MAGNETIC-FIELD DRAGGING IN ACCRETION DISKS

We consider a thin accretion disc of half-thickness 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 integro-differential equation for the evolution of the magnetic field, subject to magnetic diffusivity eta and disc accretion with radial velocity upsilon(r). The evolution equation is solved numerically, and a steady state is reached. The evolution equation depends upon a single, dimensionless parameter D = 2eta/(3H\upsilon(r)\ = (R/H)(eta/upsilon), where the latter equality holds for a viscous disc having viscosity upsilon. At the disc surface, field tines 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 centre, because the field lines are dragged substantially inwards.