The terminal bulk Lorentz factor of relativistic electron-positron jets

Abstract

We present a numerical simulation of the bulk Lorentz factor of a relativistic electron-positron jet driven by the Compton rocket effect from accretion disc radiation. The plasma is assumed to have a power-law distribution ne(γ) ∝ γ−s with 1 < γ < γmax and is continuously reheated to compensate for radiation losses. We include the full Klein-Nishina (hereafter KN) cross-section, and study the role of the energy upper cut-off γmax, spectral index s and source compactness. We determine the terminal bulk Lorentz factor in the cases of supermassive black holes, relevant to AGN, and stellar black holes, relevant to galactic microquasars. In the latter case, Klein-Nishina cross-section effects are more important and induce a terminal bulk Lorentz factor smaller than in the former case. Our result are in good agreement with bulk Lorentz factors observed in Galactic (GRS 1915+105, GRO J1655-40) and extragalactic sources. Differences in scattered radiation and acceleration mechanism efficiency in the AGN environment can be responsible for the variety of relativistic motion in those objects. We also take into account the influence of the size of the accretion disc; if the external radius is small enough, the bulk Lorentz factor can be as high as 60.