The structure of protostellar accretion disks and the origin of bipolar flows

Mark Wardle*, Arieh Königl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

237 Citations (Scopus)


We study the vertical structure of magnetized protostellar accretion disks that power centrifugally driven outflows. The disks are assumed to be threaded by a large-scale, open magnetic field that removes the angular momentum of the accreted matter by driving a wind from the disk surface. The field is coupled to the weakly ionized disk material by ion-neutral and electron-neutral collisions: these collisions provide a diffusion mechanism that allows a steady state field configuration to be maintained against radial advection and azimuthal shearing. We further assume that the disks are nearly Keplerian, geometrically thin, and axisymmetric, and focus on the parameter regime where the temperature and ion density are effectively constant. Under these assumptions, the fluid equations for the neutrals, the ions, and the electrons as well as the induction equation for the magnetic field can be reduced to a set of ordinary differential equations that describe the vertical structure of the disk at a fixed radius. This formulation complements the global, radially self-similar model studied by Königl. We construct explicit solutions for the disk structure and identify the parameter regime where they are self-consistent and physically viable. We show that if a wind is to be centrifugally driven from the disk surface, then the disk must be confined primarily by magnetic stresses rather than by the tidal field of the central object. Most of the disk material in a self-consistent solution is in quasi-hydrostatic equilibrium, with the thermal pressure gradient balancing the magnetic squeezing. In this region the field is dragged around by the matter, and the magnetic stresses act to remove angular momentum from the inflowing neutral gas and to slow it to sub-Keplerian rotation speeds. As the gas density falls off with height, the field comes to dominate the energy density and the field lines behave like rigid wires that are carried around by the material in the disk. Eventually a point is reached where the relative azimuthal speed between the field lines and the neutrals vanishes and the disk becomes Keplerian. We identify this point as the base of the wind and derive a condition on the magnetic field at this location that generalizes the Blandford & Payne criterion for centrifugal acceleration from the disk surface. Beyond this point the field transfers angular momentum back to the matter and drives it out and away from the disk. The solution exhibits a sonic transition close to the surface of the disk and can in principle be extended into a large-scale wind solution that remains valid at greater heights. We examine how our solutions are affected by a slow radial diffusion of the field lines and by electron-ion drift (corresponding to the Hall term in the generalized Ohm's law). We also discuss the expected stability properties of the disks and the construction of global disk-wind solutions. We argue that disk-driven outflows of this type offer an attractive explanation of bipolar flows in young stellar objects, and we show how our solutions can in principle be used to relate the properties of these outflows to those of the associated circumstellar disks. Finally, we point out that our model may also be applicable to other cosmic outflow sources, notably active galactic nuclei.

Original languageEnglish
Pages (from-to)218-238
Number of pages21
JournalAstrophysical Journal
Issue number1
Publication statusPublished - 10 Jun 1993
Externally publishedYes


  • Accretion, accretion disks
  • ISM: jets and outflows
  • MHD
  • Stars: mass loss


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