Terminal Speed of On-Axis Jets from a Supercritical Accretion Disk

Abstract

For on-axis jets from a luminous supercritical accretion disk, we examine equilibrium speeds without gravity and terminal speeds with gravity, taking account of radiative flux as well as radiation drag. We assume a self-similar model for the supercritical disk. The equilibrium speed approaches the speed of light far from the disk, since the luminous region is centrally condensed. The terminal speed, on the other hand, is generally less than the speed of light due to the existence of gravity. In addition, it uniquely depends on the accretion rate, since the terminal speed depends on the size, shape, and luminosity of the disk, which are uniquely determined by the accretion rate. We found a fitting formula for the terminal speed ($v_\infty$) at infinity, as a function of the accretion rate or disk luminosity in the case of electron–proton normal plasmas. The first one is $v_\infty/c \sim 1-\pi / \sqrt{\dot{m}}$, where $\dot{m}$ is the normalized accretion rate. The other is $\gamma_\infty \sim 1 + 0.223 \Gamma$, where $\gamma_\infty = 1 / \sqrt{1-(v_\infty/c)^2}$, and $\Gamma$ is the normalized disk luminosity. These relations can be tested observationally. Under the present model, in the case of SS 433, where the jet speed is about $0.26 \,c$, the normalized accretion rate is about 20, while it is about 2000 in the case of GRS 1915$+$105 and GRO J1655$-$40, where the jet speed is about $0.92 \,c$.