Relativistic Radiative Flow in a Luminous Disk

Radiatively driven transfer flow perpendicular to a luminous disk was examined under a fully special relativistic treatment, taking into account radiation transfer. The flow was assumed to be vertical, and the gravity, the gas pressure, and the viscous heating were ignored. In order to construct the boundary condition at the flow top, the magic speed above the flat source was re-examined, and it was found that the magic speed above a moving source can exceed that above a static source ($\sim 0.45~c$). Then, the radiatively driven flow in a luminous disk was numerically solved, from the flow base (disk ``inside''), where the flow speed is zero, to the flow top (disk ``surface''), where the optical depth is zero. For a given optical depth and appropriate initial conditions at the flow base, where the flow starts, a loaded mass in the flow was obtained as an eigenvalue of the boundary condition at the flow top. Furthermore, a loaded mass and the flow final speed at the flow top were obtained as a function of the radiation pressure at the flow base; the flow final speed increases as the loaded mass decreases. Moreover, the flow velocity and radiation fields along the flow were obtained as a function of the optical depth. Within the present treatment, the flow three velocity $v$ is restricted to be within the range of $v < c/\sqrt{3}$, which is the relativistic sound speed, due to the relativistic effect.Comment: 8 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

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

Hoyle-Lyttleton Accretion onto Accretion Disks

We investigate Hoyle-Lyttleton accretion for the case where the central source is a luminous accretion disk. %In classical Hoyle-Lyttleton accretion onto a ``spherical'' source, accretion takes place in an axially symmetric manner around a so-called accretion axis. The accretion rate of the classical Hoyle-Lyttleton accretion onto a non-luminous object and $\Gamma$ the luminosity of the central object normalized by the Eddington luminosity. %If the central object is a compact star with a luminous accretion disk, the radiation field becomes ``non-spherical''. %Although the gravitional field remains spherical. In such a case the axial symmetry around the accretion axis breaks down; the accretion radius $R_{acc}$ generally depends on an inclination angle $i$ between the accretion axis and the symmetry axis of the disk and the azimuthal angle $\phi$ around the accretion axis. %That is, the cross section of accretion changes its shape. Hence, the accretion rate $\dot{M}$, which is obtained by integrating $R_{acc}$ around $\phi$, depends on $i$. % as well as $M$, $\Gamma$, and $v_\infty$. %In the case of an edge-on accretion ($i=90^{\circ}$), The accretion rate is larger than that of the spherical case and approximately expressed as $\dot{M} \sim \dot{M}_{HL} (1-\Gamma)$ for $\Gamma \leq 0.65$ and $\dot{M} \sim \dot{M}_{HL} (2-\Gamma)^2/5$ for $\Gamma \geq 0.65$. %Once the accretion disk forms and the anisotropic radiation fields are produced around the central object,the accretion plane will be maintained automatically (the direction of jets associated with the disk is also maintained). %Thus, the anisotropic radiation field of accretion disks drastically changes the accretion nature, that gives a clue to the formation of accretion disks around an isolated black hole.Comment: 5 figure

Optical Light Curves of Luminous Eclipsing Black Hole X-ray Binaries

We examine optical V-band light curves in luminous eclipsing black hole X-ray binaries, using a supercritical accretion/outflow model that is more realistic than the formerly used ones. In order to compute the theoretical light curve in the binary system, we do not only apply the global analytic solution of the disk, but also include the effect of the optically thick outflow. We found that the depth of eclipse of the companion star by the disk changes dramatically when including the effect of the outflow. Due to the effect of outflow, we can reproduce the optical light curve for typical binary parameters in SS433. Our model with outflow velocity v~3000 km/s can fit whole shape of the averaged V-band light curve in SS433, but we found a possible parameter range consistent with observations, such as \dot{M}~5000-10000 L_E/c^2 (with L_E being the Eddington luminosity and $c$ being the speed of light) and T_C~10000K-14000 K for the accretion rate and donor star temperature, respectively. Furthermore, we briefly discuss observational implications for ultraluminous X-ray sources.Comment: 8 pages, 9 figures, accepted for publication in PAS

Radiative Flow in a Luminous Disk

Radiatively-driven flow in a luminous disk is examined in the subrelativistic regime of $(v/c)^1$, taking account of radiation transfer. The flow is assumed to be vertical, and the gravity and gas pressure are ignored. When internal heating is dropped, for a given optical depth and radiation pressure at the flow base (disk ``inside''), where the flow speed is zero, the flow is analytically solved under the appropriate boundary condition at the flow top (disk ``surface''), where the optical depth is zero. The loaded mass and terminal speed of the flow are both determined by the initial conditions; the mass-loss rate increases as the initial radiation pressure increases, while the flow terminal speed increases as the initial radiation pressure and the loaded mass decrease. In particular, when heating is ignored, the radiative flux $F$ is constant, and the radiation pressure $P_0$ at the flow base with optical depth $\tau_0$ is bound in the range of $2/3 < cP_0/F < 2/3 + \tau_0$. In this case, in the limit of $cP_0/F = 2/3 + \tau_0$, the loaded mass diverges and the flow terminal speed becomes zero, while, in the limit of $cP_0/F = 2/3$, the loaded mass becomes zero and the terminal speed approaches $(3/8)c$, which is the terminal speed above the luminous flat disk under an approximation of the order of $(v/c)^1$. We also examine the case where heating exists, and find that the flow properties are qualitatively similar to the case without heating.Comment: 7 pages, 4 figure

Effect of Radiation Drag on Hoyle-Lyttleton Accretion

Hoyle-Lyttleton type accretion is investigated, by taking account of not only the effect of radiation pressure but the effect of radiation drag. We calculate the trajectories of particles for three cases: only the effect of gravity is considered (case A); the effect of radiation pressure is taken into account (case B); the effect of radiation drag as well as radiation pressure is taken into account (case C). The accretion radii for former two cases are $2GM/v_{\infty}^2$ for case A and $2GM(1-\Gamma)/v_{\infty}^2$ for case B, where M is the mass of the accreted object, $v_{\infty}$ the relative velocity, and Gamma the normalized luminosity of the accreted object. We found that the accretion radius for case C is in between those of cases A and B under the present approximation; i.e., the accretion radius decreases due to radiation pressure while it increases due to radiation drag. In addition, the accretion radius for case C becomes larger as the incident velocity becomes fast. The effect of radiation drag becomes more and more important when the velocity of the incident particle is comparable to the light speed.Comment: 11 pages, LaTeX with 6 eps figures, accepted by Publications of the Astronomical Society of Japa

Radiative Transfer in Accretion-Disk Winds

Radiative transfer equation in an accretion disk wind is examined analytically and numerically under the plane-parallel approximation in the subrelativistic regime of $(v/c)^1$, where $v$ is the wind vertical velocity. Emergent intensity is analytically obtained for the case of a large optical depth, where the flow speed and the source function are almost constant. The usual limb-darkening effect, which depends on the direction cosine at the zero-optical depth surface, does not appear, since the source function is constant. Because of the vertical motion of winds, however, the emergent intensity exhibits the {\it velocity-dependent} limb-darkening effect, which comes from the Doppler and aberration effects. Radiative moments and emergent intensity are also numerically obtained. When the flow speed is small ($v \leq 0.1c$), the radiative structure resembles to that of the static atmosphere, where the source function is proportional to the optical depth, and the usual limb-darkening effect exists. When the flow speed becomes large, on the other hand, the flow speed attains the constant terminal one, and the velocity-dependent limb-darkening effect appears. We thus carefully treat and estimate the wind luminosity and limb-darkening effect, when we observe an accretion disk wind.Comment: 8 pages, 5 figure