2. Basic non-stationary accretion disk equation
where is the Kepler angular velocity; M is the mass of the central gravitating object, constant in time; cm3g-1s-2 is the gravitational constant. This is a good approximation to the law of motion for particles in the standard sub-Eddington disk. In the advection-dominated accretion flow (ADAF) the particles are substantially subjected to the radial gradient of pressure and thus have the velocity different from that given by (1). Following the model by Narayan & Yi (1994), one can assume that the angular velocity in ADAF is .
where is the angular velocity in the disk; - the surface density of the matter, and is the height-integrated viscous shear stresses between adjacent layers. The time-independent angular velocity is assumed although there can possibly be certain variations of in the non-Keplerian advective disks when a time-dependent pressure gradient is involved (see, e.g. Ogilvie 1999).
It is convenient to introduce the following variables: , henceforth means the total moment of viscous forces acting between the adjacent layers, - the specific angular momentum of the matter in the disk, and . From Eq. (2) in view of (1) it follows that
In the case of the Keplerian disk . The advection-dominated solution by Narayan and Yi (1994) yields , where is a dimensionless constant.
© European Southern Observatory (ESO) 2000
Online publication: March 28, 2000