Quasi-linear diffusion driving the synchrotron emission in active galactic nuclei

TL;DR

This paper investigates how quasi-linear diffusion influences X-ray emission in active galactic nuclei by examining electron dynamics and wave interactions near black holes and the light cylinder, revealing a balance that sustains pitch angles for synchrotron radiation.

Contribution

It demonstrates that quasi-linear diffusion can sustain pitch angles in ultra-relativistic electrons, enabling X-ray emission in AGN magnetospheres, considering wave-particle interactions and forces affecting electron motion.

Findings

QLD generates soft and hard X-rays near black hole and light cylinder scales.

Cyclotron instability excites waves that influence electron pitch angles.

A balance between forces and diffusion maintains non-zero pitch angles.

Abstract

We study the role of the quasi-linear diffusion (QLD) in producing X-ray emission by means of ultra-relativistic electrons in AGN magnetospheric flows. We examined two regions: (a) an area close to the black hole and (b) the outer magnetosphere. The synchrotron emission has been studied for ultra-relativistic electrons and was shown that the QLD generates the soft and hard X-rays, close to the black hole and on the light cylinder scales respectively. By considering the cyclotron instability, we show that despite the short synchrotron cooling timescales, the cyclotron modes excite transverse and longitudinal-transversal waves. On the other hand, it is demonstrated that the synchrotron reaction force and a force responsible for the conservation of the adiabatic invariant tend to decrease the pitch angles, whereas the diffusion, that pushes back on electrons by means of the aforementioned waves, tends to increase the pitch angles. By examining the quasi-stationary state, we investigate a regime in which these two processes are balanced and a non-vanishing value of pitch angles is created.