Simulation of high energy emission from gamma-ray bursts

Gamma-Ray Bursts (GRBs) are the must violent explosions after the Big-Bang. Their high energy radiation can potentially carry information about the most inner part of the accretion disk of a collapsing star, ionize the surrounding material in the host galaxy and thereby influence the process of star formation specially in the dense environment at high redshifts. They can also have a significant contribution in the formation of high energy cosmic-rays. Here we present new simulations of GRBs according to a dynamically consistent relativistic shock model for the prompt emission, with or without the presence of an magnetic field. They show that the properties of observed bursts are well reproduced by this model up to GeV energies. They help to better understand GRB phenomenon, and provide an insight into characteristics of relativistic jets and particle acceleration which cannot yet be simulated with enough precision from first principles.

💡 Research Summary

The paper presents a comprehensive numerical study of the high‑energy (up to GeV) prompt emission from gamma‑ray bursts (GRBs) using a dynamically consistent relativistic shock framework. Recognizing the shortcomings of traditional fireball, internal‑shock, and magnetized‑flow models—such as their inability to reproduce the fast‑rise‑exponential‑decay (FRED) light‑curve shape, the low‑energy spectral index problem (α≈−4/3), and the limited efficiency of synchrotron self‑Compton (SSC) processes—the authors construct a more flexible model that incorporates several key physical ingredients.

First, the collision distance between shells is set to a relatively short range (10¹⁰–10¹² cm) rather than the canonical 10¹⁴ cm, allowing variability on millisecond timescales, consistent with the fastest observed GRB fluctuations. Second, the electron energy distribution is not a pure power‑law; instead it follows a broken power‑law with an exponential cutoff, Nₑ(γₑ)∝γₑ^{−(p+1)} exp(−γₑ/γ_cut), a form motivated by recent particle‑in‑cell (PIC) simulations of relativistic shocks. Third, the authors introduce an “active region” – a thin radiating shell whose thickness Δr′ evolves with radius according to phenomenological prescriptions (steady‑state, exponential, or dynamically coupled to the shock parameters) rather than being fixed.

The dynamical evolution of the system is governed by energy and momentum conservation equations (Eqs. 1–2) written in the rest frame of the slower shell. These equations couple the Lorentz factor γ′, the bulk velocity β′, the baryon density n′, and the emitted synchrotron/SSC power E′_sy. Because β′(r′) lacks an analytical solution, the authors employ an iterative numerical scheme. Two dimensionless coupling parameters, A (internal magnetic field) and A₁ (external, precessing magnetic field), encapsulate the strength of synchrotron and SSC processes, while allowing the fractions of kinetic energy transferred to electrons (ε_e) and magnetic fields (ε_B) to vary with time.

Radiation is calculated by integrating the standard synchrotron emissivity over the electron distribution and over the relativistically beamed solid angle (≈1/2Γ). The resulting flux expression (Eq. 6) includes a dominant term and sub‑dominant corrections F(ω,r), which are shown to be negligible for the parameter space explored. The model also accounts for the phase shift between electric and magnetic components of the electromagnetic energy structure (EES) at the shock front, a feature that enhances SSC scattering and is essential for reproducing the delayed high‑energy tail observed in many GRBs.

Simulation results demonstrate that the model can reproduce several salient observational features: (i) a non‑thermal Band‑like spectrum extending to >100 GeV, (ii) a delayed high‑energy component that appears tens of seconds after the low‑energy peak, (iii) rapid variability on sub‑millisecond scales, and (iv) generally smooth light curves with only weak or absent coherent oscillations, even when an external magnetic field is included. When the external field is strong and its precession period is long, modest oscillatory signatures appear, but these are typically below detection thresholds, consistent with the rarity of such features in real GRB data.

In summary, by allowing (a) a short, dynamically evolving collision radius, (b) a realistic electron spectrum with exponential cutoff, (c) time‑dependent ε_e and ε_B, and (d) the inclusion of an external precessing magnetic field, the authors resolve many of the long‑standing tensions of SSC‑based GRB models. Their semi‑analytic yet numerically tractable approach provides a valuable tool for interpreting current Fermi‑LAT observations and for guiding future high‑energy gamma‑ray missions.