A simplified global solution for an advection-dominated accretion flow

Abstract

When we model black hole accretion sources such as active galactic nuclei and black hole X-ray binaries as advection-dominated accretion flows (ADAFs), it is neccesary to use the global solution to the equations rather than the simpler self-similar solution, since the latter is inaccurate in the region near the black hole where most of the radiation is emitted. However, technically, it is a difficult task to calculate the global solution because of the transonic nature of the flow, which makes it a two-point boundary value problem. In this paper we propose a simplified approach for calculating the global ADAF solution. We replace the radial momentum equation by a simple algebraic relation between the angular velocity of the gas and the Keplerian angular velocity, while keeping all other equations unchanged. It is then easy to solve the differential energy equations to obtain an approximate global solution. By adjusting the free parameters, we find that for almost any accretion rate and for $\alpha =0.1-0.3$ we can get good simplified global solutions. The predicted spectra from the approximate solutions are very close to the spectra obtained from the true global solutions.

12 pages, 4 figures, accepted by ApJ

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• Dynamical Structure of Viscous Accretion Disks with Shocks
• Stability of Cloud Orbits in the Broad Line Region of Active Galactic Nuclei
• The multiwavelength spectrum of NGC 3115: Hot accretion flow properties
• Exploring the disk-jet connection from the properties of narrow line regions in powerful young radio-loud AGNs
• Global Transonic Solution of Hot Accretion Flow with Thermal Conduction
• A 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in black hole systems: A higher order polynomial approximation. I
• A Simplified Model of ADAF with the Jet Driven by the Large-Scale Magnetic Field
• A magnetic model for low/hard state of black hole binaries