Relativistic radiative transfer and relativistic spherical flows: Relation between the mass-loss rate and terminal speed

Abstract

Abstract Radiatively driven relativistic spherical flows are numerically investigated under the fully special relativistic treatment and relativistic radiative transfer. We first solve the relativistic radiative transfer equation for spherically symmetric outflows iteratively, using a trial velocity distribution, and obtain specific intensities as well as moment quantities, and the Eddington factor. Using the obtained comoving flux, we next solve the relativistic equation of motion, and obtain the refined velocity distribution, the mass-loss rate being determined as an eigenvalue. Until both the intensity and velocity distributions converge, we repeat these double iteration processes. We found that the flows are quickly accelerated near to the central lumious core to reach the terminal speed. The Eddington factor has a complicated behavior, depending on the optical depth and flow speed. We further found that a relation between the flow terminal speed βout normalized by the speed of light and the mass-loss rate $\dot{m}$ normalized by the critical one is roughly approximated as $\dot{m} \propto \tau _* \beta _{\rm out}^{-5/2}$, where τ* is a typical optical depth of the flow, whereas we can analytically derive the relation of $\dot{m} \propto \tau _* \beta _{\rm out}^{-2}$ using a back-of-the-envelope calculation in the nonrelativistic case.