AN INVERSE COMPTON ORIGIN FOR THE 55 GeV PHOTON IN THE LATE AFTERGLOW OF GRB 130907A

Both Fermi Gamma-ray Burst Monitor and LAT did not trigger on GRB 130907A due to the South Atlantic Anomaly (SAA) passage. Fermi resumed data taking at ∼T₀ +1.3 ks after it left the SAA, when the burst was ∼150° from the LAT boresight. It only entered the LAT field of view (FoV) at ∼T₀ +3.4 ks. Preliminary analysis showed that GRB 130907A was detected by LAT and a ∼55 GeV photon compatible with the GRB position was observed at ∼T₀ +18 ks (Vianello et al. 2013).

We analyzed the LAT data from T₀+3 ks to T₀+80 ks, which are available at the Fermi Science Support Center. The Fermi Science Tools v9r31p1 package was used to analyze the data between 100 MeV and 60 GeV. As recommended by the LAT team for this timescale, events of the P7SOURCE$\_$V6 class were used. We selected all the events within a region of interest (ROI) with a radius of 10° around the position of the GRB, excluding times when any part of the ROI was at a zenith angle >100°. We constructed a background source model including the nearby 33 point sources in the second Fermi catalog (Nolan et al. 2012), as well as the galactic diffuse emission (gal$\_$2yearp7v6$\_$v0.fits) and the isotropic component (iso$\_$p7v6source.txt). A simple power-law spectrum is assumed for the LAT emission from GRB 130907A, which is described by N(E) = N₀(E/E₀)^−Γ, where Γ is the photon index.

First, an unbinned maximum-likelihood analysis was performed for the period T₀ +3 ks to T₀ +20 ks. We obtained a test-statistic (TS; the square root of the TS is approximately equal to the detection significance for a given source; see Mattox et al. 1996) value of 41.3, corresponding to a detection significance of 6.4, consistent with the value given in Vianello et al. (2013). This analysis also gave a photon index of −1.9 ± 0.2 and an average photon flux of (5.5 ± 1.8)×10⁻⁷ cm⁻² s⁻¹. We note the detection of a 54.4 GeV photon 17,218 s after T₀, and we identify this photon as the one first mentioned in Vianello et al.(2013). We also searched through the period T₀ +20 ks to T₀ +80 ks and did not detect any significant emission. We put a 90% confidence level (c.l.) upper limit of the photon flux at 1.2×10⁻⁷ (or 6.1×10⁻⁸) cm⁻² s⁻¹ in this time interval, assuming Γ = 2.0 (or 1.5).

To firmly establish the association of the 54.4 GeV photon with GRB 130907A, we estimated the probability using two methods. First we used the gtsrcprob tool, which used the likelihood analysis as described above to assign to each photon in the ROI a probability that such photon is associated with GRB 130907A (instead of coming from the background). There are six photons with probability of >90% and 11 photons with probability of >50% from T₀ +3 ks to T₀ +20 ks. In particular, the 54.4 GeV photon at 17,218 s has a probability of >99.998% to be associated with GRB 130907A. Second, we counted the number of 50–500 GeV photons from 5 yr of LAT observations from the direction of GRB 130907A (using the point-spread function of 08 for a 50 GeV photon), which is three. Therefore, the probability of obtaining one 50–500 GeV background photon from this direction over a time interval of 20 ks is about 3.8 × 10⁻⁴. In other words, the probability that this photon is associated with GRB 130907A is higher than 99.96%.

The energy resolution of 10–100 GeV photons is on the order of 10%, therefore we will also designate this highest energy photon as a 55 GeV photon. At z = 1.238, the intrinsic photon energy of the 55 GeV photon would be 123 GeV, putting it as one of the few very high-energy γ-ray photons that originated from a GRB, after those from GRB 080916C (Atwood et al. 2013) and GRB 130427A (Tam et al. 2013).

From T₀ +3 ks to T₀ +20 ks, the GRB was in the LAT FoV during two intervals: 3000–6000 s and 14,000–20,000 s after T₀. During each interval, GRB 130907A was detected significantly, i.e., a TS value of >20 was obtained. We note that the detection in the second interval is dominated by the single 55 GeV photon. For each of the above time intervals, three or four energy bins were defined when the spectral energy distribution (SED) in the LAT band was constructed. For those fits without a well-constrained photon index, we fixed it to be Γ = 2.0 (the value obtained in the full-energy fit for the period from 3 ks to 80 ks), as well as Γ = 1.5. For those energy bins in which the TS value is smaller than 9, 90% c.l. upper limits are given, again assuming Γ = 2.0 (or Γ = 1.5). The results are summarized in Table 1.

The LAT light curve can be fitted with a single power law with a slope of −1.13 ± 0.57 as shown in Figure 1. Photon flux values are given here because the energy flux depends largely on the photon indices that are sometimes not well constrained.

Zoom In Zoom Out Reset image size

We extracted the Swift/XRT light curve and spectra during the LAT observations using the standard HEASOFT reduction pipelines and the Swift/XRT repository (Evans et al. 2007, 2009). The XRT observations of GRB 130907A started in window timing (WT) mode and data were taken in the photon counting (PC) mode combined with the WT mode from ∼T₀ +7000 s. The PC spectrum can be fitted by an absorbed power-law model with a photon index 1.67 ± 0.19 in the time interval from 3000 to 10,000 s from T₀, and 1.79 ± 0.12 from 14,000 to 20,000 s from T₀. The X-ray light curve can be fitted with a smoothed broken power law with a break at ∼19.6 ks, the pre-break decay index is −1.05 ± 0.07, and the post-break decay index is −2.43 ± 0.07 as shown in Figure 1.

By equating the synchrotron cooling time in the magnetic field with the Lamour time of the electrons, one can obtain the Lorentz factors of the maximum energy electrons, which is γ_{e, max}∝B^−1/2, where B is the strength of the magnetic field. In the same magnetic field, the maximum synchrotron photon energy produced by these electrons is about 50 MeV in the shock comoving frame. Considering the bulk motion boosting by the forward shock which has a Lorentz factor Γ_ext(t), the maximum synchrotron photon energy is ∼50Γ_ext(t) MeV. As the Lorentz factor of the forward shock decreases significantly at late times, one would expect $E_{\rm max,\rm syn}\lesssim 1.3(E_{54}/n_0)^{1/8}T_4^{-3/8}$GeV. The presence of a 54.4 GeV photon at ∼T₀ +5 hr is incompatible with a synchrotron origin even assuming the highest acceleration. It is more likely to originate from the inverse-Compton process, as also suggested by the detailed modeling of >10 GeV photons from GRB 130427A and other bursts (e.g., Wang et al. 2013; Liu et al. 2013). The modeling of the broadband SED, as shown in the following section, supports this explanation. Such a high-energy SSC emission has been predicted to be present in the high-energy afterglow emission for over a decade (e.g., Zhang & Mészáros 2001; Sari & Esin 2001).

In the standard synchrotron afterglow spectrum, there are three break frequencies, ν_a, ν_m, and ν_c, which are caused by synchrotron self-absorption, electron injection, and electron cooling, respectively. According to, e.g., Sari et al. (1998) and Wijers & Galama (1999), the cooling Lorentz factor and the minimum Lorentz factor of electrons in forward shocks are given by

$$\begin{equation} \gamma _m=7.5\times 10^{2} f(p) \epsilon _{e,-1} E_{54}^{1/8} n_0^{-1/8}(1+z)^{3/8} T_4^{-3/8}, \end{equation} \tag{ 1 }$$

and

$$\begin{equation} \gamma _c=3.5\times 10^6 E_{54}^{-3/8} n_0^{-5/8} \epsilon _{B,-5}^{-1}(1+z)^{-1/8}(1+Y_c)^{-1} T_4^{1/8}, \end{equation} \tag{ 2 }$$

where E is the kinetic energy of the spherical shock, _e is the fraction of the shock energy that goes into the electrons, _B is the fraction of the shock energy that goes into the magnetic fields, n is the particle number density of the uniform medium, and Y_c is the Compton parameter for electrons of energy γ_c and f_p = 6(p − 2)/(p − 1), with p being the electron index. These three characteristic frequencies are given by

$$\begin{equation} \nu _a=8.9\times 10^{9} f^{-1}(p) \epsilon _{e,-1}^{-1} E_{54}^{1/5} n_0^{3/5}\epsilon _{B,-5}^{1/5}(1+z)^{-1}\ {\rm Hz}, \end{equation} \tag{ 3 }$$

$$\begin{equation} \nu _m=1.2\times 10^{12} f^2(p) \epsilon _{e,-1}^2 E_{54}^{1/2} \epsilon _{B,-5}^{1/2}(1+z)^{1/2} T_4^{-3/2}\ {\rm Hz}, \end{equation} \tag{ 4 }$$

and

$$\begin{equation} \nu _c=2.5\times 10^{19} E_{54}^{-1/2} n_0^{-1}\epsilon _{B,-5}^{-3/2} (1+Y_c)^{-2} (1+z)^{-1/2} T_4^{-1/2}\ {\rm Hz}. \end{equation} \tag{ 5 }$$

We can also get the peak flux of the synchrotron emission by

$$\begin{equation} F_{\nu,m}=3.5\times 10^4 E_{54} n_0^{1/2}\epsilon _{B,-5}^{1/2} D_{28}^{-2}(1+z)\ \mu {\rm Jy}, \end{equation} \tag{ 6 }$$

where D is the luminosity distance. For the SSC emission, we get the corresponding quantities according to Sari & Esin (2001), i.e.,

$$\begin{equation} h\nu _m^{{\rm IC}}=5.4 f^4(p) \epsilon _{e,-1}^4 E_{54}^{3/4} \epsilon _{B,-5}^{1/2}(1+z)^{5/4} T_4^{-9/4} {\rm \,keV}, \end{equation} \tag{ 7 }$$

$$\begin{equation} h\nu _c^{{\rm IC}}=2.5\times 10^{6} E_{54}^{-5/4} n_0^{-9/4}\epsilon _{B,-5}^{-7/2} (1+Y_c)^{-4} (1+z)^{3/4} T_4^{1/4}\,{\rm TeV}, \end{equation} \tag{ 8 }$$

and

$$\begin{equation} F_{\nu,m}^{{\rm IC}}=5.6\times 10^{-3} E_{54}^{5/4} n_0^{5/4}\epsilon _{B,-5}^{1/2} D_{28}^{-2}(1+z)^{-3/4}T_4^{-1/4}\, \mu {\rm Jy}. \end{equation} \tag{ 9 }$$

Due to the fact that the inverse-Compton scatterings between γ_c electrons and the peak energy photons at frequency ν_c are typically in the Klein–Nishina (KN) regime, the SSC emission indeed peaks at

$$\begin{eqnarray} h \nu ^{{\rm IC}}_{\rm peak}=\Gamma _{\rm ext} m_e c^2 \gamma _c&=&44(1+Y_c)^{-1}E_{54}^{-1/4}n_0^{-3/4}\epsilon _{B,-5}^{-1}\nonumber\\ &&\times(1+z)^{1/4}T_4^{-1/4}\,{\rm TeV}, \end{eqnarray} \tag{ 10 }$$

where Γ_ext is the bulk Lorentz factor of the external forward shock. Above the peak $h \nu ^{{\rm IC}}_{\rm peak}$, the spectrum has the form similar to Equation (50) in Nakar et al. (2009). In order to calculate Y_c, we need to consider the SSC emission in the KN scattering regime. Following Wang et al. (2010), we define a critical frequency, above which the scatterings with electrons of energy γ_c just enter the KN scattering regime, i.e.,

$$\begin{equation} \nu _{{\rm KN}}(\gamma _c)=8.7\times 10^{14} E_{54}^{1/2} n_0^{-1/2}\epsilon _{B,-5}^{-1/2} (1+Y_c) (1+z)^{-1/2} T_4^{-1/2}\, {\rm Hz}. \end{equation} \tag{ 11 }$$

In a broad parameter space, we find ν_m < ν_KN(γ_c) < ν_c, and thus, following Wang et al. (2010), we have Y_c(1 + Y_c) = (_e/_B)(γ_c/γ_m)^{2 − p}(ν_KN(γ_c)/ν_c)^{(3 − p)/2} (which is also consistent with Equation (47) in Nakar et al. 2009). Therefore, Y_c is in the range from 4 to 6 in the time range between 1 ks and 20 ks after the burst for the reference parameter values of _{e, −1} = _{B, −5} = E₅₄ = n₀ = 1.

The multi-wavelength light curves are shown in Figure 1. The X-ray light curves (3–10 keV) initially decay as t^{−1.05 ± 0.07} in the first 20 ks and then steepens to a faster decay as t^{−2.43 ± 0.07}. The early X-ray decay slope −1.05 ± 0.07 and the spectral index β_X = 0.67 ± 0.19 are consistent with α = −(3p − 3)/4 and β = −(p − 1)/2 (F_ν∝t^αν^β) predicted by the standard afterglow synchrotron emission in the slow-cooling regime (i.e., ν_m < ν_X < ν_c) with p ≃ 2.3, assuming that the blast wave expands into a constant density circumburst medium. The wind medium scenario is not favored because the predicted decay slope in the wind medium scenario α_w = −(3p − 1)/4 is too steep. By fitting the I-band data from Skynet (Trotter et al. 2013b) and i-band data from RATIR (Butler et al. 2013a, 2013b; Lee et al. 2013, converted to I-band data according to Blanton & Roweis 2007), we obtained the decay slope −0.87  ±  0.09, which is consistent with ∼0.9 in Trotter et al. (2013b). The decay slope is consistent with the predicted slope α = −(3p − 3)/4 when the optical frequency ν_O is also located at ν_m < ν_O < ν_c. It is puzzling that the optical light curve does not show a break, as seen in X-rays. We speculate that there might be some extra contribution to the late-time optical flux, such as the host galaxy or another possible outflow component. Such chromatic break behavior has been seen before in other GRBs as well, e.g., Panaitescu et al. (2006).

The LAT emission decays as t^{−1.13 ± 0.57} with a large error bar in the decay slope due to the small number of high-energy photons. The decay slope is consistent with the predicted slope α = −(3p − 2)/4, as the LAT energy window is above the cooling frequency ν_c. Note that the time evolution of the Compton parameter (defined as Y(γ_*) in Wang et al. 2010) for the high-energy emission could steepen the LAT synchrotron decaying light curve, since the high-energy synchrotron flux scales as 1/(1 + Y(γ_*)). The value of Y(γ_*) is ≃ 2 at a few ks. However, because the measured decay slope has a large error (i.e., −1.13 ± 0.57), such effect is hard to discern from the data.

Below we model the multi-band SED with the synchrotron plus SSC emission model.

The LAT flux at hν = 100 MeV is about (6.0 ± 3.3) × 10⁻⁴ μJy around 6000 s after the burst. Since at hν = 100 MeV the flux is dominated by synchrotron emission, we have

$$\begin{eqnarray} F_\nu ({\rm 100{\rm \,MeV}}, t=6{\rm \,ks})&=&F_{\nu,m}\left(\frac{\nu _c}{\nu _m}\right)^{-(p-1)/2}\left(\frac{100{\rm \,MeV}}{h\nu _c}\right)^{-p/2}\nonumber\\ &=&(6.0\pm 3.3)\times 10^{-4}\mu {\rm \,Jy}. \end{eqnarray} \tag{ 12 }$$

The X-ray flux density at 1 keV around 17 ks is about (11.6 ± 2.1) μJy which was derived from the Swift XRT data, as discussed above, and we have

$$\begin{eqnarray} F_\nu (1{\rm \,keV}, t=17{\rm \,ks})&=&F_{\nu,m}\left(\frac{1{\rm \,keV}}{h\nu _m}\right)^{-(p-1)/2}\nonumber\\ &=&(11.6\pm 2.1) \,\mu {\rm Jy}. \end{eqnarray} \tag{ 13 }$$

VLA observations started at ∼T₀ +14 ks and ended at ∼T₀ +20 ks at ν = 24.5 GHz; the flux is (1.2 ± 0.09) mJy (Corsi 2013). Since the high frequency of the radio band is located between the self-absorption frequency ν_a and ν_m, we have

$$\begin{eqnarray} F_\nu (24.5{\rm \,GHz}, t=4\,{\rm hr})&=&F_{\nu,m}\left(\frac{24.5{\rm \,GHz}}{\nu _m}\right)^{1/3}\nonumber\\ &\simeq& (1.2\pm 0.09)\, {\rm m}{\rm Jy}. \end{eqnarray} \tag{ 14 }$$

The flux at 10GeV at 17,000s after the burst should be dominated by SSC emission as discussed above. With a flux of (1.75 ± 1.48) × 10⁻⁵μJy at 10 GeV, we have ($h\nu _m^{{\rm IC}}<10\,{\rm GeV}<h\nu _c^{{\rm IC}}$)

$$\begin{eqnarray} F_\nu (10\,{\rm GeV}, t=17\,{\rm ks})&=&F_{\nu,m}^{{\rm IC}}\left(\frac{10\,{\rm GeV}}{h\nu _m^{{\rm IC}}}\right)^{-(p-1)/2}\nonumber\\ &=&(1.75\pm 1.48) \times 10^{-5}\mu {\rm Jy}. \end{eqnarray} \tag{ 15 }$$

We find that the following parameter values are consistent with the observed data: E₅₄ = 0.75, _{e, −1} = 3.2, _{B, −5} = 0.55, and n = 1.8 cm⁻³. The obtained value of _B is quite small and the obtained value of the kinetic energy implies a very large efficiency in producing gamma-rays. For these parameter values, we find that Y_c is about 12–16 in the time between 1 ks and 20 ks after the burst, and the assumption ν_m < ν_KN(γ_c) < ν_c holds in this time range. Since in our case the forward shock electrons are in the slow-cooling regime (i.e., γ_m < γ_c), Y_c roughly reflects the total luminosity ratio between the SSC component and the synchrotron component (Nakar et al. 2009). The fluence emitted by the SSC component can be estimated from the SED in Figure 2, which is roughly F ∼ 2 × 10⁻⁵ erg cm⁻², so the energy radiated in the SSC component is about 8 × 10⁵² erg. The fluence in the synchrotron component is about a factor of 10 smaller than the SSC component, consistent with the estimated value of Y_c. Thus, the total energy in the afterglow emission is about one order of magnitude lower than the inferred kinetic energy of the forward shock, which is E = 7.5 × 10⁵³ erg.

Zoom In Zoom Out Reset image size

Guided by the above parameter values, we model the multi-band SED with the synchrotron plus SSC emission model, as shown in Figure 2. For the synchrotron component, we use a series of smoothly connected power laws with two breaks at ν_m and ν_c as well as an exponential cutoff at $E_\mathrm{\rm max,\rm syn}$. For the SSC component, we use a series of smoothly connected power laws with breaks at $\nu _m^{IC}$ and $\nu _{\rm peak}^{IC}$. The results favor the SSC component producing the >10 GeV emission.

Fermi/LAT has detected long-lasting high-energy photons (>100 MeV) from about 60 GRBs as of 2014 Feb,⁴ with the highest energy photons reaching about 100 GeV. One widely discussed scenario is that this emission is the afterglow synchrotron emission produced by electrons accelerated in the forward shocks. It has been pointed out that although this scenario can explain the extended 100 MeV–GeV emission very well, it has difficulty in explaining >10 GeV photons, especially in the late afterglow, since the maximum synchrotron photon energy is limited (Piran & Nakar 2010; Barniol Duran & Kumar 2011; Sagi & Nakar 2012; Wang et al. 2013). The late >10 GeV emission could in principle be produced by the afterglow SSC emission, as indeed has been invoked to explain the late >10 GeV emission in, e.g., GRB130427A (Tam et al. 2013; Fan et al. 2013; Liu et al. 2013; Panaitescu et al. 2013) and GRB090926A (Wang et al. 2013).

In this paper, we report the analysis of Fermi/LAT observations of GRB 130907A and the detection of one 55 GeV photon compatible with the position of GRB 130907A about 5 hr after the burst. The probability that this photon is associated with GRB 130907A was found to be higher than 99.96%. At this late time, the energy of this photon exceeds the maximum synchrotron photon energy. We modeled the broadband SED of the afterglow emission and find that this high-energy photon is consistent with the SSC emission of the afterglow.