Slim Disk: Viscosity Prescriptions and Observational Implications

Abstract

We examine the effects of the different viscosity prescriptions and the magnitude of the viscosity parameter, $α$, on the structure of the slim disk, and discuss the observational implications on accretion-flow into a stellar-mass black hole. For the range of $α= 10^{-2} \sim 10^{0}$ we calculate the disk spectra and from spectral fitting we derive $\Tin$, maximum temperature of the disk, $\Rin$, the size of the region emitting blackbody radiation with $\Tin$, and $p\equiv -{\rm dln} T_{\rm eff}/{\rm dln}~r$, the slope of the effective temperature distribution. It was founded that the estimated $\Tin$ slightly increases as $α$ increases. This is because the larger the magnitude of viscosity is, the larger becomes the accretion velocity and, hence, the more enhanced becomes advective energy transport, which means less efficient radiative cooling and thus higher temperatures. Furthermore we check different viscosity prescriptions with the form of the viscous stress tensor of $t_{r φ} = -αβ^μp_{\rm total}$, where $β$ is the ratio of gas pressure to total pressure, and $μ$ is a parameter ($0 \le μ\le 1$). For $μ=0$ we have previously found that as luminosity approaches the Eddington, $L_{\rm E$, $\Rin$ decreases below 3$\rg$ (with $r_{\rm g}$ being Schwarzschild radius) and the effective temperature becomes flatter, $T_{\rm eff} \propto r^{-1/2}$. Such a slim-disk nature does not appear when $μ$ is large, $μ\sim 0.5$, even at $L_{\rm E}$. Hence, the temperature of the innermost region of the disk sensitively depends on the $μ$ value. We can rule out the case with large $μ~(\sim 0.5)$, since it will not be able to produce a drop in $\Rin$ with an increase in luminosity as was observed in an ultraluminous X-ray source, IC~342, source 1.