The sonic scale does not determine the core separation in turbulent molecular clouds

TL;DR

The study investigates whether the sonic scale $ell_s$ governs core separations in turbulence-dominated molecular clouds. Using 3D isothermal turbulence simulations at $M=4$ and $8$ with forcing scales $k_{for}=1-2$, $2-4$, $4-8$ and no self-gravity, cores are identified via dendrograms and analyzed against the velocity-structure-derived $ell_s$. They find no statistical correlation between $S_{2D}$ and $ell_s$ or with the forcing scale; core separations span the range between the sonic scale and the injection scale, and the fragmentation pattern depends on the turbulent driving (Mach number) rather than an intrinsic cascade scale. These results challenge the idea that the sonic scale universally dictates fragmentation, suggesting observational core spacings may reflect cloud-specific driving conditions rather than universal turbulence physics.

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 turbulent simulations with Mach numbers $\mathcal{M}=4$ 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 with the driving scale. Instead, for each run, the core separation spans the entire range of values between these two scales. Our results indicate that fragmentation in turbulence-dominated clouds is not governed by an intrinsic scale in the turbulent cascade. 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.

Figures (5)

• Figure 1: Column density maps at $t=4 \times t_{\rm c}$ for Mach=4 models along the x–axis for forcing scales $k_{\rm for}=1$–$2$ (left), $k_{\rm for}=2$–$4$ (centre), and $k_{\rm for}=4$–$8$ (right). Each panel displays the same logarithmic colour scale, with black plus symbols marking core centroids identified by the dendrogram.
• Figure 2: Same as Fig \ref{['fig:M4']} but for models with Mach=8.
• Figure 3: Characteristic velocity differences $\delta v(\ell)$, normalized by the sound speed $c_s$ as a function of spatial lag $\ell$, for all models. The horizontal red dashed line denotes the sonic scale, defined by the condition $\delta v(\ell_{s}) / c_s = 1$, while the corresponding value of $\ell_s$ for each model is indicated in the legend and denoted by the vertical dashed lines. Each curve represents a distinct combination of turbulent Mach number and forcing scale, as specified in the labels.
• Figure 4: Histograms of the nearest-neighbour distances ($S_{\rm 2D}$) with logarithmic binning for the simulations with $\mathcal{M} = 4$ (top panel) and $\mathcal{M} = 8$ (lower panel). Each histogram combines the $S_{\rm 2D}$ distributions from the three orthogonal projections. The horizontal lines indicate the sonic scale (dashed lines), the median $S_{\rm 2D}$ (solid lines), and the physical forcing scale ($\lambda_{\rm for} = L_{\rm box}/k_{\rm for}$; dotted lines).
• Figure 5: Median inter‑core separations versus sonic scale ($\ell_s$) (or forcing scale, $k_{\rm for}$) for the two turbulence regimes, $\mathcal{M} = 4$ (bluish colors) and $\mathcal{M} = 8$ (orangish colors). The error bars represent the standard deviation of each distribution. The systematic offset between boxes confirms that lower Mach numbers yield larger average separations at all forcing scales.