2025A&A...702A.133K

ALMA-IMF is a Large Program of the Atacama Large Millimeter/submillimeter Array (ALMA) that aims to determine the origin of the core mass function (CMF) of 15 massive Galactic protoclusters (∼1.0-25.0 × 10³ M_⊙ within ∼2.5 × 2.5 pc²) located toward the Galactic plane. In addition, the objective of the program is to obtain a thorough understanding of their physical and kinematic properties. Here we study the turbulence in these protoclusters with the C¹⁸O (2-1) emission line using the sonic Mach number analysis (M_s) and the size-linewidth relation. The probability distribution functions (PDFs) for M_s show a similar pattern, exhibiting no clear trend associated with evolutionary stage, peaking in the range between 4 and 7, and then extending to ∼25. Such values of M_s indicate that the turbulence in the density regime traced by the C¹⁸O line inside the protoclusters is supersonic in nature. In addition, we compared the non-thermal velocity dispersions (σ_nth,C18O) obtained from the C¹⁸O (2-1) line with the non-thermal line widths (σ_nth, DCN_) of the cores obtained from the DCN (3-2) line. We observed that, on average, the non-thermal linewidth in cores is half that of the gas surrounding them. This suggests that turbulence diminishes at smaller scales or dissipates at the periphery of the cores. Furthermore, we examined the size-linewidth relation for the structures we extracted from the position-position-velocity C¹⁸O (2-1) line emission cube with the dendrogram algorithm. The power-law index (p) obtained from the size-linewidth relation is between 0.41 and 0.64, steeper than the Kolmogorov law of turbulence, as expected for compressible media. In conclusion, this work is one of the first to carry out a statistical study of turbulence for embedded massive protoclusters.