The sonic scale of interstellar turbulence

Understanding the physics of turbulence is crucial for many applications, including weather, industry and astrophysics. In the interstellar medium1,2, supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars3-8. Here we present a simulation of interstellar turbulence with a grid resolution of 10,0483 cells that allows us to determine the position and width of the sonic scale (ℓs)—the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, with the velocity as a function of scale, v(ℓ) ∝ ℓp, where we measure psup = 0.49 ± 0.01 and psub = 0.39 ± 0.02, respectively. We find that ℓs agrees with the relation ℓs=ϕsL M−1 /psup , where M is the three-dimensional Mach number, L is either the driving scale of the turbulence or the diameter of a molecular cloud, and ϕs is a dimensionless factor of order unity. If L is the driving scale, we measure ϕs=0.4 2−0.09+0.12 , 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 ϕs=0.9 1−0.20+0.25 . In both cases, ϕs ≲ 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.