Constraining the shear acceleration model for the X-ray emission of large-scale extragalactic jets

TL;DR

This paper investigates a shear acceleration model for X-ray emission in large-scale extragalactic jets, constraining the magnetic field and turbulence spectrum to explain observations without exceeding jet power limits.

Contribution

It applies a shear acceleration scenario with a Fokker-Planck approach to specific jets, constraining magnetic fields and turbulence spectra to match observed emissions.

Findings

Magnetic field above 10 μG is required for the model.

Kolmogorov turbulence spectrum allows acceleration faster than cooling.

Bohm-like turbulence spectrum cannot satisfy acceleration conditions.

Abstract

The nature of the intense X-ray emission from powerful extragalactic jets at large ($>1$ kpc) scale is still debated. The scenario that invokes the inverse Compton scattering of the CMB by electrons is challenged by the lack of gamma-ray emission in the GeV band. An alternative assumes synchrotron emission by a distinct population of ultra-high energy electrons. Here we present a concrete attempt to apply this scenario, exploring the specific model in which the ultra-high energy electrons are accelerated in a shear layer surrounding the jet. We limit the study to non-relativistic flows and particle acceleration is treated by a Fokker-Planck equation. The observed relation between low energy (radio, optical) and X-ray emission prompts us to assume that the required population of pre-accelerated particles is provided by a shock responsible for the acceleration of the electrons emitting at low frequencies. We apply the model to the emission of the principal knots of the jets of PKS 0637-752 and PKS 1136-135, two of the best studied objects. For the set of fiducial parameters adopted, the condition that the jet power does not exceeds a limiting value of $10^{48}$ erg s$^{-1}$ constrains the magnetic field above $10$ $\mu$G and indicates moderate beaming ($\delta\simeq 2$) for PKS 0637-752. For both sources, the requirement that acceleration of the electrons proceeds faster than radiative cooling can be met if the magnetic turbulence in the shear layer follows a Kolmogorov spectrum, $I(k)\propto k^{-q}$ with $q=5/3$, but cannot satisfied in the Bohm-like case ($q=1$).