Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary disks. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface. Magnetically-driven mixing has implications for disk chemistry and evolution of the grain population, and the effective viscous response of the disk determines whether planets migrate inwards or outwards. However, the weak ionisation of protoplanetary disks means that magnetic fields may not be able to effectively couple to the matter. I examine the magnetic diffusivity in a minimum solar nebula model and present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas, except at the disk surfaces where the low density of neutrals permits the ions to remain attached to the field lines. For a standard population of 0.1 mu m grains the active surface layers have a combined column Sigma(active) approximate to 2 g cm(-2) at 1 AU; by the time grains have aggregated to 3 mu m, Sigma(active) approximate to 2 g cm(-2). Ionisation in the active layers is dominated by stellar X- rays. In the absence of grains, X- rays maintain magnetic coupling to 10% of the disk material at 1 AU ( i. e. Sigma(active) approximate to 150 g cm(-2)). At 5 AU the Sigma(active) approximate to Sigma(total) once grains have aggregated to 1 mu m in size.