Radiative Transfer and Limb Darkening of Accretion Disks

Transfer equation in a geometrically thin accretion disk is reexamined under the plane-parallel approximation with finite optical depth. Emergent intensity is analytically obtained in the cases with or without internal heating. For large or infinite optical depth, the emergent intensity exhibits a usual limb-darkening effect, where the intensity linearly changes as a function of the direction cosine. For small optical depth, on the other hand, the angle-dependence of the emergent intensity drastically changes. In the case without heating but with uniform incident radiation at the disk equator, the emergent intensity becomes isotropic for small optical depth. In the case with uniform internal heating, the limb brightening takes place for small optical depth. We also emphasize and discuss the limb-darkening effect in an accretion disk for several cases.Comment: 7 pages, 4 figure

Relativistic Radiative Flow in a Luminous Disk II

Radiatively-driven transfer flow perpendicular to a luminous disk is examined in the relativistic regime of $(v/c)^2$, taking into account the gravity of the central object. The flow is assumed to be vertical, and the gas pressure as well as the magnetic field are ignored. Using a velocity-dependent variable Eddington factor, we can solve the rigorous equations of the relativistic radiative flow accelerated up to the {\it relativistic} speed. For sufficiently luminous cases, the flow resembles the case without gravity. For less-luminous or small initial radius cases, however, the flow velocity decreases due to gravity. Application to a supercritical accretion disk with mass loss is briefly discussed.Comment: 7 pages, 5 figure

Relativistic Radiation Hydrodynamical Accretion Disk Winds

Accretion disk winds browing off perpendicular to a luminous disk are examined in the framework of fully special relativistic radiation hydrodynamics. The wind is assumed to be steady, vertical, and isothermal. %and the gravitational fields is approximated by a pseudo-Newtonian potential. Using a velocity-dependent variable Eddington factor, we can solve the rigorous equations of relativistic radiative hydrodynamics, and can obtain radiatively driven winds accelerated up to the {\it relativistic} speed. For less luminous cases, disk winds are transonic types passing through saddle type critical points, and the final speed of winds increases as the disk flux and/or the isothermal sound speed increase. For luminous cases, on the other hand, disk winds are always supersonic, since critical points disappear due to the characteristic nature of the disk gravitational fields. The boundary between the transonic and supersonic types is located at around $\hat{F}_{\rm c} \sim 0.1 (\epsilon+p)/(\rho c^2)/\gamma_{\rm c}$, where $\hat{F}_{\rm c}$ is the radiative flux at the critical point normalized by the local Eddington luminosity, $(\epsilon+p)/(\rho c^2)$ is the enthalpy of the gas divided by the rest mass energy, and $\gamma_{\rm c}$ is the Lorentz factor of the wind velocity at the critical point. In the transonic winds, the final speed becomes 0.4--0.8$c$ for typical parameters, while it can reach $\sim c$ in the supersonic winds.Comment: 6 pages, 5 figures; PASJ 59 (2007) in pres