Relativistic slim disks with vertical structure

Abstract

We report on a scheme for incorporating vertical radiative energy transport into a fully relativistic, Kerr-metric model of optically thick, advective, transonic alpha disks. Our code couples the radial and vertical equations of the accretion disk. The flux was computed in the diffusion approximation, and convection is included in the mixing-length approximation. We present the detailed structure of this "two-dimensional" slim-disk model for α = 0.01. We then calculated the emergent spectra integrated over the disk surface. The values of surface density, radial velocity, and the photospheric height for these models differ by 20%-30% from those obtained in the polytropic, height-averaged slim disk model considered previously. However, the emission profiles and the resulting spectra are quite similar for both types of models. The effective optical depth of the slim disk becomes lower than unity for high values of the alpha parameter and for high accretion rates.

The Extreme Ultraviolet Variability of Quasars

“…This would be the configuration of a significant elevation of EUV flux in magnitude and time. Within standard accretion disk theory, this increase is associated with an increase of the effective temperature of the surface layer (Sadowski et al 2011). The second frame shows an epoch with decreased emissivity.…”

“…This section is an attempt to make a speculative assessment on the implied size of the EUV emitting region based on models of slim disks (Sadowski et al 2011). Being located just shortward of the peak of the SED, the EUV continuum that is sampled in Tables 1-3 likely represents the highest frequency optically thick thermal emission from the accretion flow.…”

“…Thus, we consider the most recent slim disk model solutions (Sadowski et al 2011 (Marziani et al 2003b). Our sample is entirely Population A type spectra.…”

“…This is the gas that is responsible for the observed EUV flux. The slim disk has vertical structure and the velocity that is calculated in Sadowski et al (2011) is vertically averaged. We are actually only interested in the radial velocity of the optically thin surface layer.…”

On the Eddington limit for relativistic accretion discs

“…On the other hand, the slim-disc model does not account for the vertical structure but rather operates with verticallyaveraged equations. In Sadowski et al (2011), the vertical structure of a slim-disc was considered. However, the vertical structure itself was in this paper assumed to be decoupled from the radial structure of the disc, the vertical epicyclic frequency (corresponding to Ωz or Ωµ of the present work) was assumed to be constant with the vertical coordinate z, as well as all the velocity components, that means that the disc was in fact treated as thin.…”