Star formation and the Hall Effect

Magnetic fields play an important role in star formation by regulating the removal of angular momentum from collapsing molecular cloud cores. Hall diffusion is known to be important to the magnetic field behaviour at many of the intermediate densities and field strengths encountered during the gravitational collapse of molecular cloud cores into protostars, and yet its role in the star formation process is not well-studied. This thesis describes a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, presenting similarity solutions that demonstrate that the Hall effect has a profound influence on the dynamics of collapse. Two asymptotic power law similarity solutions to the collapse equations on the inner boundary are derived. The first of these represents a Keplerian disc in which accretion is regulated by the magnetic diffusion; with an appropriate value of the Hall diffusion parameter a stable rotationally-supported disc forms, but when the Hall parameter has the opposite sign disc formation is suppressed by the strong diffusion. The second solution describes the infall when the magnetic braking is so efficient at removing angular momentum from the core that no disc forms and the matter free falls onto the protostar. The full similarity solutions show that the size and sign of the Hall parameter can change the size of the protostellar disc by up to an order of magnitude and the accretion rate onto the protostar by 1.5 x 10 [superscript] -6 M [subscript circle with dot] yr [superscript] -1 when the ratio of the Hall to ambipolar diffusion parameters moves between the extremes of -0.5 [le] tilde eta H / tilde eta A [le] 0.2. These variations (and their dependence upon the orientation of the magnetic field with respect to the axis of rotation) create a preferred handedness to the solutions that could be observed in protostellar cores using next-generation instruments such as ALMA. Hall diffusion also determines the strength of the magnetic diffusion and centrifugal shocks that bound the pseudo and rotationally-supported discs, and can introduce subshocks that further slow accretion onto the protostar. In cores that are not initially rotating Hall diffusion can even induce rotation, which could give rise to disc formation and resolve the magnetic braking catastrophe. The Hall effect clearly influences the dynamics of gravitational collapse and its role in controlling the magnetic braking and radial diffusion of the field would be worth exploring in future numerical simulations of star formation.