Modified Slim-Disk Model Based on Radiation-Hydrodynamic Simulation Data: The Conflict Between Outflow and Photon Trapping

There are two key processes which appear when the disk luminosity approaches the Eddington luminosity: photon trapping and radiation pressure-driven outflow, and both are multi-dimensional effects. At very high luminosity, the accretion rate should also be very high, and so is the optical depth. Then, the photon diffusion timescale in the vertical direction may become shorter than the accretion time of gas. If this happens, photons generated deep inside the accretion flow are not able to reach the surface before the material is swallowed by a black hole. This is the photon trapping effects (Katz 1977;Begelman 1978;Begelman & Meier 1982;Flammang 1984;Blondin 1986;Colpi 1988;Wang & Zhou 1999;Ohsuga et al. 2002). Furthermore, the flow of high luminosities are supported by radiation pressure, which is likely to induce outflow (Bisnovatyi-Kogan & Blinnikov 1977;Meier 1979;Icke 1980;Tajima & Fukue 1998). For complete understanding of the supercritical accretion flow, we need to solve the multi-dimensional radiation-hydrodynamic (RHD) equations. This has become possible quite recently thanks to the rapid developments of high-speed computers. Ohsuga et al. (2005) were the first to succeed in the global RHD simulations of the supercritical accretion flow until the flow settles down on the quasi-steady phase. They have demonstrated that the accretion rate can be arbitrarily high, that the Eddington luminosity can be exceeded, and that the luminosity increases with an increase of the mass input rate in a logarithmic fashion (see also Ohsuga 2006). The reason for the occurrence of super-Eddington luminosity is the combination of two effects: significant radiation anisotropy and photon trapping (Ohsuga & Mineshige 2007).

The slim-disk model was proposed by Abramowicz et al. (1988) as a simplified model of supercritical accretion flow. This model is constructed on (radially) the one-dimensional formulation, like Shakura & Sunyaev (1973), and the photon trapping effects are expressed as the (radial) advection of radiation entropy, though the outflow effect is not considered. Despite this weakness this model has been used by many authors as a “standard model” of the supercritical accretion because of its technical simplicity (e.g., Szuszkiewicz et al. 1996;Beloborodov 1998;Watarai & Fukue 1999;Mineshige et al. 2000;Fukue 2000;Watarai et al. 2000;Kawaguchi 2003;Gu & Lu 2007).

It is not easy to construct one-dimensional models (like the slim-disk model) which incorporate both of photon trapping and outflow effects, since the combined effects are essentially multidimensional. There have been several attempts (e.g., Lipunova 1999;Kitabatake et al. 2002;Fukue 2004;Kohri et al. 2007;Poutanen et al. 2007), but these studies rely on simplifications and assumptions. It will be much more preferable to study this issue by using the multi-dimensional RHD simulations, but such simulations are expensive and it is not easy to gain physical insight from simulation data. In the present study we thus construct a one-dimensional model as an extension of the slim-disk model based on the information regarding the conflict between photon trapping and outflow, which we gain from the simulation data. Our goal is to examine how the flow structure and its appearance are affected by the counteracting effects of photon trapping and outflow.

The plan of this paper is as follows: In the next section, we overview the RHD simulations of supercritical accretion flow and calculate the accretion rate and the mass outflow rate of the simulated flow. In section 3, we present our improved slim-disk model and see some details of the flow structure. We then discuss several important effects of the supercritical flow based on our simple model. The final section is devoted to summary.

Through the studies based on the slim-disk model two key observational signatures of the supercritical flow have bec

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