the origin of the afterglow GeV emission. Our results are summarized in Section 5 with some discussion.

GRB 080916C was a long burst with a duration T₉₀ ≃ 66 s (Abdo et al. 2009a) and was at a redshift z ∼ 4.35 ± 0.15 (Greiner et al. 2009b). A few hundred high-energy photons have been detected by the Large Area Telescope (LAT) onboard the Fermi satellite and three of them are above 10 GeV. The joint analysis of the LAT and Gamma-ray Bursts Monitor (GBM) data suggests a featureless Band spectrum in the energy range 8 keV–10 GeV (Abdo et al. 2009a). A straightforward interpretation of the spectrum is the synchrotron radiation of internal shock electrons. Such an interpretation, if correct, demands a very large bulk Lorentz factor Γ_i ∼ 10³ of the emitting/shocked region (Abdo et al. 2009a; Greiner et al. 2009b). In the internal shock scenario, the fast shells should move faster and the corresponding bulk Lorentz factor should be Γ_f ∼ 5Γ_i, otherwise the internal shock efficiency will be too low to match the observations (e.g., Piran 1999). The photosphere radius of the fast shells is R_ph ∼ 5 × 10⁹ cm L₅₄ Γ⁻³_f,3.7 (Paczynski 1990), where L is the total luminosity of the outflow.⁷ On the other hand, for a baryonic shell we have Γ_f ⩽ R_ph/R₀ ∼ 5 × 10³L₅₄ Γ⁻³_f,3.7R⁻¹_0,6 (Piran 1999), where R₀ ⩾ 10⁶ cm is the size of the central engine. So the shell becomes transparent at the late stage of its acceleration. As a result, the thermal radiation of these shells will be too strong to be effectively outshone by the internal shock non-thermal emission, in disagreement with the data (Fan 2009; see Zhang & Pe'er 2009 for the other approach). Hence we would not discuss the standard/unmagnetized internal shock model for this burst.

An interesting possibility is that the prompt emission has a very soft MeV–GeV spectrum and the GeV photons are due to the synchrotron radiation of the external forward shock (Kumar & Barniol Duran 2009). Here we outline a few potential challenges of such a model. (1) In the forward shock model, the variability of the radiation is determined by the angular timescale T_ang, which is ∼t as long as the edge of the emitting region is invisible (Piran 1999). So the light curve should be smooth. The variability shown in the LAT data then disfavors the forward shock emission model. (2) For the initial outflow expanding into the wind medium (see Section 3 for the medium identification), strong reverse shock may form. The bulk Lorentz factor of the shocked medium will be almost a constant (Chevalier & Li 2000). A strong reverse shock exists till t ∼ T₉₀/2. In such a phase, we have the magnetic field strength B ∝ t⁻¹, the maximum specific flux F_ν,max ∝ t⁰, the typical synchrotron frequency ν_m ∝ t⁻¹, and the cooling frequency ν_c ∝ t. Hence the synchrotron radiation flux in the LAT band can be estimated as F_LAT ∝ F_ν,maxν^{(p − 1)/2}_mν^1/2_c ∝ t^(2−p)/2 for hν_c < 100 MeV, inconsistent with the observation, where p is the power-law distribution index of the accelerated electrons at the shock front (see Xue et al. 2009, for extensive discussion). Since the reverse shock emission has not been detected in most GRBs and it is not clear whether the model suffers some disadvantages, we do not take the current temporal inconsistence as a conclusive argument. (3) To reproduce the prompt spectrum, the forward shock emission at t ∼ 10 s should have hν_m ⩾ 300 keV. At such early time, the synchrotron self-Compton radiation is in extreme Klein–Nishina regime and the Compton parameter Y ∼ 0. With proper parameters, ν_c can be comparable to ν_m. So the sub-MeV spectrum can be F_ν ∝ ν^1/3, steep enough to be consistent with the data. However, if ν_m ∼ 10²⁰(t/10)^−3/2 Hz, the XRT light curve will be $F_{\nu _{\rm x}} \propto t^0$ for t < 10³ s and the optical light curve will be $F_{\nu _{\rm opt}} \propto t^{0}$ for t < 10⁵ s. These behaviors are very unusual and have not been detected in other GRB afterglows so far. The lack of observation of early afterglow of GRB 080916C, however, hampers us to test the model.

If the prompt high-energy emission of GRB 080916C was from the soft gamma-ray emitting region, a plausible origin of the GeV photons is the synchrotron radiation of electrons accelerated in magnetic energy dissipation of a Poynting-flux dominated outflow (Zhang & Pe'er 2009). A disadvantage of such a scenario is the difficulty of reproducing the hard low-energy spectrum (Fan 2009).

GRB 090510 was a short burst at a redshift z ∼ 0.903 (Abdo et al. 2009b). The high-energy emission is much more intense than that of GRB 080916C and shows some variability, which disfavors the external forward shock model. In the time interval 0.5–0.6 s, the sub-MeV spectrum is very hard but the high-energy spectrum is very soft (Abdo et al. 2009b), possibly dominated by the photosphere emission of the baryonic shell.⁸ In the time interval 0.5–0.8 s, the high-energy spectrum gets harder and harder but the "thermal"-like MeV component is still evident. GeV emission is naturally produced in the IC scattering of the "photosphere" photons by the shocked electrons. The photosphere radius is ∼6 × 10¹¹ cm L₅₄Γ⁻³_sh,3, where Γ_sh is the bulk Lorentz factor of the shell. The internal shocks take place at a rather larger radius R_γ ∼ Γ²_icδt/(1 + z) ∼ 1.5 × 10¹⁵ cm Γ²_i,3(δt/0.1 s), where δt is the detected variability timescale of the prompt emission. In the comoving frame of the emitting region, the seed/photosphere photons are moving along the radial direction and are highly anisotropic. In such a case, the strongest IC radiation is from an angle ∼1/Γ_i relative to the line of sight (Fan & Piran 2006b). The arrival of the GeV photons will be delayed by a time ∼δt and the GeV radiation duration will be extended, in agreement with the observation. Below we show how to reproduce the high-energy spectrum F_ν ∝ ν^−0.54 in time interval 0.8–0.9 s. If the cooling of the electrons is dominated by the prompt soft gamma-rays with a luminosity L_γ, the cooling Lorentz factor can be estimated by γ_c,ic ∼ 5L⁻¹_γ,53.3R_γ,15Γ³_i,3 (Fan & Piran 2008). Here we do not take L_γ ∼ 10⁵² erg s^-1, the luminosity of the simultaneous soft gamma-ray emission, since in the photosphere-internal shock model the arrival of the upscattered photons is delayed, as already mentioned. The corresponding IC radiation frequency ε_c,ic ∼ γ²_c,icE_p ∼ 25 MeV(E_p/1 MeV)L⁻²_γ,53.3R²_γ,15.3Γ⁶_i,3, where E_p is the typical energy of the seed photons. On the other hand, γ_m,i ≈ _e,i(m_p/m_e)(Γ_sh − 1)/3 ≈ 100(_e,i/0.5)[(Γ_sh − 1)/0.3] for p ∼ 2.5, where Γ_sh is the parameter denoting the strength of the shocks. The corresponding IC radiation frequency is ε_m,ic ∼ γ²_m,iE_p ∼ 10 GeV(γ_m,i/100)²(E_p/1 MeV). The spectrum in the energy range ∼10 MeV–10 GeV is F_ν ∝ ν^−1/2, consistent with the data. We note that in the time interval 0.9–2 s the soft gamma-ray emission is very weak while the GeV emission is still strong. These delayed GeV photons may be produced by the IC scattering of the soft gamma-rays by the electrons accelerated by the reverse shock or by the shocks generated in the collision of the late time (t > 0.5 s) outflow with the precursor outflow.

GRB 080916C. Swift XRT started to observe this source at about 17 hr after the Fermi trigger. In our data analysis, the X-ray light curve can be fitted by a single power law $F_{\nu _{\rm x}}\propto t^{-1.30 \pm 0.07}$ for 6.1 × 10⁴ < t < 1.3 × 10⁶ s and the XRT spectrum is F_ν ∝ ν^{−0.50 ± 0.16}. The earliest optical/infrared observation started at t ∼ 26.7 hr after the burst. The optical/NIR light curve can be well described by $F_{\nu _{\rm opt}} \propto t^{-1.40\pm 0.05}$. The optical to X-ray spectrum is consistent with a single power law F_ν ∝ ν^−0.63 (Greiner et al. 2009b). These facts suggest that the optical to X-ray afterglow emission is within the same regime. In the standard external shock model (e.g., Zhang & Mészáros 2004), the slow cooling spectrum takes the form F_ν ∝ ν^{−(p − 1)/2} and the decline should be either t^3(1−p)/4 (ISM) or t^{(1 − 3p)/4} (wind medium). One can see that the X-ray and optical afterglow data are in agreement with the wind medium model for p ∼ 2.2 (see also Zou et al. 2009).

Assuming a GRB efficiency ∼ 0.2, the isotropic-equivalent kinetic energy of the outflow is E_k ∼ 4 × 10⁵⁵ erg. In the wind case, the equations that govern the forward shock emission are (e.g., Yost et al. 2003)

$$\begin{equation} \nu _{\mbox{m}}\approx 1.3\times 10^{14}\ {\rm Hz }\ { \epsilon _{e,-1}^{2}\epsilon _{B}^{1/2}C_{p}^{2}E_{k,55.6}^{1/2}(1+z)^{1/2}t_{4.8}^{-3/2}}, \end{equation} \tag{ 1 }$$

$$\begin{equation} \nu _{\rm c}\approx 1.7\times 10^{13}\ {\rm Hz}\ \epsilon _{B}^{-3/2}E_{k,55.6}^{1/2}A_{\ast }^{-2}(1+z)^{-3/2}t_{4.8}^{1/2}(1+Y)^{-2}, \end{equation} \tag{ 2 }$$

$$\begin{equation} F_{\nu, \max }\approx 100 \;{\rm mJy}\ \epsilon _{B}^{1/2}E_{k,55.6}^{1/2}A_{\ast } t_{4.8}^{-1/2}(1+z)^{3/2}D_{L,29.1}^{-2}, \end{equation} \tag{ 3 }$$

where C_p ≡ 13(p − 2)/[3(p − 1)] for p > 2.05, $A_{\ast }=(\dot{M}/10^{-5}\;M_{\odot } {\rm \;yr^{-1}})[v_{\rm w}/(10^{8} \;{\rm cm \;{\rm s^{-1}}})]^{-1}$ is the wind parameter, v_w is the speed of the wind, $\dot{M}$ is the mass-loss rate (Chevalier & Li 2000), and $Y=[-1+\sqrt{1+4\eta \eta _{_{\rm KN}}\epsilon _{e}/\epsilon _{B}}]/2$, η ≃ min{1, (ν_m/ν_c)^{(p − 2)/2}}, and η_KN is the factor reflecting the importance of the Klein–Nishina correction (see Appendix A of Fan & Piran 2006a for the expression).

Since ν_m decreases with time while ν_c increases with time, the current afterglow data suggest that ν_m(t = 10⁵ s) ⩽ ν_opt/IR and ν_c(t = 6 × 10⁴ s) ⩾ ν_x ∼ 10¹⁸ Hz, i.e.,

$$\begin{equation} \epsilon _{e,-1}^{2}\epsilon _{B}^{1/2}\le 5, \epsilon _{B}^{-3/2}A_{\ast }^{-2}(1+Y)^{-2} \ge 7\times 10^{5}. \end{equation} \tag{ 4 }$$

At t ∼ 10⁵ s, the K_s-band flux is ∼3 × 10⁻⁵ Jy (Greiner et al. 2009b), which gives us another constraint

$$\begin{eqnarray} &&\epsilon _{e,-1}^{1.2} \epsilon _{B}^{0.8}A_{\ast } \sim 7\times 10^{-5}. \end{eqnarray} \tag{ 5 }$$

Substituting $Y\sim \sqrt{\epsilon _{\rm e}/50\epsilon _{\rm B}}$ (due to the slow cooling and the Klein–Nishina correction) in Equations (4) and (5), we have A_* ⩾ 10⁻⁵²_e,-1, _B ⩾ 10^−4−1.3_e,-1. Though the shock parameters cannot be uniquely determined, we see that the "reasonable" parameters (_e, _B, A_*) ∼ (0.1, 2.5 × 10⁻³, 0.01) can reproduce the data.

GRB 090510. In our data analysis, before and after the break at t_b ∼ 676(1 + z) s, the X-ray declines are t^{−0.72 ± 0.08} and t^{−1.89 ± 0.06}, respectively. The X-ray spectrum can be reasonably fitted by F_ν ∝ ν^{−0.63 ± 0.06}. We reduced the UVOT data in a standard way with the aid of reduction threads at http://www.swift.ac.uk/UVOT.shtml. The combined V-band and white light curves show a rise since the beginning of UVOT observation to a peak around 1000 s after the BAT trigger, which is followed by an apparent decay leading to the optical flux lower than the threshold of UVOT quickly. Our results are generally in agreement with those of De Pasquale et al. (2009). Within the standard external shock model, the above data are roughly consistent with a slow cooling ejecta expanding into the ISM for p ∼ 2, while the break can be interpreted as the jet effect (Piran 1999; Zhang & Mészáros 2004). The slowly rising optical emission may suggest that the observer's frequency is below ν_m. In the ISM case, the equations that govern the forward shock emission are (e.g., Sari et al. 1996; Yost et al. 2003)

$$\begin{eqnarray} &&\nu _{\rm c} \approx 5.2\times 10^{18}\ {\rm Hz }\ E_{k,54}^{-1/2}\epsilon _{B,-4}^{-3/2}n_{0}^{-1}(1+z)^{-1/2}t_{3.1}^{-1/2}(1+Y)^{-2},\nonumber\\ \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} &&\nu _{{\rm m}}=7.0\times 10^{13}\ \mbox{Hz}\ E_{k,54}^{1/2}\epsilon _{B,-4}^{1/2}\epsilon _{e,-1}^{2}C_{p}^{2}(1+z)^{1/2}t_{3.2}^{-3/2}, \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &&F_{\nu,{\rm max}}=2.7\times 10^{-3}\ {\rm Jy }\ (1+z)D_{L,28.26}^{-2}\epsilon _{B,-4}^{1/2}E_{k,54}n_{0}^{1/2}, \end{eqnarray} \tag{ 8 }$$

please note that we have C_p ≃ 0.23 for p ∼ 2.

The conditions that ν_c(t = 1284 s)>ν_x, ν_m(t ∼ 1000 s) ∼ 5 × 10¹⁴ Hz, and F_ν,max ⩾ 1 × 10⁻⁴ Jy (De Pasquale et al. 2009) yield

$$\begin{equation} E_{k,54}^{-1/2}\epsilon _{B,-4}^{-3/2}n_{0}^{-1}(1+Y)^{-2} \ge 0.2, \end{equation} \tag{ 9 }$$

$$\begin{equation} E_{k,54}^{1/2}\epsilon _{B,-4}^{1/2}\epsilon _{e,-1}^{2}\sim 50, \epsilon _{B,-4}^{1/2}E_{k,54}n_{0}^{1/2}\ge 0.02. \end{equation} \tag{ 10 }$$

The parameters (E_k,54, _B,-4, _e,-1, n₀) ∼ (1, 1, 7, 0.01) satisfy the above constraints (note that $Y\ll \sqrt{\epsilon _{\rm e}/\epsilon _{\rm B}}$ thanks to the Klein–Nishina correction). The jet break time t_b = 1284 s suggests a half-opening angle θ_j = 6 × 10⁻³t^3/8_3.1E^−1/8_k,54^1/8_−0.7n^1/8_0,−2. So the true gamma-ray energy released is E_γ,jet ≃ θ²_jE_γ/2 = 2 × 10⁴⁸ erg, where E_γ ∼ 1.4 × 10⁵³ erg is the isotropic-equivalent gamma-ray energy.

4.1. IC Scattering in the Forward Shock Region?

If the high-energy afterglow is due to the IC radiation of the forward shock electrons, there is a simple method to estimate the number of seed photons, regardless of the origin of the seed photons (either the late prompt emission from the central engine or the synchrotron radiation of the forward shock electrons). Following Fan & Piran (2006b), the possibility of one seed photon being scattered (i.e., the optical depth) in the forward shock region can be estimated as

$$\begin{equation} \tau _{\rm ISM} \sim 4.2\times 10^{-8} E_{k,53}^{1/4}n_0^{3/4}t_3^{1/4}[(1+z)/2]^{-1/4}, \end{equation} \tag{ 11 }$$

$$\begin{equation} \tau _{\rm wind} \sim 7.3 \times 10^{-6} A_*^{3/2}E_{k,53}^{-1/2}t_3^{-1/2}[(1+z)/2]^{1/2}, \end{equation} \tag{ 12 }$$

respectively. With the parameters derived for GRBs 080916C and 090510, we have

$$\tau _{\rm wind}({\rm 080916C}) \sim 10^{-9} A_{*,-2}^{3/2}E_{k,55.6}^{-1/2}t_{2.6}^{-1/2},$$

$$\tau _{\rm ISM}(090510) \sim 7\times 10^{-10} E_{k,54}^{1/4}n_{-2}^{3/4}t_1^{1/4},$$

respectively.

If the detected high-energy afterglow photons are indeed the IC radiation of the forward shock electrons, the number flux of the seed photons will be

$$\begin{equation} {F}_{\rm seed} \sim {{F}_{\rm >100 \;MeV}/ \tau }. \end{equation} \tag{ 13 }$$

For GRB 080916C, in the time interval ∼100–1400 s (i.e., Δt = 1300 s), F_{>100 MeV} ∼ 7 × 10⁻⁶ ph cm^-2 s⁻¹ (Abdo et al. 2009a), so the number of total seed photons is

$$\begin{equation} N_{\rm se} \sim {4\pi D_{\rm L}^2 \over (1+z)^{2}} \Delta t {F}_{\rm seed}\sim 6\times 10^{64}. \end{equation} \tag{ 14 }$$

If most seed photons are in the X-ray band, the total energy will be ∼10⁵⁶ erg, which is too large to be realistic. If the seed photons are mainly in optical/infrared band, the total energy will be ∼10⁵³ erg. Though bright infrared/optical flare can be produced in the afterglow phase by the prolonged activity of the central engine (for example, the infrared flare detected in GRB 080129; Greiner et al. 2009a; Gao 2009), it is clear that such events are very rare. So we think this kind of model is less likely.

For GRB 090510, the Fermi collaboration has not published the high-energy afterglow data yet. According to Giuliani et al. (2009), the high-energy photon flux recorded by AGILE is ∼0.01(t/2 s)^−1.3 ph cm^-2 s⁻¹. In the IC scattering model, the number of seed photons is needed to be N_se ∼ 10⁶⁵. Even all the seed photons are in near-infrared band (∼1 eV), the total energy should be 10⁵³ erg, seeming unreasonably large for GRB 090510.

4.2. Synchrotron Radiation of Forward Shock Electrons?

In this work, we have interpreted the high-energy emission and the afterglow of GRBs 080916C and 090510. For the prompt high-energy emission of GRB 080916C with a featureless Band spectrum, the standard/unmagnetized internal shock model is disfavored. The main reason is that in such a model the fast shells move with a very high bulk Lorentz factor (∼5 × 10³) and the thermal radiation from their photospheres will be too strong to be hidden by the non-thermal emission of the internal shocks. As for the idea that the prompt GeV photons are the synchrotron radiation of the forward shock electrons, we predict very unusual X-ray (for t < 10³ s) and optical (for t < 1 day) afterglow light curves. The lack of early afterglow observation, however, hampers us to test the model. If the prompt GeV photons and the soft gamma-rays are from the same region, a non-baryonic component seems needed (Zhang & Pe'er 2009; Fan 2009). For GRB 090510, the prompt spectrum consists of two distinct components. The MeV emission may be from the photosphere, while the GeV emission is produced in the IC scattering of the photosphere photons by the shocked electrons. We suggest that the outflow of GRB 090510 is baryonic.

The circum-burst medium of GRBs 080916C and 090510 is wind-like and ISM, respectively. The standard external shock model can reproduce the afterglow data reasonably well. The common features are the low density of the medium they are expanding into and the very high isotropic-equivalent kinetic energy of the outflows. We have proposed a simple method to estimate the total number of seed photons supposing the GeV afterglow emission is due to the IC radiation of the forward shock electrons. Such a model is disfavored because the seed photons needed in the modeling are too many to be realistic. Though other possibilities, for example, the GeV afterglow photons are the synchrotron self-Compton radiation of the extended X-ray emission, cannot be ruled out, the high-energy afterglow detected in these two bursts may be just the synchrotron radiation of the forward shock electrons. Our analysis is then in support of the "prediction" of Zou et al. (2009) in GRB 080319B and the suggestion of Kumar & Barniol Duran (2009) for GRB 080916C. GRBs 080319B, 080916C, and 090510 are very unusual. They are extremely bright⁹ and may have a very large initial bulk Lorentz factor. Both facts are helpful to give rise to a strong GeV synchrotron radiation of the forward shock. The number density of the circum-burst medium is very low, which lowers the detection prospect of the IC radiation component for LAT. For normal GRBs, the detection prospect of the GeV synchrotron radiation of the forward shock will be much less promising.

We are grateful to R. Margutti for providing XRT data and P. Kuin for communication. This work was supported in part by the National Natural Science Foundation of China under grant 10603003 (for W.H.G.), the Danish National Science Foundation, Chinese Academy of Sciences, and National basic research program of China under grant 2009CB824800 (for Y.Z.F.).