Magnetic fields in giant planet formation and protoplanetary discs

Protoplanetary discs channel accretion onto their host star. How this is achieved is critical to the growth of giant planets which capture their massive gaseous atmosphere from the surrounding flow. Theoretical studies find that an embedded magnetic field could power accretion by hydromagnetic turbulence or torques from a large-scale field. This thesis presents a study of the inuence of magnetic fields in three key aspects of this process: circumplanetary disc accretion, gas flow across gaps in protoplanetary discs, and magnetic-braking in accretion discs. The first study examines the conditions needed for self-consistent accretion driven by magnetic fields or gravitational instability. Models of these discs typically rely on hydromagnetic turbulence as the source of effective viscosity. However, magnetically coupled,accreting regions may be so limited that the disc may not support sufficient inflow. An improved Shakura-Sunyaev α disc is used to calculate the ionisation fraction and strength of non-ideal effects. Steady magnetically-driven accretion is limited to the thermally ionised, inner disc so that accretion in the remainder of the disc is time-dependent. The second study addresses magnetic flux transport in an accretion gap evacuated by a giant planet. Assuming the field is passively drawn along with the gas, the hydrodynamical simulation of Tanigawa, Ohtsuki & Machida (2012) is used for an a posteriori analysis of the gap field structure. This is used to post-calculate magnetohydrodynamical quantities. This assumption is self-consistent as magnetic forces are found to be weak, and good magnetic coupling ensures the field is frozen into the gas. Hall drift dominates across much of the gap, with the potential to facilitate turbulence and modify the toroidal field according to the global field orientation. The third study considers the structure and stability of magnetically-braked accretion discs. Strong evidence for MRI dead-zones has renewed interest in accretion powered by large-scale fields. An equilibrium model is presented for the radial structure of an axisymmetric, magnetically-braked accretion disc connected to a force-free external field. The accretion rate is multivalued at protoplanetary disc column densities, featuring an `S-curve' associated with models of accretion outbursting. A local, linear analysis of the stability of radial modes finds that the rapidly accreting, middle and upper solution branches are unstable, further highlighting the potential for eruptive accretion events.