Self-Similar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics

We construct a two-parameter family of models for self-collimated, magnetized outflows from accretion disks. As in previous magnetocentrifugal wind solutions, a flow at zero initial poloidal speed leaves the surface of a disk in Kepler rotation about a central star, and is accelerated and redirected toward the pole by rotating, helical magnetic fields which thread the disk. At large distances from the disk, the flow streamlines asymptote to wrap around the surfaces of nested cylinders, with velocity v and magnetic field B directed in the axial (ˆ z) and toroidal (ˆ ϕ) directions. In the asymptotic regime, the velocity secularly decreases with cylindrical radius R from the inside to the outside of the flow because successive streamlines originate in the circumstellar disk in successively shallower portions of the stellar potential. In contrast to previous disk wind modeling, we have explicitly implemented the cylindrical asymptotic boundary condition to examine the consequences for flow dynamics. The present solutions are developed within the context of r-self-similar flows, such that v, the density ρ, and B scale with spherical radius r as v ∝ r −1/2 , ρ ∝ r −q , and B ∝ r −(1+q)/2 ; q must be smaller that unity in order to achieve cylindrical collimation. We self-consistently obtain the shapes of magnetic field lines and the θ-dependence of all flow quantities. The solutions are characterized by q together with the ratios R A /R 1 and R 0 /R 1 , where for a given streamline R 0 is the radius of its footpoint in the disk, R A is the cylindrical radius where the flow makes an Alfvén transition, and R 1 is its final asymptotic cylindrical radius. For given q and R 0 /R 1 , R A /R 1 must be found as an eigenvalue such that the Alfvén transition is made smoothly. In the solutions we have found, the asymptotic poloidal speed v z on any streamline is typically just a few tenths of the Kepler speed ΩR 0 at the corresponding disk footpoint, while the asymptotic rotation speed v ϕ may be a few tenths to several tenths of ΩR 0. The asymptotic toroidal Alfvén speed v A,ϕ = B ϕ / √ 4πρ is, however, a few times ΩR 0 ; thus the outflows remain magnetically dominated, never making a fast-MHD transition. We discuss the implications of these models for interpretations of observed …