TY - JOUR
T1 - Diffusive Shock Acceleration
T2 - Breakdown of Spatial Diffusion and Isotropy
AU - Keshet, Uri
AU - Arad, Ofir
AU - Lyubarski, Yuri
N1 - Publisher Copyright:
© 2020. The American Astronomical Society. All rights reserved.
PY - 2020/3/10
Y1 - 2020/3/10
N2 - We point out that particles accelerated in a nonrelativistic shock of compression ratio r do not necessarily attain the standard, p = (r + 2)/(r - 1) spectral index. Previous derivations of the spectrum, based on the approximations of spatial diffusion or negligible anisotropy, are shown to rely on unjustified implicit assumptions. We prove analytically that the standard result is nevertheless valid in the limit of an isotropic medium. For an anisotropic medium, the problem generally requires a numerical treatment; the standard result remains valid as long as the anisotropy is not too strong, but p can substantially deviate from the standard result for sufficiently anisotropic scattering, even in the small-angle scattering limit. Additional spectral modifications, for example, by motions of scattering modes at intermediate optical depths from the shock, are discussed.
AB - We point out that particles accelerated in a nonrelativistic shock of compression ratio r do not necessarily attain the standard, p = (r + 2)/(r - 1) spectral index. Previous derivations of the spectrum, based on the approximations of spatial diffusion or negligible anisotropy, are shown to rely on unjustified implicit assumptions. We prove analytically that the standard result is nevertheless valid in the limit of an isotropic medium. For an anisotropic medium, the problem generally requires a numerical treatment; the standard result remains valid as long as the anisotropy is not too strong, but p can substantially deviate from the standard result for sufficiently anisotropic scattering, even in the small-angle scattering limit. Additional spectral modifications, for example, by motions of scattering modes at intermediate optical depths from the shock, are discussed.
UR - http://www.scopus.com/inward/record.url?scp=85083918051&partnerID=8YFLogxK
U2 - 10.3847/1538-4357/ab765e
DO - 10.3847/1538-4357/ab765e
M3 - Article
AN - SCOPUS:85083918051
SN - 0004-637X
VL - 891
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 2
M1 - 117
ER -