Electron transport with re-acceleration and radiation in the jets of X-ray binaries

Abstract

This paper studies acceleration processes of background thermal electrons in X-ray binary jets via turbulent stochastic interactions and shock collisions. By considering turbulent magnetized jets mixed with fluctuation magnetic fields and ordered, large-scale one, and numerically solving the transport equation along the jet axis, we explore the influence of such as magnetic turbulence, electron injections, location of an acceleration region, and various cooling rates on acceleration efficiency. The results show that (1) the existence of the dominant turbulent magnetic fields in the jets is necessary to accelerate background thermal electrons to relativistic energies. (2) Acceleration rates of electrons depend on magnetohydrodynamic turbulence types, from which the turbulence type with a hard slope can accelerate electrons more effectively. (3) An effective acceleration region should be located at the distance $>10^3R_{\rm g}$ away from the central black hole ($R_{\rm g}$ being a gravitational radius). As a result of acceleration rates competing with various cooling rates, background thermal electrons obtain not only an increase in their energies but also their spectra are broadened beyond the given initial distribution to form a thermal-like distribution. (4) The acceleration mechanisms explored in this work can reasonably provide the electron maximum energy required for interpreting high-energy $\gamma$-ray observations from microquasars, but it needs to adopt some extreme parameters in order to predict a possible very high-energy $\gamma$-ray signal.