Abstract
Relativistic accretion disk winds driven by disk radiation are numerically examined by calculating the relativistic radiative transfer equation under a plane-parallel approximation. We first solve the relativistic transfer equation iteratively, using a given velocity field, and obtain specific intensities as well as moment quantities. Using the obtained flux, we then solve the vertical hydrodynamical equation under the central gravity, and obtain a new velocity field and the mass-loss rate as an eigenvalue. We repeat these double iteration processes until both the intensity and velocity profiles converge. We further calculate these vertical disk winds at various disk radii for appropriate boundary conditions, and obtain the mass-loss rate as a function of a disk radius for a given disk luminosity. Since in the present study we assume a vertical flow, and the rotational effect is ignored, the disk wind can marginally escape for the Eddington disk luminosity. When the disk luminosity is close to the Eddington one, the wind flow is firstly decelerated at around z ∼ r, and then accelerated to escape. For a larger disk luminosity, on the other hand, the wind flow is monotonically accelerated to infinity. Under the boundary condition that the wind terminal velocity is equal to the Keplerian speed at the disk, we find that the normalized mass-loss rate per unit area, $\skew9\hat{\skew9\dot{J}}$, is roughly expressed as $\skew9\hat{\skew9\dot{J}} \sim 3 (r_{\rm in}/r_{\rm S}) \Gamma _{\rm d} \tau _{\rm b} (r/r_{\rm S})^{-5/2}(1-\sqrt{r_{\rm in}/r})$, where rin is the disk inner radius, rS is the Schwarzschild radius of the central object, Γd is the disk normalized luminosity, τb is the wind optical depth, and r is the radial distance from the center.
Delta-slow solution to explain B supergiant stars' winds
