The Origin of the Rotation Profiles in Star Forming Clouds

Angular momentum distribution and its redistribution are of crucial importance in formation and evolution of circumstellar disks. Many molecular line observations toward young stellar objects indicate that radial distributions of the specific angular momentum $j$ are more or less universal. In small scales, typically $R\lesssim$ 100 AU, the specific angular momenta distribute like $j\propto r^{1/2}$, indicating existence of rotationally supported disk. In outer regions, $R\gtrsim$ 5000 AU, $j$ increases as the radius increases and the slope is steeper than unity, which is supposed to reflect the original angular momentum distributions in the maternal molecular clouds. And lastly there is a connecting region, 100 AU $\lesssim R \lesssim$ 5000 AU, in which $j$-distribution looks almost flat. While this is often interpreted as a consequence of conservation of the specific angular momentum, it actually is insufficient and requires a stronger condition that the initial distribution of $j$ must be spatially uniform. However, this requirement is unrealistic and inconsistent with observations. In this work, we propose a simple alternative explanation; the flat $j$ profile is produced by strong prolongation due to the large velocity gradient in the accreting flow no matter what the initial $j$ distribution is. We provide a simple analytic model for gravitational collapse of molecular clouds. This model can be used to estimate ages of protostars based solely on the observed rotation profile. We demonstrate its validity in comparison with hydrodynamic simulations, and apply the model to young stellar objects such as L1527 IRS, TMC-1A and B335.