Relativistic radiative transfer and relativistic spherical shell flows

Abstract

Abstract We examine a radiatively driven spherical flow from a central object, whose thickness is smaller than the radius of the central object, and a plane-parallel approximation can be used—a spherical shell flow. We first solve the relativistic radiative transfer equation iteratively, using a given velocity field, and obtain specific intensities as well as moment quantities. Using the obtained comoving flux, we then solve the relativistic hydrodynamical equation, and obtain a new velocity field. We repeat these double iteration processes until both the intensity and velocity profiles converge. We found that the flow speed v(τ) is roughly approximated as β ≡ v/c = βs(1 − τ/τb), where τ is the optical depth, τb the flow total optical depth, and c the speed of light. We further found that the flow terminal speed vs is roughly expressed as $\beta _{\rm s} \equiv v_{\rm s}/c = (\Gamma \hat{F}_0-1)\tau _{\rm b}/\dot{m}\,$, where Γ is the central luminosity normalized by the Eddington luminosity, $\hat{F}_0$ the comoving flux normalized by the incident flux, and of the order of unity, and $\dot{m}$ the mass-loss rate normalized by the critical mass loss.