Collapse in Self-gravitating Turbulent Fluids
  Motivated by the nonlinear star formation efficiency found in recent
numerical simulations by a number of workers, we perform high-resolution
adaptive mesh refinement simulations of star formation in self-gravitating
turbulently driven gas. As we follow the collapse of this gas, we find that the
character of the flow changes at two radii, the disk radius $r_d$, and the
radius $r_*$ where the enclosed gas mass exceeds the stellar mass. Accretion
starts at large scales and works inwards. In line with recent analytical work,
we find that the density evolves to a fixed attractor, $\rho(r,t ) \rightarrow
\rho(r)$, for $r_d<r<r_*$; mass flows through this structure onto a
sporadically gravitationally unstable disk, and from thence onto the star. In
the bulk of the simulation box we find that the random motions $v_T \sim r^p$
with $p \sim 0.5$, in agreement with Larson's size-linewidth relation. In the
vicinity of massive star forming regions we find $ p \sim 0.2-0.3$, as seen in
observations. For $r<r_*$, $v_T$ increases inward, with $p=-1/2$. Finally, we
find that the total stellar mass $M_*(t)\sim t^2$ in line with previous
numerical and analytic work that suggests a nonlinear rate of star formation.
