Non-thermal Gamma-ray Emission from Delayed Pair Breakdown in a Magnetized and Photon-rich Outflow

TL;DR

This paper models delayed gamma-ray emission in magnetized outflows from gamma-ray bursts, showing how pair breakdown and relativistic effects produce spectra consistent with observations, highlighting the importance of turbulence and anisotropy.

Contribution

It introduces a self-consistent kinetic model of pair and photon evolution in magnetized outflows, emphasizing the role of turbulence and anisotropy in GRB spectra.

Findings

High-energy power-law spectra consistent with GRB observations

Saturation of scattering depth at $ au_T \,\sim\,1-4$

Contrast with continuous heating models showing inconsistent spectral evolution

Abstract

We consider delayed, volumetric heating in a magnetized outflow that has broken out of a confining medium and expanded to a high Lorentz factor ($\Gamma \sim 10^2-10^3$) and low optical depth to scattering ($\tau_{\rm T} \sim 10^{-3}-10^{-2}$). The energy flux at breakout is dominated by the magnetic field, with a modest contribution from quasi-thermal gamma rays whose spectrum was calculated in Paper I. We focus on the case of extreme baryon depletion in the magnetized material, but allow for a separate baryonic component that is entrained from a confining medium. Dissipation is driven by relativistic motion between these two components, which develops once the photon compactness drops below $ 4\times 10^3(Y_e/0.5)^{-1}$. We first calculate the acceleration of the magnetized component following breakout, showing that embedded MHD turbulence provides significant inertia, the neglect of which leads to unrealistically high estimates of flow Lorentz factor. After re-heating begins, the pair and photon distributions are evolved self-consistently using a one-zone kinetic code that incorporates an exact treatment of Compton scattering, pair production and annihilation, and Coulomb scattering. Heating leads to a surge in pair creation, and the scattering depth saturates at $\tau_{\rm T} \sim$ 1-4. The plasma maintains a very low ratio of particle to magnetic pressure, and can support strong anisotropy in the charged particle distribution, with cooling dominated by Compton scattering. High-energy power-law spectra with photon indices in the range observed in GRBs ($-3 < \beta < -3/2$) are obtained by varying the ratio of heat input to the seed energy in quasi-thermal photons. We contrast our results with those for continuous heating across an expanding photosphere, and show that the latter model produces soft-hard evolution that is inconsistent with observations of GRBs.