Synchrotron self-Compton emission from afterglow shocks as the origin of the sub-TeV emission in GRB 180720B and GRB 190114C
Recently, very high-energy photons above 100 GeV were reported to be detected from GRB 190114C and GRB 180720B at, respectively, 100-1000 s and 10 hr after the burst. We model the available broad-band data of both GRBs with the synchrotron plus synchrotron self-Compton (SSC) emission of the afterglow shocks. We find that the sub-TeV emission of of GRB 180720B can be interpreted as the SSC emission for a constant density circum-burst medium. The SSC emission of GRB 190114C dominates over the synchrotron component from GeV energies at s, which can explain the possible hard spectrum of the GeV emission at this time. The extrapolated flux of this SSC component to sub-TeV energies can explain the high-significance detection of GRB 190114C by the MAGIC telescope. The parameter values (such as the circum-burst density and shock microphysical parameters) in the modeling are not unusual for both GRBs, implying that the detection of sub-TeV photons from these two bursts should be attributed to their large burst energies and low redshifts.
Subject headings:gamma-rays: bursts
Very high-energy (VHE) photons probe the most energetic particles accelerated in GRBs, so they are crucial to study the particle acceleration and radiation physics in GRBs. Intense efforts have been made to detect VHE gamma-rays ( GeV) from gamma-ray bursts (e.g., Aliu et al. 2014; Abramowski et al. 2014; Abeysekara et al. 2015), but it was only until recently that such VHE photons are detected from GRB 190114C and GRB 180720B (Mirzoyan 2019; Ruiz-Velasco 2019). MAGIC slew to the direction of GRB 190114C about 50 s after the trigger and detected GeV photons for the first 20 minutes from this burst with a significance higher than (Mirzoyan 2019). HESS starts to observe GRB 180720B at about 10 hr after the burst and detected GeV photons at such late times (Ruiz-Velasco 2019). Both GRBs have a relatively low redshift, with and for GRB 190114C and GRB 180720B respectively (Selsing et al. 2019; Vreeswijk et al. 2019) . They are also bright bursts with the isotropic energy of and respectively (Hamburg et al. 2019; Frederiks et al. 2018).
It has been argued that high-energy photons above 100 MeV detected by Fermi Large Area Telescope (LAT) are produced by synchrotron radiation in the afterglow shocks (Kumar & Barniol Duran 2009; Ghisellini et al. 2010; Wang et al. 2010). However, the synchrotron emission has a maximum energy of , where is the bulk Lorentz factor of the emitting region, so it is hard to explain GeV photons detected at s where the shock has been decelerated, i.e., (Piran & Nakar 2010). It was argued that these GeV photons should be produced by SSC emission in the afterglow shocks (Wang et al. 2013). Recent detections of sub-TeV emission from from GRB 190114C and GRB 180720B strengthen the difficulty for synchrotron radiation model. One may naturally think about the inverse-Compton (IC) mechanism for such sub-TeV photons. Indeed, afterglow SSC emission has long predicted to be able to produce high-energy photons (e.g., Zhang & Mészáros 2001; Sari & Esin 2001). Another interesting question is whether the sub-TeV emissions at quite different times have a common origin. In this paper, we will study whether the SSC mechanism can explain the sub-TeV emission. In §2, we first derive the light curves of SSC emission and compare them with the sub-TeV data GRB 180720B. In §3, we study whether the absorption and Klein-Nishina suppression affect the sub-TeV emission. In §4, we model the observed light curves and spectral energy distribution (SED) and of the available multi-band data for both GRBs. Finally we give discussions and conclusions in §5.
2. The light curve of the SSC emission
The temporal decay slope of SSC emission depends on the density profile of the circum-burst medium. We first derive the slope and then compare it with the available data of sub-TeV emission. As an rough approximation, the afterglow SSC spectrum can be described by broken power-laws with two break frequencies at and and a peak flux at , generally resembling the spectrum of the synchrotron emission (Sari & Esin 2001). For a wind medium of , we have , , and , where is the optical depth of the inverse-Compton (IC) scattering, which scales as . The frequency of VHE observations should be above from very early time. Thus, for the wind environment, for and for . So the flux decays very quickly in both cases111Note that the KN effect does not affect the spectrum below . Above , the spectrum may become softer due to the KN effect, then the temporal decay may becomes even faster.. The energy flux of GRB 180720B observed by HESS at 10 hr is about (100–440 GeV). To be conservative, assuming a decay slope of , the flux extrapolated to s would be nearly , which is unreasonably high. Thus, the wind environment scenario for GRB 180720B is disfavored.
On the other hand, for a constant density ISM environment, , , and . As , we get . Thus, for the ISM environment, for and for . For , the decay slope is in the range to . Such a slope is acceptable for GRB 180720B. In the following part of the paper, we will assume a constant-density interstellar medium (ISM) for the circum-burst environment.
3. The absorption and KN suppression
Sub-TeV photons of energy will suffer from pair-production absorption by interacting with target photons with energy . For a bulk Lorentz factor of at s, the energy of target photons will be 0.1-10 keV. So the X-ray afterglows cause the main absorption to sub-TeV photons. The opacity of sub-TeV photons is given by , where the number of target photons is given by . Requiring and using , we get
As and , we get
As the X-ray afterglows of GRBs typically have , the constraint on the circum-burst density is insensitive to the observation time.
As the sub-TeV photons are produced by IC process, these photons may also suffer from Klein-Nishina (KN) scattering suppression. The SSC energy output is dominated by and electrons, respectively, in the fast and slow cooling regime. Here and are, respectively, the injection break and cooling break in the electron distribution spectrum. As pointed out by Nakar et al. (2009), the first KN break at is very mild and a clear steepening in the spectrum is expected to be observed at , where .
VHE photons of GRB 180720B are detected at hr. At such a late time, we expect . Then the KN-induced break is expectedly at
where is Compton parameter for electrons with energy . Requiring for GRB 180720B, we obtain
Thus a low magnetic field equipartition factor is inferred for GRB 180720B. Note that the energy of the KN-induced break decreases rather slowly with time (), which is helpful for late-time detection of VHE photons from GRBs.
For GRB 190114C, at s, both and are, in principle, possible. If , the above constraint is applicable. If , we have
where and is the fraction of shock internal energy transferred to accelerated electrons. Requiring for GRB 190114C, we have
This constraint can be satisfied for sub-TeV photons detected at early times, such as those in GRB 190114C. However, for sub-TeV photons detected at late times, such as those detected at in GRB 180720B, this constraint is hardly satisfied.
4. Modeling of the multi-wavelength data
As pointed out by Ruiz-Velasco (2019), there is one striking similarity between GRB 190114C and GRB 180720B, i.e., both GRBs have very high X-ray afterglow flux. This may indicate that X-ray photons serve as the synchrotron target photons for IC scatterings. The sub-TeV emission in GRB 180720B has the same level of flux as that of X-rays, indicating that the Compton parameter is close to unity. We perform a modeling of the available multi-wavelength data for GRB 180720B and GRB 190114C. The modeling is based on the numerical code that has been applied to GRB 130427A (Liu et al. 2013). In this code, a strict inverse-Compton scattering cross section has been used. The KN effect may also affect the electron distribution (Nakar et al. 2009, Wang et al. 2010) and we have calculated the electron distribution self-consistently.
GRB 180720B: The fits to the light curve and spectral energy distribution (SED) of the afterglow of GRB 180720B are shown in Figure 1. The synchrotron and SSC components are denoted by dotted and dashed curves respectively. The break at the highest energy part of the SED corresponds to the the energy of electrons (i.e., in the observer frame), whose value is given by Eq. 3. It can also be seen that KN suppression starts earlier than this break, softening the spectrum from a photon index of to about . Another feature is the transition from the synchrotron component to the SSC component at about 1 GeV, above which a moderate spectral hardening is visible. However, since the GeV flux of GRB 180720B is below the sensitivity of Fermi/LAT at 10 hrs, this transition can not be identified in the data.
GRB 190014C: The fits to the light curve and SED of the afterglow of GRB 190114CB are shown in Figure 2. The optical flux of the first data point exceeds the model flux and it should be produced by the reverse shock emission (Laskar et al. 2019). The X-ray flux at also exceeds the model flux and the excess flux could be attributed to the reverse shock emission as well (Laskar et al. 2019). The X-ray flux at day is below the model flux, which is likely due to the presence of a jet break, as has been commonly seen in bright GRBs. The late-time excess of the optical emission is not well-understood, and we speculate that density-jump encountered by the shock might cause such a brightening. In the LAT band, the model flux can explain the flux after 50 s, and the early GeV emission should be attributed to the prompt emission or reverse shock emission (Fraija et al. 2019). The plot of the SED around s shows the transition from the synchrotron component to the SSC component. Interestingly, the SSC component already contributes dominantly to the flux at energies above GeV. There is a signature of a hard spectrum for the GeV emission with a photon index of , which is consistent with the SSC origin. The sub-TeV flux expected from this SED fitting is comparable to the GeV flux, which can explain the detection by MAGIC (Mirzoyan 2019).
5. Discussions and Conclusions
It is useful to obtain the transition energy from the synchrotron component to the SSC component, as this transition energy could be identified if observation energy coverage is sufficiently wide. This is also the critical frequency above which spectrum hardens. Assuming the transition energy is above , the transition frequency can be obtained by
Then we obtain
For , we obtain
The transition energy is sensitive to the microphysical parameters, and , and also the ISM density. For some parameter space, the transition energy could locate in Fermi/LAT energy. In this case, one will see a hard GeV spectrum in the LAT energy range, contributed mainly by the SSC emission. Interestingly, the possible hard spectrum of GeV emission in GRB 190114C around s could be such an example. There is also tentative evidence for the presence of a hard spectral component in the GeV afterglow of GRB 130427 from 100 s up to one day after the burst (Tam et al. 2013), which has been interpreted as arising from the SSC emission (Liu et al. 2013).
The two bursts that have sub-TeV photons share some common features: 1) both have low redshifts, which is useful to avoid the EBL absorption; 2) both are strong bursts with high fluence; 3) the circum-burst media are likely to be uniform ISM, rather than wind-like media. These properties may explain the rare detection of VHE photons so far. On the other hand, the detection of high-significance sub-TeV emission at 100–1000 s from GRB 190114C and the late-time detection (at 10 hr) from GRB 180720B are inspiring for ground-based VHE observations. These detections demonstrate that the IC component of the afterglow emission is as strong as the synchrotron component. The detection at late time also implies that the KN suppression and absorption to VHE emission does not increase with time. This is important for long-term VHE observations of GRBs.
Long-term observations can give us information about the spectral evolution and light curves of VHE afterglow. As pointed out in §2, the temporal decay slope of VHE emission is useful to diagnose the environment of the circum-burst medium. Although the light curves of afterglow synchrotron emission are also different for the wind-like medium and ISM-like medium, the difference in the decay slopes between the two cases is at most (Chevalier & Li 1999), which makes it hard to identify the type of the circum-burst medium sometimes. On the other hand, the difference in the decay slope of the SSC emission between the two media is large, which is for the case of and for the case of . Thus, measurements of the light curves of the VHE emission of GRBs would be able to distinguish between the two types of circum-burst more clearly.
X.Y.W. is supported by the National Key R & D program of China under the grant 2018YFA0404203 and the NSFC grants 11625312 and 11851304. .
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