Geometrically thin disk accreting into a black hole

A numerical model of a steady state, thin accretion disk with a constant effective speed of sound is presented. We demonstrate that a no torque'' inner boundary condition is a reasonable approximation provided that the disk thickness, including the thickness of the torquing magnetic fields, is small everywhere. It is likely that this conclusion is correct also for nonsteady disks, as long as the total thickness at the sonic point, H-c, is much smaller than the radius there, r(c)approximate tor(ms). The very existence of thin disks is not proved or disproved in this work, but such disks are believed to exist for moderate accretion rates. Within our model there is a small torque at r(ms), which may increase disk luminosity by several percent. An important result of our analysis is that the physically acceptable steady state solutions in our toy model exist only for alpha<0.14(100v(s)/c)(1/3). A significant torque may be applied to a thin disk if there is a large-scale magnetic field, like in a modified Blandford-Znajek mechanism.