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.
