The terminal bulk Lorentz factor of relativistic electron-positron jets

We present numerical simulation of bulk Lorentz factor of relativistic electron-positron jet driven by Compton rocket effect from accretion disc radiation. The plasma is assumed to have a power-law distribution $n_{e}(\gamma) \propto \gamma^{-s}$ whith $1 < \gamma< \gamma_{max}$ and is continuously reheated to compensate for radiation losses. We include full Klein-Nishina (hereafter KN) cross section, and study the role of energy upper cut-off $\gamma_{max}$, spectral index $s$, and source compactness. We determine terminal bulk Lorentz factor in the case of supermassive black holes relevant to AGN and stellar black holes relevant to galactic microquasars. In the latter case, Klein-Nishina cross section effect are more important, and induce terminal bulk Lorentz factor smaller than in the former case. Our result are in good agreement with bulk Lorentz factors observed in galactic sources (GRS1915+105, GROJ1655-40) and extragalactic ones. Differences in scattered radiation and acceleration mechanism efficiency in 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.