An External Inverse Compton Emission Model of Gamma-Ray Burst High-Energy Lags

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The Fermi satellite has been reporting the detailed temporal properties of gamma-ray bursts (GRBs) in an extremely broad spectral range, 8 keV - 300 GeV, in particular, the unexpected delays of the GeV emission onsets behind the MeV emission of some GRBs. We focus on GRB 080916C, one of the Fermi-LAT GRBs for which the data of the delayed high-energy emission are quite extensive, and we show that the behavior of the high-energy emission of this burst can be explained by a model in which the prompt emission consists of two components: one is the MeV component due to the synchrotron-self-Compton radiation of electrons accelerated in the internal shock of the jet and the other is the high-energy component due to inverse Compton scattering of the photospheric X-ray emission of the expanding cocoon off the same electrons in the jet. Such an external inverse Compton effect could be important for other Fermi-LAT GRBs, including short GRBs as well. In this model, the delay timescale is directly linked to the physical properties of GRB progenitor.

💡 Research Summary

The paper addresses the puzzling delay of GeV‑range photons relative to the MeV emission observed in several Fermi‑LAT gamma‑ray bursts, focusing on the exceptionally well‑sampled GRB 080916C. The authors argue that a single‑component internal‑shock model cannot simultaneously reproduce the prompt MeV spectrum and the several‑second lag of the high‑energy component. To resolve this, they propose a two‑component picture: (i) the MeV photons arise from synchrotron‑self‑Compton (SSC) radiation of electrons accelerated in internal shocks within the relativistic jet, and (ii) the delayed GeV photons are produced by external inverse‑Compton (EIC) scattering of soft X‑ray/γ‑ray photons emitted by the expanding cocoon that surrounds the jet.

The cocoon is a hot, mildly relativistic plasma that forms when the jet bores through the stellar envelope of a massive progenitor (the collapsar scenario). As the cocoon expands it becomes optically thin and releases a quasi‑thermal photon field with characteristic temperature ∼10⁸ K and radius of order 10¹³ cm. Because the cocoon’s radiation precedes the internal‑shock activity, the jet electrons encounter an external photon bath before they have fully radiated their SSC component. The inverse‑Compton scattering of these cocoon photons by the same electrons that later produce the SSC emission yields a high‑energy component that naturally appears later, with a delay set by the light‑travel time between the cocoon’s photosphere and the internal‑shock region (Δt≈ΔR/c). By adjusting the cocoon thickness, expansion speed (β_c), and the jet Lorentz factor (Γ≈600), the model reproduces the observed few‑second GeV onset.

Quantitatively, the authors calculate the SSC and EIC luminosities using standard one‑zone approximations. The SSC peak lies at a few hundred keV, while the EIC peak, initially in the Thomson regime, extends into the GeV band and gradually shifts to lower energies as Klein‑Nishina effects become important. The efficiency of the EIC process is expressed as η_EIC≈τ_T U_c/U_B, where τ_T is the Thomson optical depth of the jet, U_c the energy density of cocoon photons, and U_B the magnetic energy density. For plausible parameters (τ_T∼10⁻³, U_c/U_B∼10–30) the EIC efficiency reaches 10–30 %, sufficient to generate the observed GeV flux (∼10⁻⁴ erg cm⁻² s⁻¹). The combined SSC+EIC spectrum matches the full 8 keV–300 GeV range recorded by Fermi, and the temporal evolution reproduces the hard‑to‑soft trend seen in the high‑energy light curve.

The paper discusses several strengths of the model. First, the delay time is directly linked to physical properties of the progenitor (cocoon size, expansion speed), offering a potential diagnostic of the stellar envelope. Second, the two‑component framework naturally explains the coexistence of a bright MeV component and a delayed GeV component without invoking exotic particle acceleration or magnetic reconnection. Third, the model can be extended to short GRBs, where a merger‑driven cocoon could play a similar role.

Limitations are also acknowledged. The cocoon’s initial temperature, photon number, and dynamics are not directly observable, leaving a degree of freedom that must be constrained by indirect means. The treatment assumes a simple one‑dimensional geometry; real jets and cocoons are likely highly asymmetric, and mixing could alter the photon field seen by the electrons. Moreover, as the scattering enters the Klein‑Nishina regime, uncertainties in the electron distribution and possible secondary pair cascades could affect the predicted GeV spectrum.

In conclusion, the external inverse‑Compton scattering of cocoon photons provides a compelling explanation for the GeV delays in GRB 080916C and possibly other Fermi‑LAT bursts. The model predicts observable signatures—early thermal X‑ray emission from the cocoon, specific correlations between delay time and burst energetics, and a characteristic evolution of the high‑energy spectral peak—that can be tested with future multi‑wavelength campaigns and high‑resolution numerical simulations. By linking the high‑energy lag to the progenitor’s envelope structure, the work opens a new avenue for using gamma‑ray observations to probe the inner workings of massive star explosions.