Self‐similar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics

Abstract

We construct a two-parameter family of models for self-collimated, magnetized outÑows from accretion disks. As in previous magnetocentrifugal wind solutions, a Ñow at zero initial poloidal speed leaves the surface of a disk in Kepler rotation about a central star, and it is accelerated and redirected toward the pole by rotating, helical magnetic Ðelds that thread the disk. At large distances from the disk, the Ñow streamlines asymptote to wrap around the surfaces of nested cylinders, with velocity and magnetic Ðeld ¿ B directed in the axial and toroidal directions. In the asymptotic regime, the velocity secularly (zü) (r ü) decreases with cylindrical radius R from the inside to the outside of the Ñow 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 Ñow dynamics. The present solutions are developed within the context of rÈself-similar Ñows, such that the density o, and B scale with spherical radius r as ¿, ¿ P r~1@2, o P r~q, and B P r~(1`q)@2 ; q must be smaller than unity in order to achieve cylindrical colli-mation. We self-consistently obtain the shapes of magnetic Ðeld lines and the h-dependence of all Ñow quantities. The solutions are characterized by q together with the ratios and where for a R A /R