The sonic scale revealed by the world's largest supersonic turbulence
  simulation
  Understanding the physics of turbulence is crucial for many applications,
including weather, industry, and astrophysics. In the interstellar medium
(ISM), supersonic turbulence plays a crucial role in controlling the gas
density and velocity structure, and ultimately the birth of stars. Here we
present a simulation of interstellar turbulence with a grid resolution of
10048^3 cells that allows us to determine the position and width of the sonic
scale (l_s) - the transition from supersonic to subsonic turbulence. The
simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~
l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02,
respectively. We find that l_s agrees with the relation l_s / L = phi_s
Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is
either the driving scale of turbulence or the diameter of a molecular cloud. If
L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily
because of the separation between the driving scale and the start of the
supersonic cascade. For a supersonic cascade extending beyond the cloud scale,
we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find
that the supersonic cascade transitions smoothly to the subsonic cascade over a
factor of 3 in scale, instead of a sharp transition. Our measurements provide
quantitative input for turbulence-regulated models of filament structure and
star formation in molecular clouds.
