The sonic scale does not determine the core separation in turbulence-dominated molecular clouds

ABSTRACT It has recently been suggested that the typical separation between cores in molecular clouds dominated by turbulence is determined by the sonic scale, the size scale at which the turbulent velocity dispersion equals the sound speed. In this work, we test this hypothesis using a suite of non self-gravitating, purely hydrodynamic turbulent simulations with Mach numbers $\mathcal {M}=$ 2, 4, and 8, and three turbulent forcing wavenumbers ($k_{\rm for}=2,4$, and 8). Dense cores are identified through dendrogram analysis of column density maps, and their separations are compared to the sonic scale measured from velocity structure functions. We find no statistical correlation between the core separation and the sonic scale nor the driving scale. Instead, for each run, the core separation spans the entire range of values between the resolution and the injection scale, and peaks at a scale apparently dependent on the resolution, even when the sonic scale has converged. This could be the consequence of the distribution of core separations being given by the distribution of travelling shock-compressed layers. Our results indicate that the mean separation between the smallest density structures in non-self-gravitating, supersonically turbulent flow is determined in simulations by the global sonic Mach number and the resolution, with no limit imposed by the sonic scale. This finding calls into question the use of the sonic scale as a predictive quantity in star formation theories and cautions against interpreting observational core spacings as evidence for universal turbulent fragmentation physics.