Jun Fukue

Relativistic Milne-Eddington-Type Solutions with a Variable Eddington Factor for Relativistic Plane-Parallel Flows

Relativistic radiative transfer in a relativistic plane-parallel flow is examined in a fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several cases, such as the radiative equilibrium or local thermodynamical equilibrium, and obtain relativistic Milne-Eddington-type solutions. In all the cases, the solutions exhibit an exponential behavior on the optical depth; the solutions are expressed by the linear combination of the exponential terms. In addition, the optical depth τ in the exponential term is replaced by the apparent optical depth Γτ ,w hereΓ is a function of the flow speed v. This is the essential properties of the relativistic regime of the radiative transfer. In the case of the radiative equilibrium, the radiation energy density in the comoving frame approaches a constant value, while the radiative flux becomes zero as the optical depth increases. In addition, with uniform heating, the radiative quantity in the comoving frame generally decreases compared with that in the case without heating, whereas, if there is advection cooling, the radiative quantity generally increases. In the case of the local thermodynamic equilibrium, the radiative quantity approaches the LTE values as the optical depth increases. Subject Index: 420, 425, 426, 480

Analytical Solutions of Relativistic Plane-Parallel Flows

Relativistic radiative transfer in a relativistic plane-parallel flow is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, we obtain simple analytical solutions of the relativistic radiative transfer equation for relativistic planeparallel flows in the cases of linear-flow and two-stream approximations. In both cases, the solutions exhibit exponential behavior on the optical depth. In addition, the optical depth τ in the exponential term is replaced by the apparent optical depth Γτ ,w hereΓ is a function of the flow speed v (= βc); for example, in the case of the linear-flow approximation, Γ = γβ, γ being the Lorentz factor. This modification of the apparent/effective optical depth is an essential property of the relativistic radiative transfer. Furthermore, in the nonrelativistic regime, the radiative intensity in the comoving frame increases as the optical depth increases, whereas it approaches a constant value with the optical depth in the relativistic regime because of the exponential term. The radiation energy density in the comoving frame also approaches a constant value, while the radiative flux becomes zero as the optical depth increases. Such behavior of the radiative quantities in the comoving frame, which originates from the exponential term, is also an essential property of the relativistic radiative transfer. Subject Index: 420, 425, 426, 480

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

We examined 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 did not only apply the global analytic solution of the disk, but also included the effect of optically thick outflow. We found that the depth of eclipse of the companion star by the disk changed dramatically when including the effect of the outflow. Due to the effect of outflow, we could reproduce the optical light curve for typical binary parameters in SS 433. Our model with an outflow velocity of v � 3000 km s � 1 could fit the whole shape of the averaged V -band light curve in SS 433, but we found a possible parameter range consistent with observations, such as P M � 5000–10000LE=c 2 (with LE being the Eddington luminosity and c being the speed of light) and TC = 10000 K–14000 K for the accretion rate and donor star temperature, respectively. Furthermore, we briefly discuss observational implications for ultraluminous X-ray sources.