| Abstract
| - Context. Ideal magnetohydrodynamical (MHD) simulations have revealed catastrophic magnetic braking in the protostellar phase, which prevents the formation of a centrifugal disk around a nascent protostar. Aims. We determine if non-ideal MHD, including the effects of ambipolar diffusion and Ohmic dissipation determined from a detailed chemical network model, will allow for disk formation at the earliest stages of star formation. Methods. We employ the axisymmetric thin-disk approximation in order to resolve a dynamic range of 9 orders of magnitude in length and 16 orders of magnitude in density, while also calculating partial ionization using up to 19 species in a detailed chemical equilibrium model. Magnetic braking is applied to the rotation using a steady-state approximation, and a barotropic relation is used to capture the thermal evolution. Results. We resolve the formation of the first and second cores, with expansion waves at the periphery of each, a magnetic diffusion shock, and prestellar infall profiles at larger radii. Power-law profiles in each region can be understood analytically. After the formation of the second core, the centrifugal support rises rapidly and a low-mass disk of radius ≈ 10 R⊙ is formed at the earliest stage of star formation, when the second core has mass ~10 -3M⊙. The mass-to-flux ratio is ~10 4 times the critical value in the central region. Conclusions. A small centrifugal disk can form in the earliest stage of star formation, due to a shut-off of magnetic braking caused by magnetic field dissipation in the first core region. There is enough angular momentum loss to allow the second collapse to occur directly, and a low-mass stellar core to form with a surrounding disk. The disk mass and size will depend upon how the angular momentum transport mechanisms within the disk can keep up with mass infall onto the disk. Accounting only for direct infall, we estimate that the disk will remain ≲10 AU, undetectable even by ALMA, for ≈ 4 × 10 4 yr, representing the early Class 0 phase.
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