Hall effect-driven formation of gravitationally unstable discs in magnetized molecular cloud cores

We demonstrate the formation of gravitationally unstable discs in magnetized molecular cloud cores with initial mass-to-flux ratios of 5 times the critical value, effectively solving the magnetic braking catastrophe. We model the gravitational collapse through to the formation of the stellar core, using Ohmic resistivity, ambipolar diffusion and the Hall effect and using the canonical cosmic ray ionization rate of $\zeta_\text{cr} = 10^{-17}$ s$^{-1}$. When the magnetic field and rotation axis are initially aligned, a $\lesssim1$~au disc forms after the first core phase, whereas when they are anti-aligned, a gravitationally-unstable 25~au disc forms during the first core phase. The aligned model launches a 3~km~s$^{-1}$ first core outflow, while the anti-aligned model launches only a weak $\lesssim 0.3$~km~s$^{-1}$ first core outflow. Qualitatively, we find that models with $\zeta_\text{cr} = 10^{-17}$ s$^{-1}$ are similar to purely hydrodynamical models if the rotation axis and magnetic field are initially anti-aligned, whereas they are qualitatively similar to ideal magnetohydrodynamical models if initially aligned.