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 (LN) and power-law (PL) form. This is in contrast to previous analytic SFR models that are governed primarily by interstellar turbulence, which sets purely LN density probability distribution functions (PDFs). In the gravoturbulent SFR model described herein, low-density gas resides in the LN portion of the PDF. Gas becomes gravitationally unstable past a critical density (rho(crit)), and the PDF begins to form a PL. As the collapse of the cloud proceeds, the transitional density (rho(t)) between the LN and PL portions of the PDF moves toward lower density while the slope of the PL (alpha) becomes increasingly shallow. The SFR per free-fall time is calculated via an integral over the LN from rho(crit) to rho(t) and an integral over the PL from rho(t) to the maximum density. As a becomes shallower, the SFR accelerates beyond the expected values calculated from an LN density PDF. We show that the star formation efficiency per free-fall time in observations of local molecular clouds increases with shallower PDF PL 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.