Particle acceleration in shearing flows: the case for large-scale jets

Abstract

X-ray observations of kilo-parsec scale jets indicate that a synchrotron origin of the sustained non-thermal emission is likely. This requires distributed acceleration of electrons up to near PeV energies along the jet. The underlying acceleration mechanism is still unclear. Shear acceleration is a promising candidate, as velocity-shear stratification is a natural consequence of the collimated flow of a jet. We study the details of shear acceleration by solving the steady-state Fokker-Planck-type equation and provide a simple general solution for trans-relativistic jets for a range of magnetohydrodynamic turbulent power-law spectra. In general, the accelerated particle population is a power-law spectrum with an exponential-like cut-off, where the power-law index is determined by the turbulence spectrum and the balance of escape and acceleration of particles. Adopting a simple linearly decreasing velocity profile in the boundary of large-scale jets, we find that the multi-wavelength spectral energy distribution of X-ray jets, such as Centaurus A and 3C 273, can be reproduced with electrons that are accelerated up to ∼ PeV. In kpc-scale jets, protons may be accelerated up to ∼ EeV, supporting the hypothesis that large-scale jets are strong candidates for ultra-high-energy-cosmic-ray sources within the framework of shear acceleration.

Particle Acceleration in Relativistic Shearing Flows: Energy Spectrum

“…The treatment presented here does not include radiative losses (e.g., synchrotron). The latter could lead to a pileup in the particle distribution at the momentum scale where acceleration balances losses (e.g., Tavecchio 2021; Wang et al 2021). Taking this constraint into account, our present findings are providing a useful guide to cosmic-ray or electron shear acceleration over the energy regime for which radiative losses might be neglected.…”

“…In AGNs, for example, lateral shearing could be intrinsically (jet−wind topology) or extrinsically (interaction with the environment, matter entrainment) induced. The growing realization that such shear flows can be conducive to efficient Fermi-type particle acceleration (e.g., Lemoine 2019;Rieger 2019) has in recent times motivated a variety of studies exploring its role for the production of high-energy particles and emission (e.g., Webb et al 2018Webb et al , 2019Webb et al , 2020Rieger 2019;Rieger & Duffy 2019, 2021Merten et al 2021;Tavecchio 2021;Wang et al 2021). Early models of particle transport in shearing flows implied that in the absence of radiative losses the accelerated particle (momentum) distribution in steady state follows a powerlaw spectrum, f (p) ∝ p − s , with spectral index s = (3 + α) for a mean scattering time scaling as τ ∝ p α (Berezhko & Krymskii 1981;Berezhko 1982;Rieger & Duffy 2006).…”

Active Galactic Nuclei as Potential Sources of Ultra-High Energy Cosmic Rays

“…Given the short synchrotron cooling timescale t cool ∝ 1/γ e and cooling length, ct acc 1 kpc, of these electrons, the operation of a distributed acceleration mechanism is required to keep electrons energized and to account for the extended emission. Stochastic (2nd order Fermi) and shear particle acceleration are among the most promising acceleration mechanisms in this regard [123][124][125][126], cf. Figure 10.…”

“…Insights from multi-wavelength SED modelling, for example, can be used to constrain key physical parameters of the jet (e.g., magnetic field strength, flow speed), e.g. [126], and thereby inform our understanding.…”

The Kelvin-Helmholtz instability at the boundary of relativistic magnetized jets

“…In jet boundaries with flow-aligned magnetic fields, KH vortices can wrap up the field lines onto themselves, leading to particle acceleration via reconnection [19]. Particles pre-energized by reconnection [e.g., [20][21][22] can then experience sheardriven acceleration [23,24] -i.e., particles scatter in between regions that move toward each other because of the velocity shear, akin to the Fermi process in converging flows [25]. The KHI may then constitute a fundamental building block for our understanding of the origin of radio-emitting electrons in limb-brightened relativistic jets (e.g., in Cygnus A [26] and M87 [27]), and for the prospects of shear-driven acceleration at jet boundaries in generating Ultra High Energy Cosmic Rays.…”