The density distribution and the physical origins of density
  intermittency in sub- to trans-Alfvenic supersonic turbulence
  The probability density function (PDF) of the logarithmic density contrast,
$s=\ln (\rho/\rho_0)$, with gas density $\rho$ and mean density $\rho_0$, for
hydrodynamical supersonic turbulence is well-known to have significant
signatures of intermittency that monotonically increase with the turbulent Mach
number, $\M$. By studying the mass- and volume-weighted $s$-PDF for an ensemble
of 16 sub- to trans-Alf\'venic mean-field, supersonic, isothermal turbulence
simulations, relevant to molecular gas in the cool interstellar medium, we show
that a more intricate picture emerges for the intermittency of $s$. Using four
independent measures of the intermittency we find hydrodynamical-like
intermittency in the highly magnetised plasma for $\mathcal{M} \lesssim 4$.
However, for $\mathcal{M} \gtrsim 4$, the signatures of intermittency
disappear, leaving approximately lognormal $s$-statistics -- exactly the
opposite of hydrodynamical turbulence in the high-$\mathcal{M}$ limit. To
understand the $\mathcal{M} \lesssim 4$ intermittency we use one-dimensional
(1D) pencil beams to explore the dynamics along and across the mean magnetic
field, $\mathbf{B}_0$. We discuss kinetic, density and magnetic field
fluctuations from the pencil beams, and identify physical sources of
intermittency as single, strong shocks coupled to fast magnetosonic
compressions that form along $\Bo$ and create large, volume-poor
under-densities. These under-densities contribute significantly to the skewness
of the $s$-PDF. We confirm this result independently using 1D fluid shock
simulations. We discuss the Gaussianisation of the $\mathcal{M} \gtrsim 4$
$s$-fields through the lens of two phenomenologies: the self-similarity of the
$s$-field and homogenisation of the dynamical timescales between the over- and
under-dense regions in the compressible gas.
