Magnetic fields in gaps surrounding giant protoplanets

Giant protoplanets evacuate a gap in their host protoplanetary disc, which gas must cross before it can be accreted. A magnetic field is likely carried into the gap, potentially influencing the flow. Gap crossing has been simulated with varying degrees of attention to field evolution [pure hydrodynamical, ideal, and resistive magnetohydrodynamical (MHD)], but as yet there has been no detailed assessment of the role of the field accounting for all three key non-ideal MHD effects: Ohmic resistivity, ambipolar diffusion, and Hall drift. We present a detailed investigation of gap magnetic field structure as determined by non-ideal effects. We assess susceptibility to turbulence induced by the magnetorotational instability (MRI) and angular momentum loss from large-scale fields. As full non-ideal simulations are computationally expensive, we take an a posteriori approach, estimating MHD quantities from the pure hydrodynamical gap-crossing simulation by Tanigawa, Ohtsuki & Machida. We calculate the ionization fraction and estimate field strength and geometry to determine the strength of non-ideal effects. We find that the protoplanetary disc field would be easily drawn into the gap and circumplanetary disc. Hall drift dominates, so that much of the gap is conditionally MRI unstable depending on the alignment of the field and disc rotation axes. Field alignment also influences the strong toroidal field component permeating the gap. Large-scale magnetic forces are small in the circumplanetary disc, indicating that they cannot drive accretion there. However, turbulence will be key during satellite growth as it affects critical disc features, such as the location of the ice line.