ADVECTION-DOMINATED ACCRETION - SELF-SIMILARITY AND BIPOLAR OUTFLOWS

We consider axisymmetric viscous accretion flows where a fraction f of the viscously dissipated energy is stored in the accreting gas as entropy and a fraction 1 - f is radiated. Assuming alpha-viscosity we obtain a two-parameter family of self-similar solutions. Very few such exact self-consistent solutions are known for viscous differentially rotating flows. When the parameter f is small, that is, when there is very little advection, our solutions resemble standard thin accretion disks in many respects except that they have a hot tenuous corona above the disk. In the opposite advection-dominated limit, when f --> 1, the solutions approach nearly spherical accretion. The gas is almost at virial temperature and rotates at much below the Keplerian rate, and the flow is much more akin to Bondi accretion than to disk accretion. None of the solutions have funnels. We compare our exact self-similar solutions with approximate solutions which have been previously obtained using a height-integrated system of equations. We find that various dynamical variables such as the radial velocity, angular velocity, and sound speed estimated from the approximate solutions agree very well with the corresponding spherically averaged quantities in the exact solutions. We conclude that the height-integration approximation is an excellent one for a wide range of accretion conditions, including nearly spherical flows, provided the equations are interpreted as spherical averages. We find that the Bernoulli parameter is positive in all our solutions, especially close to the rotation axis. This effect is produced by viscous transport of energy from small to large radii and from the equator to the poles. In addition, all the solutions are convectively unstable, and the convection is especially important near the rotation axis. For both reasons, we suggest that a bipolar outflow will develop along the axis of these flows, fed by material from the surface layers of the equatorial inflow.