Magnetocentrifugally driven winds: Comparison of MHD simulations with theory

Stationary MHD outflows from a rotating accretion dish: are investigated nu merically by time-dependent axisymmetric simulations. The initial magnetic field is taken to be a split-monopole poloidal field configuration frozen i nto the disk. The disk is treated as a perfectly conducting, time-independe nt density boundary [rho(r)] in Keplerian rotation. The outflow velocity fr om this surface is not specified but rather is determined self-consistently from the MHD equations. The temperature of the matter outflowing from the disk is small in the region where the magnetic field is inclined away from the symmetry axis (c(s)(2) much less than v(K)(2)) but relatively high (c(s )(2) less than or similar to v(K)(2)) at very small radii in the disk, wher e the magnetic field is not inclined away from the axis. We have found a la rge class of stationary MHD winds. Within the simulation region, the outflo w accelerates from thermal velocity (similar to c(s)) to a much larger asym ptotic poloidal flow velocity of the order of 1/2 root GM/r(i), where dd is the mass of the central object and r(i) is the inner radius of the disk. T his asymptotic velocity is much larger than the local escape speed and is l arger than fast magnetosonic speed by a factor of similar to 1.75. The acce leration distance for the outflow, over which the flow accelerates from sim ilar to 0% to, say, 90% of the asymptotic speed, occurs at a flow distance of about 80r(i). The outflows are approximately spherical, with only small collimation within the simulation region. The collimation distance over whi ch the flow becomes collimated (with divergence less than, say, 10 degrees) is much larger than the size of our simulation region. Close to the disk t he outflow is driven by the centrifugal force, while at all larger distance s the flow is driven by the magnetic force, which is proportional to -del(r B(phi))(2) where B-phi is the toroidal field. Our stationary numerical solu tions allow us to (1) compare the results with MHD theory of stationary flo ws, (2) investigate the influence of different outer boundary conditions on the flows, and (3) investigate the influence of the shape of the simulatio n region on the flows. Different comparisons were made with the theory. The ideal MHD integrals of motion (constants on flux surfaces) were calculated along magnetic field lines and were shown to be constants with an accuracy of 5%-15%. Other characteristics of the numerical solutions were compared with the theory, including conditions at the Alfven surface. Different oute r boundary conditions on the toroidal component of the magnetic field were investigated. We conclude that the commonly used "free" boundary condition on the toroidal field leads to artificial magnetic forces on the outer boun daries, which can significantly influence to the calculated flows. New oute r boundary conditions are proposed and investigated that do not give artifi cial forces. We sinew that simulated flows may depend on the shape of the s imulation region. Namely, if the simulation region is elongated in the z-di rection, then Mach cones on the outer cylindrical boundary may be partially directed inside the simulation region. Because of this, the boundary can h ave an artificial influence on the calculated flow. This effect is reduced if the computational region is approximately square or if it is spherical. Simulations of MHD outflows with an elongated computational region can lead to artificial collimation of the flow.