Selfsimilar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics
Abstract
We construct a twoparameter family of models for selfcollimated, 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 it is accelerated and redirected toward the pole by rotating, helical magnetic fields that 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 (ẑ) and toroidal (ϕ̂) 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 rselfsimilar 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 than unity in order to achieve cylindrical collimation. We selfconsistently obtain the shapes of magnetic field lines and the θdependence 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)^{1/2} is, however, a few times ΩR_{0} thus the outflows remain magnetically dominated, never making a fastMHD transition. We discuss the implications of these models for interpretations of observed optical jets and molecular outflows from young stellar systems, and we suggest that the difficulty of achieving strong collimation in vector velocity simultaneously with a final speed comparable to ΩR_{0} argues against isolated jets and in favor of models with broader winds.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1997
 DOI:
 10.1086/304513
 arXiv:
 arXiv:astroph/9705226
 Bibcode:
 1997ApJ...486..291O
 Keywords:

 Accretion;
 Accretion Disks;
 ISM: Jets and Outflows;
 Magnetohydrodynamics: MHD;
 Stars: PreMainSequence;
 Astrophysics
 EPrint:
 39 pages, Latex (uses AAS Latex macros), 6 eps figures, postscript preprint with embedded figures available from http://www.astro.umd.edu/~ostriker/professional/publications.html , to appear in ApJ 9/1/97