Disc formation in turbulent cloud cores: is magnetic flux loss necessary to stop the magnetic braking catastrophe or not?

Recent numerical analysis of Keplerian disk formation in turbulent, magnetized cloud cores by Santos-Lima, de Gouveia Dal Pino, & Lazarian (2012) demonstrated that reconnection diffusion is an efficient process to remove the magnetic flux excess during the build up of a rotationally supported disk. This process is induced by fast reconnection of the magnetic fields in a turbulent flow. In a similar numerical study, Seifried et al. (2012) concluded that reconnection diffusion or any other non-ideal MHD effects would not be necessary and turbulence shear alone would provide a natural way to build up a rotating disk without requiring magnetic flux loss. Their conclusion was based on the fact that the mean mass-to-flux ratio ({\mu}) evaluated over a spherical region with a radius much larger than the disk is nearly constant in their models. In this letter we compare the two sets of simulations and show that this averaging over large scales can mask significant real increases of {\mu} in the inner regions where the disk is built up. We demonstrate that turbulence-induced reconnection diffusion of the magnetic field happens in the initial stages of the disk formation in the turbulent envelope material that is accreting. Our analysis is suggestive that reconnection diffusion is present in both sets of simulations and provides a simple solution for the "magnetic braking catastrophe" which is discussed in the literature in relation to the formation of protostellar accretion disks.