Protostellar disc structure and dynamics during star formation from cloud-scale initial conditions

The early evolution of protostellar, star-forming discs, including their density structure, turbulence, magnetic dynamics, and accretion variability, remains poorly understood. We present high-resolution magnetohydrodynamic simulations, using adaptive mesh refinement to capture detailed disc dynamics down to sub-AU scales. Starting from initial conditions derived from a molecular cloud simulation, we model the collapse of a dense core into a protostellar disc over 10,000 yr following sink particle (star) formation, achieving a maximum effective resolution of 0.63 AU. This simulation traces the evolution of the disc density, accretion rates, turbulence, and magnetic field structures. We find that the protostellar disc grows to a diameter of approximately 100 AU, with mass accretion occurring in episodic bursts influenced by the turbulence of the core from which the disc builds up. The disc is highly turbulent with a sonic Mach number of $\sim2$. Episodic accretion events within the disc cause intermittent increases in mass and magnetic energy density, resulting in an equipartition of the thermal and magnetic pressure, i.e., leading to an Alfv\'en Mach number of $\sim2$. Some regions above and below the disc mid-plane show sub-Alfv\'enic conditions with intermittent outflow activity. The disc density profiles steepen over time, following a power law consistent with observed young stellar discs and the minimum mass solar nebula. These results underscore the role of turbulence in early accretion variability and offer new insights into the physical and magnetic structure of young protostellar discs, especially with respect to their turbulent components.