Radiative Flow in a Luminous Disk

Abstract

Radiatively driven flow in a luminous disk is examined in the subrelativistic regime of $(v/c)^1$, taking account of radiation transfer. The flow is assumed to be vertical, and the gravity and gas pressure are ignored. When internal heating is dropped, for a given optical depth and radiation pressure at the flow base (disk “inside”), where the flow speed is zero, the flow is analytically solved under the appropriate boundary condition at the flow top (disk “surface”), where the optical depth is zero. The loaded mass and terminal speed of the flow are both determined by the initial conditions; the mass-loss rate increases as the initial radiation pressure increases, while the flow terminal speed increases as the initial radiation pressure and the loaded mass decrease. In particular, when heating is ignored, the radiative flux $F$ is constant and the radiation pressure $P_0$ at the flow base with optical depth $\tau_0$ is bound in the range of $2/3 < cP_0/F < 2/3 + \tau_0$. In this case, at the limit of $cP_0/F = 2/3 + \tau_0$, the loaded mass diverges and the flow terminal speed becomes zero, while, at the limit of $cP_0/F = 2/3$, the loaded mass becomes zero and the terminal speed approaches $(3/8) \, c$, which is the terminal speed above the luminous flat disk under an approximation of the order of $(v/c)^1$. We also examine the case where heating exists, and find that the flow properties are qualitatively similar to the case without heating.