The Star Formation Rate in the Gravoturbulent Interstellar Medium

Abstract

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 (ρ crit ), and the PDF begins to forms a power law. As the collapse of the cloud proceeds, the transitional density (ρ t ) between the lognormal and power law portions of the PDF moves towards lower-density while the slope of the power law (α) becomes increasingly shallow. The star formation rate per free-fall time is calculated via an integral over the lognormal from ρ crit to ρ t and an integral over the power law from ρ t to the maximum density. As α 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.

Dense gas is not enough: environmental variations in the star formation efficiency of dense molecular gas at 100 pc scales in M 51

“…At fixed molecular gas surface density, this model would imply an exponentially decreasing SFE as a function of velocity dispersion, which might be in agreement with our observations; other numerical simulations and models have also found a decreasing trend between SFE and σ (e.g. Bertram et al 2015;Burkhart 2018).…”

Star Clusters Across Cosmic Time

“…The earliest version of such an argument appeared in Krumholz & McKee (2005), but this has been superseded by numerous later works that model the density PDF and the evolution of its self-gravitating parts with increasing accuracy ( The consensus of recent models is that turbulence does substantially reduce ff , but not all the way to ff ≈ 0.01 as required by the observations. As time goes by the density PDF of a self-gravitating cloud deviates develops an increasingly-prominent power-law tail on its high-density end that causes ff to rise with time (Murray & Chang 2015;Burkhart 2018). This density build-up is most likely counteracted by localized feedback processes that break up high-density regions and suppress the growth of the power-law tail; the most likely mechanism for this is protostellar outflows, since stars begin to launch outflows as soon as they form, and even low-mass stars can produce significant outflow feedback.…”

The Origin of Massive Stars: The Inertial-inflow Model

“…Analytical models of turbulent fragmentation have been developed with the common goal of converting a statisti-cal description of supersonic turbulence into a statistical theory of star formation that inherits the universal nature of the turbulence. Both the stellar initial mass function (IMF) Hennebelle & Chabrier 2008a;Hopkins 2012) and the star-formation rate (SFR) (Krumholz & McKee 2005;Padoan & Nordlund 2011b;Federrath & Klessen 2012;Burkhart 2018) have been modeled following this approach. In this work, the formation of massive stars is conceived in the context of our own turbulent-fragmentation model of the IMF , 2011a, where prestellar cores are assembled by the turbulence through the compression of regions of inertial-range scale that are not required to be gravitationally bound.…”