Effects of Ohmic and ambipolar diffusion on the formation and evolution of the first cores, protostars and circumstellar discs

We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $\beta$ of the centre of the first core becomes large, $\beta>10^4$. Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, $\beta\sim 10$ at the centre of the first core. The simulations with magnetic diffusion show that the circumstellar disc forms at almost the same time of protostar formation even with a relatively strong initial magnetic field (the value for the initial mass-to-flux ratio of the cloud core relative to the critical value is $\mu=4$). The disc has a radius of $r \sim 1$ AU at the protostar formation epoch. We confirm that the disc is rotationally supported. We also show that the disc is massive ($Q\sim 1$) and that gravitational instability may play an important role in the subsequent disc evolution.