Leptonic and Hadronic Models for the Extra Components in Fermi-LAT GRBs

If the spectral excesses in GeV and keV bands have the same origin, such a wide photon-energy range may imply the cascade emission due to hadrons. If the GRB accelerated ultra-high-energy protons, synchrotron and inverse Compton (IC) emission from an electron-positron pair cascade triggered by photopion interactions of the protons with low-energy photons [9][10][11] can reproduce power-law photon spectra as seen in Fermi-LAT GRBs. Through Monte Carlo simulations, Asano et al. [12] have shown that a proton luminosity much larger than gamma-ray luminosity is required to produce the extra spectral component in GRB 090510 as L p > 10 55 erg s -1 (see Fig. 1). Namely, the efficiency of photopion production is very low. In this case, the spectrum of the GeV component is very hard with photon index ∼ -1.6, which requires a inverse Compton (IC) contribution from the secondary pairs. The prominent IC component leads to a weaker magnetic field. This entails a lower maximum energy of protons, and hence lower photopion production efficiency. Therefore, the required proton luminosity is so large in GRB 090510.

The assumed bulk Lorentz factor in Fig. 1 is 1500, and the emission radius is R = 10 14 cm. If we adopt a smaller value of Γ, the pion production efficiency would increases as t exp /t π ∝ R -1 Γ -2 . However, we should note that there is a lower limit to Γ, which is required to make the source optically thin to GeV photons. Given the photon luminosity and spectral shape, this minimum Lorentz factor can be estimated as shown in the online supporting materials in Abdo et al. (2009) [2]. In order to lower Γ, we have to increase the emission radius R. The lower limit of the Lorentz factor ∝ R 1/(β-3) does not decrease drastically (since β ≃ -3, Γ min ∝ R -1/6 ). The required large luminosity is rather favorable for the GRB-UHECR scenario, but it imposes stringent requirements on the energy budget of the central engine.

On the other hand, GRB 090902B is encouraging for the hadronic model because of its flat spectrum (photon index ∼ -2) [13]. The Band component in this burst is an atypically narrow energy distribution as shown in Fig. 2, which may imply the photospheric emission [14]. The hadronic cascade emission can well reproduce the observed flat spectra including the soft excess feature below 50 keV (model parameters: R = 10 14 cm, Γ = 1300). Owing to the flat eConf C110509 spectral shape of the extra component, no IC component is required. We can adopt a strong magnetic field, which enhance the photomeson production efficiency. In this case the flux of the extra component is relatively low compared to the Band component, which also decreases the required proton luminosity. Therefore, the necessary nonthermal proton luminosity is then not excessive and only comparable to the Band component luminosity.

As Corsi et al. [15] discussed, the GeV emission may be due to IC emission from internal dissipation regions. However, it seems difficult to explain spectral excesses in both keV and GeV bands by IC emission. Recently, we carry out time-dependent simulations of photon emissions with leptonic models [16]. In our simulations, as the photon energy density increases with time because of synchrotron emission, the SSC component gradually grows and dominate the photon field later. This late growth of the IC component has been observed also in the simulations of Bošnjak et al. (2009) [17]. The resultant lightcurves show delayed onset of GeV emission, but the delay timescale would be within the approximate timescale of the keV-MeV pulse width. However, the longer delay compared to the pulse timescale such as observed in GRB 080916C is not explained by this effect only.

As shown in Fig. 3 (model parameters: R = 6×10 15 cm, Γ = 1000, B = 100 G, E iso = 10 54 erg, ε e,min = 11.3 GeV), the model spectrum obtained from our simulations reproduce both the low and high energy exce