Self‐similar Solution of Optically Thick Advection‐dominated Flows

Abstract

The photons released by the viscosity process in a disk with accretion rate exceeding the Eddington critical value will be trapped and restored as entropy in the accreting gas rather than being radiated from the disk surface, since the advection cooling dominates the di †usion cooling in such a Ñow. In this paper a self-similar solution of optically thick advection-dominated Ñow has been obtained. This kind of Ñow shows some interesting characteristics that di †er from both the optically thin advection-dominated disk and the standard disk. Such a Ñow is thermally stable. The Bernoulli number is not positive in a wide range of parameters unless the viscosity a is extremely small. The shape always stays slim and is independent of the accretion rateThe gas rotates with sub-Keplerian angular velocity (H/r B 1/J5). (for smaller viscosity). The luminosity of the disk weakly depends on the accretion rate, and ) B ) K /J5 the maximum luminosity is about 4.0 ] 1037 (ergs s~1) (less than the Eddington luminosity), (M/M _ ) although the accretion rate is super-Eddington. This provides a method for estimating the mass of a black hole. The validity of this solution has been tested and found to be suitable in most of the accretion disk (within the photon trapping radius). Its potential applications to the saturated accreting systems are pointed out.

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-line Region and Mass of the Central Black Hole in Mrk 142

“…Regardless of f (r, a) and using logṀ = 2.4 +1.3 −0.6 and log(M • /M ) = 6.23 +0.23 −0.45 , the corresponding radius for the 5100 Å emission is R 5100 = 0.14 +0.60 −0.11 ld. Note that for a slim disk, the presence of prominent radial advection reduces the effective temperature (Abramowicz et al 1988;Wang & Zhou 1999), making the above estimate conservative. Considering that the inferred disk size from multiwavelength reverberation mapping observations is about 3 times larger than that predicted from the standard disk model (e.g., Edelson et al 2015), the 5100 Å emission radius R 5100 would be comparable with the mean radius of zone I, but much smaller than the mean radius of zone II (see Table 5).…”

Exploring the physics of the accretion and jet in nearby narrow-line Seyfert 1 galaxies

“…Bulk of the black hole masses of the NLS1s has been measured to be ∼ 10 6−7 M ⊙ by various methods [e.g.,the reverberation mapping method (e.g., Wang et al 2014) and the luminosity-radius relation (e.g., Zhou et al 2006)]. They ⋆ E-mail: yaosu@pku.edu.cn generally have high Eddington ratios close to or even above unity, so they are often suggested to be powered by slim discs (e.g., Wang & Zhou 1999;Mineshige et al 2000).…”

Self-similar structure of magnetized advection-dominated accretion flows and convection-dominated accretion flows

“…The optically thick ADAFs with super‐Eddington accretion rates were discussed by Abramowicz et al (1988) in details (see also Begelman & Meier 1982; Eggum, Coroniti & Katz 1988). The optically thin ADAFs with low, sub‐Eddington accretion rates were discussed by Rees et al (1982) and Narayan & Yi (1994, 1995a,b) (see also Ichimaru 1977; Abramowicz et al 1995; Gammie & Popham 1998; Popham & Gammie 1998; Wang & Zhou 1999). In particular, Narayan & Yi (1994) introduced self‐similar solutions for ADAFs with the fixed ratio of the advective cooling rate to the viscous heating rate in the disc.…”

“…In particular, Narayan & Yi (1994) introduced self‐similar solutions for ADAFs with the fixed ratio of the advective cooling rate to the viscous heating rate in the disc. Wang & Zhou (1999) solved self‐similar solutions for optically thick ADAFs. The effects of general relativity were considered in Gammie & Popham (1998) and Popham & Gammie (1998).…”