Self-Similar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics

Abstract

We construct a two-parameter family of models for self-collimated, radially self-similar magnetized outflows from accretion disks. A flow at zero initial poloidal speed leaves the surface of a rotating disk and is accelerated and redirected toward the pole by helical magnetic fields threading the disk. At large distances from the disk, the flow streamlines asymptote to wrap around the surfaces of nested cylinders. In constrast to previous disk wind modeling, we have explicitly implemented the cylindrical asymptotic boundary condition to examine the consequences for flow dynamics. The solutions are characterized by the logarithmic gradient of the magnetic field strength and the ratios between the footpoint radius R_0 and asymptotic radius R_1 of streamlines; the Alfven radius must be found as an eigenvalue. Cylindrical solutions require the magnetic field to drop less steeply than 1/R. We find that the asymptotic poloidal speed on any streamline is typically just a few tenths of the Kepler speed at the corresponding disk footpoint. The asymptotic toroidal Alfven speed is, however, a few times the footpoint Kepler speed. We discuss the implications of the models for interpretations of observed optical jets and molecular outflows from young stellar systems. We suggest that the difficulty of achieving strong collimation in vector velocity simultaneously with a final speed comparable to the disk rotation rate argues against isolated jets and in favor of models with broader winds.