Radiatively driven relativistic spherical winds under relativistic radiative transfer

We numerically investigate radiatively driven relativistic spherical winds from the central luminous object with mass M and luminosity L* under Newtonian gravity, special relativity, and relativistic radiative transfer. We solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double-iteration processes, to obtain the intensity and velocity fields simultaneously. We found that the momentum-driven winds with scattering are quickly accelerated near the central object to reach the terminal speed. The results of numerical solutions are roughly fitted by a relation of |$\dot{m}=0.7(\Gamma _*-1)\tau _* \beta _* \beta _{\rm out}^{-2.6}$|⁠, where |$\dot{m}$| is the mass-loss rate normalized by the critical one, Γ* the central luminosity normalized by the critical one, τ* the typical optical depth, β* the initial flow speed at the central core of radius R*, and βout the terminal speed normalized by the speed of light. This relation is close to the non-relativistic analytical solution, |$\dot{m} = 2(\Gamma _*-1)\tau _* \beta _* \beta _{\rm out}^{-2}$|⁠, which can be re-expressed as |$\beta _{\rm out}^2/2 = (\Gamma _*-1)GM/c^2 R_*$|⁠. That is, the present solution with small optical depth is similar to that of the radiatively driven free outflow. Furthermore, we found that the normalized luminosity (Eddington parameter) must be larger than unity for the relativistic spherical wind to blow off with intermediate or small optical depth, i.e. |$\Gamma _* \gtrsim \sqrt{(1+\beta _{\rm out})^3/(1-\beta _{\rm out})}.$| We briefly investigate and discuss an isothermal wind.