Magnetically self-regulated formation of early protoplanetary discs
  The formation of protoplanetary discs during the collapse of molecular dense
cores is significantly influenced by angular momentum transport, notably by the
magnetic torque. In turn, the evolution of the magnetic field is determined by
dynamical processes and non-ideal MHD effects such as ambipolar diffusion.
Considering simple relations between various timescales characteristic of the
magnetized collapse, we derive an expression for the early disc radius, $ r
\simeq 18 \, {\rm AU} \, \left({\eta_{\rm AD} / 0.1 \, {\rm s}} \right)^{2/9}
\left({B_z / 0.1\, {\rm G}} \right) ^{-4/9} \left({M / 0.1 \msol} \right)
^{1/3},$ where $M$ is the total disc plus protostar mass, $\eta_\mathrm{AD}$ is
the ambipolar diffusion coefficient and $B_z$ is the magnetic field in the
inner part of the core. This is about significantly smaller than the discs that
would form if angular momentum was conserved.
  The analytical predictions are confronted against a large sample of 3D,
non-ideal MHD collapse calculations covering variations of a factor 100 in core
mass, a factor 10 in the level of turbulence, a factor 5 in rotation, and
magnetic mass-to-flux over critical mass-to-flux ratios 2 and 5. The disc
radius estimates are found to agree with the numerical simulations within less
than a factor 2.
  A striking prediction of our analysis is the weak dependence of circumstellar
disc radii upon the various relevant quantities, suggesting weak variations
among class-0 disc sizes. In some cases, we note the onset of large spiral arms
beyond this radius.
