Magnetic field dragging in accretion discs
Abstract
We consider a thin accretion disc of halfthickness H, vertically threaded by a magnetic field. The field is due to contributions from both the disc current and an external current (giving rise to a uniform external field). We derive an integrodifferential equation for the evolution of the magnetic field, subject to magnetic diffusivity eta and disc accretion with radial velocity nu_{r}. The evolution equation is solved numerically, and a steady state is reached. The evolution equation depends upon a single, dimensionless parameter D = 2 eta/(3 H absolute value of nu_{r}) = (R/H) (eta/v), where the latter equality holds for a viscous disc having viscosity v. At the disc surface, field lines are bent by angle i from the vertical, such that tan i = 1.52 D^{1}. For values of D somewhat less than unity, the field is strongly concentrated towards the disc center, because the field lines are dragged substantially inwards.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 March 1994
 DOI:
 10.1093/mnras/267.2.235
 Bibcode:
 1994MNRAS.267..235L
 Keywords:

 Accretion Disks;
 Interstellar Matter;
 Magnetic Diffusion;
 Magnetic Field Configurations;
 Stellar Magnetic Fields;
 Stellar Mass Accretion;
 Computational Astrophysics;
 Differential Equations;
 Integral Equations;
 Magnetohydrodynamics;
 Time Dependence;
 Astrophysics