Standard Thin Disk Model Research Articles

THE COSMOLOGICAL CONSEQUENCE OF AN OBSCURED AGN POPULATION ON THE RADIATION EFFICIENCY

In light of recent indications for a large population of obscured active galactic nuclei (AGNs), we revisit the mean radiation efficiency from accretion onto supermassive black holes (SMBHs), epsilon, applying a bayesian approach. We use the integrated comoving energy density emitted by AGNs and compare it to the mass density of local SMBHs. When considering only optically-selected unobscured AGNs, we derive log_10[epsilon]=-1.77+0.16-0.11 or epsilon=1.7+0.8-0.4%. Using the AGNs selected using hard X-rays, which include unabsorbed and Compton-thin absorbed AGNs, we find log_10[epsilon]=-1.20+0.15-0.10 or epsilon=6.4+2.6-1.3%. Using optically-selected AGNs, and correcting for the obscured population, we inferr log_10[epsilon]=-1.17+0.11-0.08 or epsilon=6.7+1.9-1.1%, which we consider our best estimate. We also repeat this calculation for intrinsically luminous AGNs (M_B<-23, quasars), comparing to the SMBH mass density in local elliptical galaxies, and find log_10[epsilon]=-1.27+0.15-0.11 or epsilon=5.4+2.2-1.2%. We discuss how our results can be used to estimate the mean spin of accreting SMBHs, both assuming the standard thin-disk model of accretion onto black holes and also comparing to more recent simulations. Our results can rule out maximally rotating SMBHs (<a>=0.998 Gm_bh/c^2) at the >=98% confidence level, as well as high rotation values (<a> >=0.9 Gm_bh/c^2) with >=92% confidence. Our preferred values of <a> are ~0.25-0.60 Gm_bh/c^2, although even these might be overestimated. Hence, we find that on average, SMBHs are not rapidly spinning during accretion. Finally, using an independent measurement of Eddington ratios, we estimate the SMBH e-folding time for the brightest AGNs (quasars) to be <tau> =100+151-60 Myr.

Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region

We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a non-spinning black hole. The disk has a thickness $h/r\sim0.05-0.1$ over the radial range $(2-20)GM/c^2$. In steady state, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $\sim2%$ of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.

Viscous Torque and Dissipation in the Inner Regions of a Thin Accretion Disk: Implications for Measuring Black Hole Spin

We consider a simple Newtonian model of a steady accretion disk around a black hole. The model is based on height-integrated hydrodynamic equations, α-viscosity, and a pseudo-Newtonian potential which results in an innermost stable circular orbit (ISCO) that closely approximates the one predicted by general relativity. We find that, as the disk thickness -->H/R or the value of α increases, the hydrodynamic model exhibits increasing deviations from the standard thin disk model of Shakura and Sunyaev. The latter is an analytical model in which the viscous torque is assumed to vanish at the ISCO. We consider the implications of the results for attempts to estimate black hole spin by using the standard disk model to fit continuum spectra of black hole accretion disks. We find that the error in the spin estimate is quite modest so long as -->H/R ≤ 0.1 and -->α ≤ 0.2. At worst, the error in the estimated value of the spin parameter is 0.1 for a nonspinning black hole; the error is much less for a rapidly spinning hole. We also consider the density and disk thickness contrast between the gas in the disk and that inside the ISCO. The contrast needs to be large if black hole spin is to be successfully estimated by fitting the relativistically broadened X-ray line profile of fluorescent iron emission from reflection off an accretion disk. In our hydrodynamic models, the contrast in density and thickness is low when -->H/R 0.1, suggesting that the iron line technique may be most reliable in extremely thin disks. We caution that these results have been obtained with a viscous hydrodynamic model. While our results are likely to be qualitatively correct, quantitative estimates of, e.g., the magnitude of the error in the spin estimate, need to be confirmed with MHD simulations of radiatively cooled thin disks.

The SED in the hot continuum of the symbiotic binary AR Pavonis: I. Tests with current models

We present the spectral energy distribution (SED) in the continuum of the eclipsing symbiotic binary AR Pav between 0.12 and 3.4 μm. This revealed a high luminosity of the hot object in the binary, L h∼2 200 ( d/4.9 kpc) 2 L ⊙. We introduce a method of disentangling the total continuum spectrum into its individual components of radiation for current models of symbiotic binaries. Applying a standard ionization model we show that the configuration of AR Pav differs significantly from that typical for symbiotic binaries during their quiescent phases. The best fit of the observed SED is provided by radiation of a simple blackbody accretion disk with L AD∼1700 ( d/4.9 kpc) 2 L ⊙, which is embedded in an extended hot corona with T e=40 000±5000 K and L N∼500 ( d/4.9 kpc) 2 L ⊙. This basic configuration of the hot object explains also the observed wavelength-dependent depth and width of the eclipse profile. The standard thin disk model requires a high accretion rate M ̇ acc ≳2×10 −4 M ⊙ yr −1 onto the central star with a radius R acc≳2 R ⊙ to balance the observed luminosity. Even irrespectively to the disk model, the accretion process limits R acc>0.1 R ⊙ for M ̇ acc >1.7×10 −5 M ⊙ yr −1 and M acc=0.75–1.0 M ⊙, which precludes a white dwarf to be the accreting star. Application of models with the disk and the boundary layer shows that the far-UV spectrum is not consistent with a large amount of a hot radiation from the boundary layer. However, the presence of such a boundary layer in the system is indirectly indicated through the strong nebular emission. This solution suggests that the hotter inner parts of the disk including the boundary layer are occulted by the disk material in the direction to the observer.

Theoretical restrictions on accretion disks

We construct a standard thin disk model taking into account the pressure from both gas and radiation, the opacity contributed by both electron scattering and absorption, and the gravity from both a central object and a disk. A simple and powerful technique for solving the non-linear equations is presented. Through a numerical algorithm for the two equationl forβ, γ, ξ, all the disk quantities are expressed as the analytical function ofβ, γ, ξ. We also discuss the solutions in the limit casesβ → 0,β → 1 and the parameter range of the linear approximation. From the numerical solutions and limit analyses, we found that it is not necessary to include the self-gravity of the disk.

Dressing up a Kerr naked singularity

We study the evolution of a naked singularity surrounded by an accreting disk of matter; we consider two kinds of disk: the standard thin-disk model and the thick barytropic model, for several initial conditions. We show that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. We evaluate the final mass, the luminosity and the time of evolution of the singularity.