TY - JOUR

T1 - Diffusive acceleration in relativistic shocks

T2 - Particle feedback

AU - Nagar, Yotam

AU - Keshet, Uri

N1 - Publisher Copyright:
© 2020 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function D, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional D that depends on f. A local D(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when D is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless D is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when D(f) rises sufficiently fast, may be realized in ab initio simulations.

AB - The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function D, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional D that depends on f. A local D(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when D is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless D is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when D(f) rises sufficiently fast, may be realized in ab initio simulations.

KW - acceleration of particles

KW - gamma-ray burst: General

KW - magnetic fields

KW - shock waves

UR - http://www.scopus.com/inward/record.url?scp=85100338573&partnerID=8YFLogxK

U2 - 10.1093/mnras/staa3596

DO - 10.1093/mnras/staa3596

M3 - Article

AN - SCOPUS:85100338573

VL - 501

SP - 329

EP - 336

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 1

ER -