Determining Star Formation Thresholds from Observations
  Most gas in giant molecular clouds is relatively low-density and forms star
inefficiently, converting only a small fraction of its mass to stars per
dynamical time. However, star formation models generally predict the existence
of a threshold density above which the process is efficient and most mass
collapses to stars on a dynamical timescale. A number of authors have proposed
observational techniques to search for a threshold density above which star
formation is efficient, but it is unclear which of these techniques, if any,
are reliable. In this paper we use detailed simulations of turbulent,
magnetised star-forming clouds, including stellar radiation and outflow
feedback, to investigate whether it is possible to recover star formation
thresholds using current observational techniques. Using mock observations of
the simulations at realistic resolutions, we show that plots of projected star
formation efficiency per free-fall time $\epsilon_{\rm ff}$ can detect the
presence of a threshold, but that the resolutions typical of current dust
emission or absorption surveys are insufficient to determine its value. In
contrast, proposed alternative diagnostics based on a change in the slope of
the gas surface density versus star formation rate surface density
(Kennicutt-Schmidt relation) or on the correlation between young stellar object
counts and gas mass as a function of density are ineffective at detecting
thresholds even when they are present. The signatures in these diagnostics
sometimes taken as indicative of a threshold in observations, which we
generally reproduce in our mock observations, do not prove to correspond to
real physical features in the 3D gas distribution.
