Decoupling of magnetic fields in collapsing protostellar envelopes and disc formation and fragmentation

Efficient magnetic braking is a formidable obstacle to the formation of rotationally supported discs (RSDs) around protostars in magnetized dense cores. We have previously shown, through 2D (axisymmetric) non-ideal magnetohydrodynamic simulations, that removing very small grains (VSGs: similar to 10 angstrom to few 100 angstrom) can greatly enhance ambipolar diffusion and enable the formation of RSDs. Here, we extend the simulations of disc formation enabled by VSG removal to 3D. We find that the key to this scenario of disc formation is that the drift velocity of the magnetic field almost cancels out the infall velocity of the neutrals in the 10(2)-10(3) au scale 'pseudo-disc' where the field lines are most severely pinched and most of protostellar envelope mass infall occurs. As a result, the bulk neutral envelope matter can collapse without dragging much magnetic flux into the disc-forming region, which lowers the magnetic braking efficiency. We find that the initial discs enabled by VSG removal tend to be Toomre-unstable, which leads to the formation of prominent spiral structures that function as centrifugal barriers. The piling-up of infall material near the centrifugal barrier often produces dense fragments of tens of Jupiter masses, especially in cores that are not too strongly magnetized. Some fragments accrete on to the central stellar object, producing bursts in mass accretion rate. Others are longer lived, although whether they can survive for a long term to produce multiple systems remains to be ascertained. Our results highlight the importance of dust grain evolution in determining the formation and properties of protostellar discs and potentially multiple systems.