The Star Formation Rate in the Gravoturbulent Interstellar Medium
  Stars form in supersonic turbulent molecular clouds that are
self-gravitating. We present an analytic determination of the star formation
rate (SFR) in a gravoturbulent medium based on the density probability
distribution function of molecular clouds having a piecewise lognormal and
power law form. This is in contrast to previous analytic SFR models that are
governed primarily by interstellar turbulence which sets purely lognormal
density PDFs. In the gravoturbulent SFR model described herein, low density gas
resides in the lognormal portion of the PDF. Gas becomes gravitationally
unstable past a critical density ($\rho_{crit}$), and the PDF begins to forms a
power law. As the collapse of the cloud proceeds, the transitional density
($\rho_t$) between the lognormal and power law portions of the PDF moves
towards lower-density while the slope of the power law ($\alpha$) becomes
increasingly shallow. The star formation rate per free-fall time is calculated
via an integral over the lognormal from $\rho_{crit}$ to $\rho_t$ and an
integral over the power law from $\rho_t$ to the maximum density. As $\alpha$
becomes shallower the SFR accelerates beyond the expected values calculated
from a lognormal density PDF. We show that the star formation efficiency per
free fall time in observations of local molecular cloud increases with
shallower PDF power law slopes, in agreement with our model. Our model can
explain why star formation is spatially and temporally variable within a cloud
and why the depletion times observed in local and extragalactic giant molecular
clouds vary. Both star-bursting and quiescent star-forming systems can be
explained without the need to invoke extreme variations of turbulence in the
local interstellar environment.
