Relativistic Radiative Flow in a Luminous Disk

Abstract

Radiatively driven transfer flow perpendicular to a luminous disk was examined under a fully special relativistic treatment, taking into account radiation transfer. The flow was assumed to be vertical, and the gravity, the gas pressure, and the viscous heating were ignored. In order to construct the boundary condition at the flow top, the magic speed above the flat source was re-examined, and it was found that the magic speed above a moving source can exceed that above a static source ($\sim 0.45 \,c$). Then, the radiatively driven flow in a luminous disk was numerically solved, from the flow base (disk “inside”), where the flow speed is zero, to the flow top (disk “surface”), where the optical depth is zero. For a given optical depth and appropriate initial conditions at the flow base, where the flow starts, a loaded mass in the flow was obtained as an eigenvalue of the boundary condition at the flow top. Furthermore, a loaded mass and the flow final speed at the flow top were obtained as a function of the radiation pressure at the flow base; the flow final speed increases as the loaded mass decreases. Moreover, the flow velocity and radiation fields along the flow were obtained as a function of the optical depth. Within the present treatment, the flow three velocity $v$ is restricted to be within the range of $v < c/\sqrt{3}$, which is the relativistic sound speed, due to the relativistic effect.