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Context: Ideal MHD simulations have revealed catastrophic magnetic braking(MB) in the protostellar phase, which prevents the formation of a centrifugaldisk around a nascent protostar. Aims: We determine if non-ideal MHD, includingthe effects of ambipolar diffusion and Ohmic dissipation determined from adetailed chemical network model, allows for disk formation at the earlieststages of star formation (SF). Methods: We employ the axisymmetric thin-diskapproximation in order to resolve a dynamic range of 9 orders of magnitude inlength and 16 in density, while also calculating partial ionization using up to19 species in a detailed chemical equilibrium model. MB is applied using asteady-state approximation, and a barotropic relation is used to capture thethermal evolution. Results: We resolve the formation of the first and secondcores, with expansion waves at the periphery of each, a magnetic diffusionshock, and prestellar infall profiles at larger radii. Power-law profiles ineach region can be understood analytically. After the formation of the secondcore, centrifugal support rises rapidly and a low-mass disk of radius ~10 R_Sunis formed, when the second core has mass ~0.001 M_Sun. The mass-to-flux ratiois ~10,000 times the critical value in the central region. Conclusions: A smallcentrifugal disk can form in the earliest stage of SF, due to a shut-off of MBcaused by magnetic field dissipation in the first core region. There is enoughangular momentum loss to allow the second collapse to occur directly, and alow-mass stellar core to form with a surrounding disk. The disk mass and sizewill depend upon how the angular momentum transport mechanisms within the diskcan keep up with mass infall onto the disk. We estimate that the disk willremain <~10 AU, undetectable even by ALMA, in the early Class 0 phase.

Bridging the gap: disk formation in the Class 0 phase with ambipolar diffusion and Ohmic dissipation