Slim Disk: Viscosity Prescriptions and Observational Implications

Abstract

We examine how different viscosity prescriptions and magnitudes affect the structure of the slim disk. Unlike the case with a standard disk, radiation from the slim disk is influenced by the viscosity parameter, $\alpha$, in such a way that the estimated maximum effective temperature of the disk slightly increases as $\alpha$ increases. This is because the larger is $\alpha$, the larger does the accretion velocity become and, hence, the more enhanced does the advective energy transport become, which means less efficient radiative cooling and thus higher temperatures. Furthermore, we checked different viscosity prescriptions with the form of the viscous stress tensor of $t_{r \varphi} =-\alpha \beta^{\mu}p_\mathrm{total}$, where $\beta$ is the ratio of the gas pressure to the total pressure, and $\mu$ is a parameter ($0 \le \mu \le 1$). In contrast with the case with $\mu=0$, which shows significant decrease in the inner-edge radius and the flattering of the effective temperature profile at high luminosities, for large $\mu$, say $\mu \sim 0.5$, neither of the inner-edge of the disk nor temperature profiles does not appreciably change even at the Eddington luminosity. We can rule out a case with large $\mu~(\sim 0.5)$, since it would not be able to produce a drop in the inner-edge radius of an increase in the luminosity, as was observed in an ultraluminous X-ray source, IC 342, source 1