ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters

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 x 10^3 solar mass within ~ 2.5 x 2.5 pc^2 ) located towards 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 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 compare the non-thermal velocity dispersions (sigma_nth, C18O) obtained from the C18O(2-1) line with the non-thermal line widths (sigma_nth, DCN ) of the cores obtained from the DCN (3-2) line. We observe 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 examine the size-linewidth relation for the structures we extracted from the position-position-velocity C18O(2-1) line emission cube with 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 such a statistical study of turbulence for embedded massive protoclusters.