The formation process of circumstellar disks is still controversial because of the interplay of complex physical processes that occurs during the gravitational collapse of prestellar cores. In this study, we investigate the effect of the Hall current term on the formation of the circumstellar disk using three- dimensional simulations. In our simulations, all non-ideal effects as well as the radiation transfer are considered. The size of the disk is significantly affected by a simple difference in the inherent properties of the prestellar core, namely whether the rotation vector and the magnetic field are parallel or anti- parallel. In the former case, only a very small disk (< 1 AU) is formed. On the other hand, in the latter case, a massive and large (> 20 AU) disk is formed in the early phase of protostar formation. Since the parallel and anti-parallel properties do not readily change, we expect that the parallel and anti-parallel properties are also important in the subsequent disk evolution and the difference between the two cases is maintained or enhanced. This result suggests that the disk size distribution of the Class 0 young stellar objects is bimodal. Thus, the disk evolution can be categorized into two cases and we may call the parallel and anti-parallel systems as Ortho-disk and Para-disk, respectively. We also show that the anti-rotating envelopes against the disk-rotation appear with a size of 200 AU. We predict that the anti-rotating envelope will be found in the future observations.
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