We study the rotational properties of magnetized and self-gravitating molecular cloud cores formed in 2 very high resolution 3D molecular cloud simulations.The simulations have been performed using the code RAMSES at an effective resolution of 4096^3.One simulation represents a mildly magnetically-supercritical cloud and the other a strongly magnetically-supercritical cloud.A noticeable difference between the 2 simulations is the core formation efficiency (CFE) of the high density cores.In the strongly supercritical simulations the CFE is ~33 % per free-fall time of the cloud tff,cl, whereas in the mildly supercritical simulations this value goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular momentum j3D distributions of the cores with the distribitions of j2D derived using synthetic 2D velocity maps of the cores,shows that the synthetic observations tend to overestimate the true value of j by a factor of ~10.The origin of this discrepancy lies in the fact that contrary to the intrinsic determination which sums up the individual gas parcels contributions to j, the determination of j using the observational procedure which is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation smoothes out the complex fluctuations present in the 3D velocity field. Our results provide a natural explanation for the discrepancy by a factor ~10 observed between the intrinsic 3D distributions of j and the corresponding distributions derived in real observations.We suggest that measurements of j which are based on the measurement of the observed global velocity gradients may need to be reduced by a factor of ~10 in order to derive a more accurate estimate of j in the cores.
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