Digging into the Interior of Hot Cores with ALMA (DIHCA). IV. Fragmentation in High-mass Star-Forming Clumps

Fragmentation contributes to the formation and evolution of stars. Observationally, high-mass stars are known to form multiple-star systems, preferentially in cluster environments. Theoretically, Jeans instability has been suggested to determine characteristic fragmentation scales, and thermal or turbulent motion in the parental gas clump mainly contributes to the instability. To search for such a characteristic fragmentation scale, we have analyzed ALMA 1.33 mm continuum observations toward 30 high-mass star-forming clumps taken by the Digging into the Interior of Hot Cores with ALMA (DIHCA) survey. We have identified 573 cores using the dendrogram algorithm and measured the separation of cores by using the Minimum Spanning Tree (MST) technique. The core separation corrected by projection effects has a distribution peaked around 5800 au. In order to remove biases produced by different distances and sensitivities, we further smooth the images to a common physical scale and perform completeness tests. Our careful analysis finds a characteristic fragmentation scale of $\sim$7000 au, comparable to the thermal Jeans length of the clumps. We conclude that thermal Jeans fragmentation plays a dominant role in determining the clump fragmentation in high-mass star-forming regions, without the need of invoking turbulent Jeans fragmentation.