2009/09/13 by A. Königl, Arieh Königl, Raquel Salmeron +2 · 57 citations
Physics and Astronomy · #Accretion (finance) #Ambipolar diffusion #Angular momentum #Astrophysical Phenomena and Observations #Astrophysics #Astrophysics and Star Formation Studies #Classical mechanics #Computational physics #Diffusion #Magnetic field #Magnetohydrodynamics #Ohm's law #Physics #Plasma #Quantum mechanics #Stellar, planetary, and galactic studies #astro-ph.SR
paper · pdf · doi:10.1111/j.1365-2966.2009.15664.x
published in Monthly Notices of the Royal Astronomical Society 401(1), 479-499 (Oxford University Press) · 23 pages, 2 figures, 4 tables; accepted for publication in MNRAS
arxiv created 2009/09/13 · openalex publication_date 2009/11/03 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study a model of weakly ionized, protostellar accretion discs that are threaded by a large-scale, ordered magnetic field and power a centrifugally driven wind. We consider the limiting case where the wind is the main repository of the excess disc angular momentum and generalize the radially localized disc model of Wardle & Königl, which focused on the ambipolar diffusion regime, to other field diffusivity regimes, notably Hall and Ohm. We present a general formulation of the problem for nearly Keplerian, vertically isothermal discs using both the conductivity-tensor and the multifluid approaches and simplify it to a normalized system of ordinary differential equations in the vertical space coordinate. We determine the relevant parameters of the problem and investigate, using the vertical-hydrostatic-equilibrium approximation and other simplifications, the parameter constraints on physically viable solutions for discs in which the neutral particles are dynamically well coupled to the field already at the mid-plane. When the charged particles constitute a two-component ion–electron plasma, one can identify four distinct sub-regimes in the parameter domain where the Hall diffusivity dominates and three sub-regimes in the Ohm-dominated domain. Two of the Hall sub-regimes can be characterized as being ambipolar diffusion-like and two as being Ohm-like: the properties of one member of the first pair of sub-regimes are identical to those of the ambipolar diffusion regime, whereas one member of the second pair has the same characteristics as one of the Ohm sub-regimes. All the Hall sub-regimes have Brb/|Bφb| (ratio of radial-to-azimuthal magnetic field amplitudes at the disc surface) >1, whereas in two Ohm sub-regimes this ratio is <1. When the two-component plasma consists, instead, of positively and negatively charged grains of equal mass, the entire Hall domain and one of the Ohm sub-regimes with Brb/|Bφb| < 1 disappear. All viable solutions require the mid-plane neutral–ion momentum exchange time to be shorter than the local orbital time. We also infer that vertical magnetic squeezing always dominates over gravitational tidal compression in this model. In a follow-up paper we will present exact solutions that test the results of this analysis in the Hall regime.