Abstract
We consider an optically thin advection-dominated accretion flow (ADAF) that is connected at a finite transition radius to an outer optically thick, geometrically thin disk. We include turbulent energy transport and examine ADAF models that satisfy the following boundary conditions at the transition radius: (1) the temperature of the gas is much lower than the virial temperature, (2) the rotation is super-Keplerian, and (3) the net radial flux of energy is outward. We numerically solve the height-integrated viscous hydrodynamic equations with these boundary conditions. We find that the Bernoulli parameter is positive for a wide range of radius, indicating that outflows may be possible from ADAFs. Turbulent energy transport enhances the Bernoulli parameter. We compare our numerical global solutions with two published analytical solutions. We find that the solution of Honma represents the transition region well, while the self-similar solution of Narayan & Yi works better away from the transition. However, neither analytical solution is able to represent the density or angular momentum profile in the inner region of the ADAF, where the flow makes a sonic transition.
Highlights
We investigate the e†ect of turbulent energy transport, a key feature of HonmaÏs transition model, and we examine the di†erences between global ADAF models with energy transport and those without
We identiÐed three ““ connection conditions ÏÏ which ADAF models should satisfy in order to be able to connect to standard thin disks : (1) the temperature and velocity of the gas should change by orders of magnitude in the transition region between the ADAF and the thin disk, (2) there should be super-Keplerian rotation in the transition region, and (3) there should be an outward energy Ñux
We derived a general form of the outer boundary conditions that global ADAF models must satisfy in order to be consistent with the three connection conditions
Summary
Three self-consistent and stable models of accretion Ñows are known (see Chen et al 1995, who discuss these three models as well as a fourth unstable model by Shapiro, Lightman, & Eardley 1976) : (1) a geometrically thin, optically thick cool accretion disk model (hereafter, standard disk) (Shakura & Sunyaev 1973), (2) a geometrically thick, optically thick advection-dominated accretion Ñow model (optically thick ADAF, known as a slim disk) (Abramowicz et al 1988), and (3) a geometrically thick, optically thin advection-dominated accretion Ñow model (optically thin ADAF) (Ichimaru 1977 ; Rees et al 1982 ; Narayan & Yi 1994 [hereafter NY], 1995a, 1995b ; Abramowicz et al 1995). If an ADAF is to be connected radially to a standard disk, the Ðrst requirement is that thermodynamic quantities like the temperature and dynamical quantities like the radial velocity must change by orders of magnitude in the transition region This feature is in some sense realized in numerical global ADAF models in the literature where thin disklike outer boundary conditions are imposed (e.g., Narayan et al 1997b ; Manmoto et al 1997 ; Nakamura et al 1997). Abramowicz, Igumenshchev, & Lasota (1998) noted that the accreting gas in an ADAF near the transition radius must rotate at a super-Keplerian angular velocity This is because there is a pressure maximum in the Ñow whenever a standard disk is connected to an ADAF across a narrow transition layer.
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