Particle Acceleration Due to Cosmic-ray Viscosity and Fluid Shear in Astrophysical Jets

Abstract

An analytical model describing the acceleration of energetic charged particles due to cosmic-ray viscosity and fluid shear in radio jets based on the diffusive transport equation for cosmic rays is developed. The model indicates that laminar shear is not a significant mechanism for particle acceleration in nonrelativistic jets but may be important in relativistic jets. The model produces a power-law momentum spectrum of particles accelerated by the shear (i.e., as , where f 0 is the isotropic phase space distribution in the scattering frame). For ultra-relativistic jets with no back-flowing cocoon, for the energetic particle diffusion coefficient case κ ∝ p α . Increasing the shear in the background flow gives harder accelerated particle momentum spectra. Monoenergetic source solutions (Green’s functions) and Green’s formula are derived and used to obtain solutions for monoenergetic particle momentum spectra specified on the edge of the jet at radius r = r 2.

An Introduction to Particle Acceleration in Shearing Flows

“…A variety of topics and applications have been discussed in the context of gradual shear acceleration [e.g., 21,22,31,33,36]. In the following three recent results are briefly mentioned:…”

“…All this suggests that a transversal velocity stratification is a generic feature of AGN-type jets. Given the challenges and complexity of observed emission properties, this has lead to a renewed interest in multi-zone/spine-shear layer acceleration and emission models [e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. One particularly interesting example concerns the emission properties of large-scale AGN jets.…”

“…This paper aims at an accessible introduction to them, reviewing some of the key findings along with some recent developments. A particular attention is given to the second one in order to recapture early ideas and developments over the years [1,28,[31][32][33]36,39,48,49,[52][53][54][55][56][57][58][59][60][61]. When viewed in context, this review shows that a variety of processes beyond conventional diffusive shock acceleration could contribute to the efficient energization of particles in jetted astrophysical sources.…”

Particle Acceleration in Shearing Flows: Efficiencies and Limits

“…When taken together, this suggests that transversal velocity stratification and shear is a generic feature of AGN-type jets. Given the diversity of observed emission properties, this has in recent times generated new interest in multi-zone or spine-shear-layer acceleration and emission models (e.g., Sahayanathan 2009;Laing & Bridle 2014;Tavecchio & Ghisellini 2015;Rieger & Duffy 2016;Liang et al 2017;Chhotray et al 2017;Liu et al 2017;Kimura et al 2018;Webb et al 2018).…”

“…When diffusive escape and radiative losses are neglected, non-relativistic gradual shear acceleration is known to lead to power-law particle spectra n(p) ∝ p 2 f (p) ∝ p −(1+α) for an energetic particle diffusion coefficient scaling as κ ∝ p α (Berezhko 1982;Rieger & Duffy 2006). With reference to an analytical steady state model based on the full particle transport equation, Webb et al (2018Webb et al ( , 2019 on the other hand recently showed that such hard power-law spectra are only achieved in relativistic shear flows, while the expected spectra become significantly softer for non-relativistic flow speeds. The present paper aims to explore and recapture this by means of a simple analysis.…”