Adiabatic Losses and Stochastic Particle Acceleration in Gamma‐Ray Burst Blast Waves

Abstract

We treat the problem of adiabatic losses and stochastic particle acceleration in gamma-ray burst (GRB) blast waves that decelerate by sweeping up matter from an external medium. The shocked fluid is assumed to be represented by a homogeneous expanding shell. The energy lost by nonthermal particles through adiabatic expansion is converted to the bulk kinetic energy of the outflow, permitting the evolution of the bulk Lorentz factor Γ of the blast wave to be selfconsistently calculated. The behavior of the system is shown to reproduce the hydrodynamic self-similar solutions in the relativistic and nonrelativistic limits, and the formalism is applicable to scenarios that are intermediate between the adiabatic and fully radiative regimes.Nonthermal particle energization through stochastic gyroresonant acceleration with magnetic turbulence in the blast wave is treated by employing energy-gain rates and diffusive escape timescales based upon expressions derived in the quasilinear regime. If the magnetic field in the shocked fluid approaches its equipartition value, this process can accelerate escaping particles to 10 20 eV energies, consistent with the hypothesis that ultra-high energy cosmic rays (UHECRs) are accelerated by GRB blast waves. Due to particle trapping by the magnetic turbulence, only the highest energy particles can escape during the prompt and afterglow phases of a GRB for acceleration by a Kolmogorov spectrum of MHD turbulence. Lower energy particles begin to escape as the blast wave becomes nonrelativistic and shock Fermi acceleration becomes more important.

Neutrino, Neutron, and Cosmic‐Ray Production in the External Shock Model of Gamma‐Ray Bursts

“…Thus, for example, the timescales of the highest energy protons shown in Figures 1a and 1b derive from this limit. Other effects that limit maximum particle energy through second-order Fermi acceleration in a GRB blast wave, such as available time and the requirement that the Larmor radius of the accelerated particle be less than the blast-wave width, are considered elsewhere (Dermer & Humi 2001).…”

“…If nonthermal power-law distributions of particles are accelerated in the blast wave, as expected in simple treatments of Fermi acceleration, then hard spectra with a nonthermal particle injection index pd2 place a large fraction of the nonthermal energy in the form of the highest energy particles. A large fraction of the blastwave energy can be dissipated as UHECRs even if pe2 if particle acceleration is sufficiently rapid that particles reach ultrahigh energies and diffusively escape on the deceleration timescale (Dermer & Humi 2001 Only the photomeson process is considered in detail in this paper; photopair and secondary production losses involving nucleon-nucleon collisions can be shown to be much less important in comparison to photomeson losses for ultrahigh-energy particles in the blast-wave environment. The two dominant channels of photomeson production for proton-photon (p þ ) interactions are p þ !…”

“…Rachen & Mésázaros (1998a) define limits on various acceleration scenarios that give large values of 0 max . Particle spectra from gyroresonant acceleration due to pitch-angle scatterings and stochastic energy diffusion in particle interactions with plasma waves can give 0 max e10 10 and can produce nonthermal spectra with pe1, although the exact value depends on the spectrum of the turbulence (Schlickeiser & Dermer 2000;Dermer & Humi 2001).…”

“…Following the first shock crossing, the blast wave intercepts the particle before its angular deflection from the shock normal is much larger than 1/C; thus, subsequent cycles lead to energy increases by only factors of $2. Second-order Fermi acceleration, for example, due to magnetohydrodynamic turbulence generated by charged dust or irregularities in the external medium (Waxman 1995;Schlickeiser & Dermer 2000;Dermer & Humi 2001) or by first-order Fermi acceleration involving putative shocks in a relativistic wind (Waxman 1995) could, however, accelerate UHECRs in GRB blast waves.…”

High-energy cosmic rays from γ-ray bursts

“…Poor fits are found if GRBs inject soft CR spectra with p > ∼ 2. However, if GRBs inject hard spectra with p ≈ 1, for example, through a second-order relativistic shock-Fermi process (21) or through the converter mechanism (22), then the highest-energy AGASA data can be fit, though the reduced χ 2 of our best fits are not compelling. Because the injection spectrum is so hard, most of the produced high-energy neutrinos are too energetic and the flux too weak to be detected with IceCube, though other telescope arrays, such as the Extreme Universe Space Observatory (EUSO), could be sensitive to these GZK neutrinos.…”