The origin of rotation profiles in star-forming clouds

The angular momentum distribution and its redistribution are of crucial importance in the formation and evolution of circumstellar discs. Many molecular line observations towards young stellar objects indicate that the radial distributions of the specific angular momentum j have a characteristic profile. In the inner region, typically R ≲ 100 au, the specific angular momenta distribute as j ∝ r^1/2, indicating the existence of a rotationally supported disc. In the outer regions, R ≳ 5000 au, j increases as the radius increases, and the slope is steeper than unity. This behaviour is assumed to reflect the original angular momentum distributions in the maternal molecular clouds. In the intermediate region, 100 au ≲ R ≲ 5000 au, the jdistribution appears to be almost flat. While this is often interpreted to be a consequence of the conservation of the specific angular momentum, the interpretation actually is insufficient and requires a stronger condition that the initial distribution of j must be spatially uniform. However, this requirement seems to be unrealistic and inconsistent with observations. In this work, we propose a simple alternative explanation: the apparently flat j profile is produced by strong elongation owing to the large velocity gradient in the accreting flow, no matter what the initial j-distribution is. In order to show this, we provide a simple analytic model for the gravitational collapse of molecular clouds. We also propose a method to estimate the ages of protostars using only the observed rotation profile. We demonstrate the validity of this method in comparison with hydrodynamic simulations, and apply the model to the young stellar objects L1527 IRS, TMC-1A and B335.