Particle Acceleration in Mildly Relativistic Shearing Flows: The Interplay of Systematic and Stochastic Effects, and the Origin of the Extended High-energy Emission in AGN Jets

Abstract

The origin of the extended X-ray emission in the large-scale jets of active galactic nuclei (AGNs) poses challenges to conventional models of acceleration and emission. Although the electron synchrotron radiation is considered the most feasible radiation mechanism, the formation of the continuous large-scale X-ray structure remains an open issue. As astrophysical jets are expected to exhibit some turbulence and shearing motion, we here investigate the potential of shearing flows to facilitate an extended acceleration of particles and evaluate its impact on the resultant particle distribution. Our treatment incorporates systematic shear and stochastic second-order Fermi effects. We show that for typical parameters applicable to large-scale AGN jets, stochastic second-order Fermi acceleration, which always accompanies shear particle acceleration, can play an important role in facilitating the whole process of particle energization. We study the time-dependent evolution of the resultant particle distribution in the presence of second-order Fermi acceleration, shear acceleration, and synchrotron losses using a simple Fokker-Planck approach and provide illustrations for the possible emergence of a complex (multicomponent) particle energy distribution with different spectral branches. We present examples for typical parameters applicable to large-scale AGN jets, indicating the relevance of the underlying processes for understanding the extended X-ray emission and the origin of ultrahigh-energy cosmic rays.

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

“…[4]) efficient electron acceleration typically requires the injection of energetic seed particles. The latter could, however, most likely be provided by conventional Fermi-type acceleration processes (Liu et al 2017;Rieger 2019). On the other hand, given their larger mean free path, shear acceleration of hadronic cosmic rays (CRs) is usually much easier to achieve.…”

“…To enable shear acceleration of cosmic-ray protons to energies E t in the laboratory frame, corresponding to E ′ t = E t /γ b in the comoving frame, CR particles need to satisfy (cf., Liu et al 2017;Webb et al 2019)…”