Global Self-Similar Protostellar Disk/Wind Models

Abstract: The magnetocentrifugal disk wind mechanism is the leading candidate for producing the large-scale, bipolar jets commonly seen in protostellar systems. I present a detailed formulation of a global, radially self-similar model for a non-ideal disk that launches a magnetocentrifugal wind. This formulation generalizes the conductivity tensor formalism previously used in radially localized disk models. The model involves matching a solution of the equations of non-ideal MHD describing matter in the disk to a solution of the equations of ideal MHD describing a "cold" wind. The disk solution must pass smoothly through the sonic point, the wind solution must pass smoothly through the Alfv\'en point, and the two solutions must match at the disk/wind interface. This model includes for the first time a self-consistent treatment of the evolution of magnetic flux threading the disk, which can change on the disk accretion timescale. The formulation presented here also allows a realistic conductivity profile for the disk to be used in a global disk/wind model for the first time. The physical constraints on the model solutions fix the distribution of the magnetic field threading the disk, the midplane accretion speed, and the midplane migration speed of flux surfaces. I present a representative solution that corresponds to a disk in the ambipolar conductivity regime with a nominal neutral-matter--magnetic-field coupling parameter that is constant along field lines, matched to a wind solution. I conclude with a brief discussion of the importance of self-similar disk/wind models in studying global processes such as dust evolution in protostellar systems.