The distribution of density in supersonic turbulence
  We propose a model for the density statistics in supersonic turbulence, which
play a crucial role in star-formation and the physics of the interstellar
medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model
considers the density to be arranged into a collection of strong shocks of
width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach
number. With two physically motivated parameters, the model predicts all
density statistics for $\mathcal{M}>1$ turbulence: the density probability
distribution and its intermittency (deviation from log-normality), the density
variance-Mach number relation, power spectra, and structure functions. For the
proposed model parameters, reasonable agreement is seen between model
predictions and numerical simulations, albeit within the large uncertainties
associated with current simulation results. More generally, the model could
provide a useful framework for more detailed analysis of future simulations and
observational data. Due to the simple physical motivations for the model in
terms of shocks, it is straightforward to generalize to more complex physical
processes, which will be helpful in future more detailed applications to the
ISM. We see good qualitative agreement between such extensions and recent
simulations of non-isothermal turbulence.
